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Tommy HultRelated papers
Space–time coding and signal processing for high data rate wireless communications
Wireless Communications and Mobile Computing, 2001
Link-optimal space-time processing with multiple transmit and receive antennas
IEEE Communications Letters, 2000
EFFICIENCY OF SPATIAL SIGNAL PROCESSING IN WIRELESS COMMUNICATIONS
Telecommunication sciences (Information and telecommunication sciences), 2012
The mathematical modeling of amplitude and phase distribution of the electromagnetic fields at the aperture of the receiving antenna system has been performed. The possibility of frequency reuse in radio relay link under condition when two transmitters operate simultaneously on the same frequency and with same polarization is substantially investigated by using the phenomenon of phase front curvature of electromagnetic wave. An effective approach to optimal spatial processing of two radio signals from two transmitters at the receiving side of radio relay link is developed. The mathematical expressions allowing the theoretical analysis of spatial processing of radio relay link signals are obtained. The results of theoretical investigations are extensively discussed. The references for practical application of obtained results at the development of microwave link equipment are given.
Canonical space-time processing for wireless communications
IEEE Transactions on Communications, 2000
IoT Technology in Sports & IoT
Most times in the past your children or your employee calling over telephone to say they are stuck or in an emergency, had operated largely in the “dark,” with their location, position, and functional state unknown or even unknowable. Thanks to digitization, caller ID facility on phones was considered a revolution and disruption. No longer, a suite of technologies and associated business processes that allow you to track and count, observe and identify, evaluate and act incircumstances heretofore effectively invisible and beyond reach.
Phane Beecher. Beecher Magistrates, West Cork (1)
Phane Beecher. Beecher Magistrates, West Cork, 2024
What started as a listing of Beecher Magistrates in West Cork from the end of the 17th century turned into something more elaborate. I was reading Dr. Jane Ohlmeyer, book on Ireland and empire and saw a reference to Phane Beecher granted lands in Bandon and Governor of St. Kitts. In fact these are two separate people but probably of the same family. I was assisted by a Beecher descendant who provided considerable information on the mid 17th century Caribbean, then the epicenter of England slave colonies growing sugar. I had not realized that forfeit Irish Land as well as producing revenue was used to give collateral security to fund slavery and sugar and tobacco enterprises. It seems that many of the grantees of Irish Land were associated with London networks such as the Thompson family heavily involved in the East India Company. Later in the end of the 17th century they were also probably involved in the Hollow Blade Company, a consortium of London merchants who financed Parliament in its war against the English King and surprise surprise they were repaid in grants of Irish confiscated land. In the same book she described in forensic detail the Irish involvement of both Irish Catholics and Protestants in the slave trade and tobacco and sugar plantations. Fane Becher was granted over 12,000 acres in county Cork, p.1 The English Caribbees in the Period of the Civil War, 1642-1646, p. 2 St. Kitts in 1639 arrived penniless one Phance Beecher, p.7 Slaving, Tobacco, Sugar, the Irish Connections from Dr. Jane Ohlmeyer, p. 10 Beecher Magistrates, West Cork, p. 12-19 Beecher/Becher Landed Estates, p. 19
Wireless mobile communication networks are
rapidly growing at an incredible rate around the
world and a number of improved and emerging
technologies are seen to be critical to the improved economics and performance of these networks. The technical revolution and continuing
growth of mobile radio communication systems
has been made possible by extraordinary advances
in the related fields of digital computing, highspeed circuit technology, the Internet and, of
course, digital signal processing. Improved third
generation (3G) and future generation wireless
communication systems must support a substantially wider and enhanced range of services with
respect to those supported by second generation
and basic 3G systems. The never-ending quest for
such personal and multimedia services, however,
demands technologies operating at higher data rates and broader bandwidths. This combined with
the unpredictability and randomness of the mobile propagation channel has created many new
technically challenging problems for which innovative, adaptive and advanced signal processing
techniques may offer new and better solutions.
Space-time processing techniques have emerged
as one of the most promising areas of research
and development in wireless communications
for the efficient utilization of the physical mobile
radio propagation channel. Space-time processing signifies the signal processing performed on
a system consisting of several antenna elements,
whose signals are processed adaptively in order
to exploit both the spatial (space) and temporal
(time) dimensions of the radio channel. This can
significantly improve the capacity, coverage, quality
and energy efficiency of wireless systems.
This thesis expands the scope of space-time processing by proposing novel applications in wireless communication systems. These include the
reduction of possibly harmful electromagnetic radiation from mobile phones, enhancing the quality
of Bluetooth links in indoor office environments,
increasing the spectral efficiency of satellite and
the novel high altitude platforms (HAPs) communication systems, enhancing the coverage and
capacity of integrated multiple-HAP 3G systems,
and improving the energy efficiency of cooperative wireless sensor networks. The performance
of these systems is assessed by theoretical analysis, by computer simulations under a range of propagation environments including realistic channel
models, advanced commercial electromagnetic
modeling software, and a proposed novel multichannel simulator suitable for various space-time
applications.
space-time processing
applications for wireless communications
ABSTRACT
Tommy Hult
ISSN 1653-2090
ISBN 978-91-7295-146-4
2008:12
2008:12
space-time processing applications
for wireless communications
Tommy Hult
Blekinge Institute of Technology
Doctoral Dissertation Series No. 2008:12
School of Engineering
Space-Time Processing Applications
for Wireless Communications
Tommy Hult
Blekinge Institute of Technology Doctoral Dissertation Series
No 2008:12
ISSN 1653-2090
ISBN 978-91-7295-146-4
Space-Time Processing Applications
for Wireless Communications
Tommy Hult
Department of Signal Processing
School of Engineering
Blekinge Institute of Technology
SWEDEN
© 2008 Tommy Hult
Department of Signal Processing
School of Engineering
Publisher: Blekinge Institute of Technology
Printed by Printfabriken, Karlskrona, Sweden 2008
ISBN 978-91-7295-146-4
ABSTRACT
Wireless mobile communication networks are rapidly growing at an incredible rate
around the world and a number of improved and emerging technologies are seen
to be critical to the improved economics and performance of these networks. The
technical revolution and continuing growth of mobile radio communication systems
has been made possible by extraordinary advances in the related fields of digital
computing, high-speed circuit technology, the Internet and, of course, digital signal
processing. Improved third generation (3G) and future generation wireless communication systems must support a substantially wider and enhanced range of services
with respect to those supported by second generation and basic 3G systems. The
never-ending quest for such personal and multimedia services, however, demands
technologies operating at higher data rates and broader bandwidths. This combined with the unpredictability and randomness of the mobile propagation channel
has created many new technically challenging problems for which innovative, adaptive and advanced signal processing techniques may offer new and better solutions.
Space-time processing techniques have emerged as one of the most promising
areas of research and development in wireless communications for the efficient utilization of the physical mobile radio propagation channel. Space-time processing
signifies the signal processing performed on a system consisting of several antenna
elements, whose signals are processed adaptively in order to exploit both the spatial
(space) and temporal (time) dimensions of the radio channel. This can significantly
improve the capacity, coverage, quality and energy efficiency of wireless systems.
This thesis expands the scope of space-time processing by proposing novel applications in wireless communication systems. These include the reduction of possibly
harmful electromagnetic radiation from mobile phones, enhancing the quality of
vi
Bluetooth links in indoor office environments, increasing the spectral efficiency of
satellite and the novel high altitude platforms (HAPs) communication systems, enhancing the coverage and capacity of integrated multiple-HAP 3G systems, and
improving the energy efficiency of cooperative wireless sensor networks. The performance of these systems is assessed by theoretical analysis, by computer simulations
under a range of propagation environments including realistic channel models, advanced commercial electromagnetic modeling software, and a proposed novel multichannel simulator suitable for various space-time applications.
vii
Acknowledgments
I would like to express my sincere gratitude to Professor Ingvar Claesson for
giving me the opportunity to be a Ph.D student at Blekinge Institute of Technology.
I am utterly grateful and indebted to my supervisor and very good friend Professor
Abbas Mohammed without whose help, insight, experience and nice discussions this
thesis would not exist.
I would also like to thank M.Sc. Zhe Yang and Dr. Ronnie Landqvist for the
nice discussions and friendship during this time. Further I would like to thank all
the collegues and friends at the Department. Special thanks to Dr. David Grace
at University of York for letting me visit his group and for our nice collaborations
within the EU COST 297 Action. I would also like to thank Professor Sven Nordebo,
who suggested the possibility to continue as a Ph.D student after my Master thesis.
Finally, I would like to thank my parents Kjell and Marianne, my sister LiseLotte, her husband Patrik and their children Axel and Elin for supporting me during
these years.
Tommy Hult
Ronneby, September 2008.
CONTENTS
List of Publications
Abbrevations and Acronyms
Symbols and Notations
1
Introduction
1.1 Outline of the Thesis and Contributions . . . . . . . .
2
A Novel Space-Time-Polarization
Channel Model for Wireless Communications
2.1 Space-Time-Polarization Channel Model .
2.1.1 Space-Polarization Channel Model
2.1.2 Statistical properties of the
global channel matrix . . . . . . . .
2.1.3 Numerical Implementation . . . . .
2.2 Simulation Results . . . . . . . . . . . . . . .
2.3 Conclusions . . . . . . . . . . . . . . . . . . .
3
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Space-Time-Polarization Processing for Capacity
Enhancement in HAP/Satellite communication systems
3.1 Platform Diversity . . . . . . . . . . . . . . . . . . . . .
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3.2
3.3
3.4
3.5
3.6
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3.1.1 Space-Polarization Channel Model . . . .
The MIMO-OFDM System . . . . . . . . . . . . .
Compact Antenna Arrays . . . . . . . . . . . . . .
3.3.1 Array Configurations . . . . . . . . . . . . .
3.3.2 The Space-Polarization Domain . . . . . .
3.3.3 Mutual Coupling and Spatial Correlation
Depolarization Analysis . . . . . . . . . . . . . . . .
Simulation Results . . . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . .
Space-Time Processing for Quality Improvement
of Short Range Wireless Communication Links
4.1 The Tested Indoor Office Environment . . .
4.1.1 The Used Antennas . . . . . . . . . .
4.1.2 The Measurements Setup . . . . . . .
4.2 Results of the Measurements . . . . . . . . .
4.3 FEM Simulations . . . . . . . . . . . . . . . .
4.3.1 The Simulated Indoor Model . . . . .
4.3.2 FEM Simulation Results . . . . . . . .
4.4 Conclusions . . . . . . . . . . . . . . . . . . . .
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Power Constrained Space-Time Processing
for Suppression of Electromagnetic Fields
5.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 The FEM model . . . . . . . . . . . . . . . . .
5.1.2 The MIMO model . . . . . . . . . . . . . . . .
5.2 The Adaptive Algorithms . . . . . . . . . . . . . . . .
5.3 Simulation Results . . . . . . . . . . . . . . . . . . . . .
5.4 Power Constraints . . . . . . . . . . . . . . . . . . . . .
5.5 The Effects of MIMO Antenna Parameters and Carrier Frequency . . . . . . . . . . . . . . . . . . . . . . .
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . .
Space-Time Processing for Interference
Mitigation in HAP WCDMA Systems
6.1 Multiple HAP system setup . . . . . . .
6.1.1 User Positioning Geometry . . .
6.1.2 Base station antenna pattern . .
6.1.3 User equipment antenna pattern
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xi
6.2
6.3
6.4
7
8
6.1.4 UE-HAP radio propagation channel
6.1.5 WCDMA Setup . . . . . . . . . . . .
6.1.6 Space-Time Processing Techniques
Interference analysis . . . . . . . . . . . . . .
Simulation Results . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . .
Cooperative Space-Time Processing for
Power Efficient Wireless Sensor Networks
7.1 Cooperative Beamforming . . . . . . .
7.2 Spatial Diversity Techniques . . . . . .
7.2.1 Cooperative MISO and SIMO
7.2.2 Cooperative MIMO . . . . . .
7.3 Simulation Results . . . . . . . . . . . .
7.4 Conclusions . . . . . . . . . . . . . . . .
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Conclusions
Appendix
181
A
A Spherical Vector Harmonics
A.1 Spherical Vector Harmonics . . . . . . . . . . . . . . .
185
187
B Antenna Types
B.1 Antenna types . . . . . . . . . . . . . . . . . . . . . . .
189
191
C WCDMA Power Control
C.1 WCDMA Power Control . . . . . . . . . . . . . . . . .
193
195
D Beamforming
D.1 Beamforming . . . . . . . . . . . . . . . . . . . . . . . .
197
199
11
List of Publications
Parts of Chapter 2 is published as:
T. Hult, A. Mohammed, Theoretical Analysis and Assessment of Depolarization Effects on the Performance of High Altitude Platforms, COST 297 HAPCOS meeting and workshop, Nicosia, Cyprus, 7-9 April 2008.
T. Hult, E. Falletti, A. Mohammed, F. Sellone, Multi-Antenna Multi-HAP
Channel Model for Space-Polarization, COST 297 - HAPCOS meeting and
workshop, Nicosia, Cyprus, 7-9 April 2008.
T. Hult, E. Falletti, A. Mohammed, F. Sellone, Multi-channel model for spacepolarization systems, European Union Conference on Antennas and Propagation, EUCAP2007, Edinburgh, UK, 11-16 November 2007.
T. Hult, A. Mohammed, E. Falletti, F. Sellone, Analysis of Depolarizing Effects and Impact on the Performance of a Multiple Satellite System Employing
Polarization Diversity, International Union of Radio Science (URSI 2007), Ottawa, Canada, July 22-26 2007.
Z. Yang, A. Mohammed, O. Awoniyi, A.O. Oladipo, T. Hult, M. Salomonsson, Comparative Analysis of Channel Models for Stratospheric Propagation, 2nd International Conference on Experiments/Process/System Modelling/Simulation&Optimization (IC-EpsMso), Athens, Greece, 2007.
T. Hult, E. Falletti, A. Mohammed and F. Sellone, The Impact of Depolarizing
Effects on a Multiple HAP System Employing Polarization Diversity, International Union of Radio Science (URSI 2007), Ottawa, Canada, July 22-26 2007.
A. Mohammed and T. Hult, Evaluation of Depolarization Effects on the Performance of High Altitude Platforms (HAPs), IEEE 67th Vehicular Technology Conference, Marina Bay, Singapore, 11-14 May, 2008.
12
Parts of Chapter 3 is published as:
T. Hult, A. Mohammed, Z. Yang and D. Grace; Performance of a Multiple
HAP System Employing Multiple Polarization, Wireless Personal Communications Journal, Springer, Invited Paper, Special Issue, Journal No. 11277,
Article No. 9511, 2008.
A. Mohammed and T. Hult, Evaluation of Depolarization Effects on the Performance of High Altitude Platforms (HAPs), IEEE 67th Vehicular Technology Conference, Marina Bay, Singapore, 11 - 14 May, 2008.
T. Hult, E. Falletti, A. Mohammed and F. Sellone; Multi-Antenna MultiHAP Channel Model for Space-Polarization, COST 297 - HAPCOS meeting
and workshop, Nicosia, Cyprus, 7-9 April, 2008.
T. Hult, E. Falletti, A. Mohammed and F. Sellone; The Impact of Depolarizing
Effects on a Multiple HAP System Employing Polarization Diversity, International Union of Radio Science, URSI 2007, Ottawa, Canada, 22-26 July, 2007.
T. Hult and A. Mohammed; Assessment of a HAP Diversity System Employing Compact MIMO-Tetrahedron Antenna, COST 297 - meeting and workshop, Prague, Czech Republic, 29-30 March, 2007.
T. Hult and A. Mohammed; Compact MIMO Antennas and HAP Diversity
for Enhanced Data Rate Communications, IEEE 65th Semiannual Vehicular
Technology Conference, Dublin, Ireland, 22 - 25 April, 2007.
A. Mohammed and T.Hult; Compact MIMO Antennas and Satellite Diversity for High Data Rate Communications, 8th annual IEEE Wireless and Microwave Technology, WAMICON06, Clearwater, USA, 4-5 December, 2006.
T. Hult and A. Mohammed; Capacity of multiple hap system employing multiple polarizations, European Union Conference on Antennas and Propagation,
EUCAP2006, Nice, France, 6-9 November, 2006.
T. Hult and A. Mohammed; Capacity of a Satellite Diversity System Employing Multiple Polarizations, European Union Conference on Antennas and
Propagation, EUCAP2006, Nice, France, 6-9 November, 2006.
13
T. Hult and A. Mohammed; Multiple HAP and Polarization Diversity for Enhanced Data Rate Communications, COST 297 - HAPCOS meeting YORK
HAPWEEK workshop, York, UK, 26-27 October, 2006.
T. Hult and A. Mohammed; Compact MIMO Antennas and HAP Diversity
for High Data Rate Communications, IEEE 64th Semiannual Vehicular Technology Conference, Montreal, Canada, 25-28 September, 2006.
T. Hult, A. Mohammed, D. Grace and Z. Yang; Performance of a Multiple
HAP System Employing Multiple Polarization, Wireless Personal Multimedia
Communications 2006, WPMC06, San Diego, USA, 17-20 September, 2006.
T. Hult and A. Mohammed; Combined Polarization and Satellite Diversity
For High Data Rate Communications, Antenn 06, Linköping, Sweden, 30 May
- 1 June, 2006.
T. Hult and A. Mohammed; MIMO Antenna Applications for High Altitude
Platforms, Antenn 06, Linköping, Sweden, 30 May - 1 June, 2006.
T. Hult and A. Mohammed; MIMO for HAPs: an idea whose time has come,
COST 297 - HAPCOS meeting and workshop, Oberpfaffenhofen, Germany,
05-07 April, 2006.
T. Hult and A. Mohammed; MIMO Antenna Applications for LEO Satellite
Communications , COST 280 - 3rd International Workshop, Prague, Czech
Republic, 6-8 June, 2005.
A. Mohammed and T.Hult; Performance Evaluation of a MIMO Satellite Diversity System, European Space Agency 10th International Workshop on Signal Processing for Space Communications, SPSC 2008, Rhodes Island, Greece,
6-8 October, 2008.
14
Chapter 4 is published as:
T. Hult and A. Mohammed; Assessment of Multipath Propagation for a 2.4
GHz Short-Range Wireless Communication System, IEEE 65th Semiannual
Vehicular Technology Conference, Dublin, Ireland, 22-25 April, 2007.
T. Hult and A. Mohammed; Multipath Propagation Assessment for a 2.4 GHz
Short-Range Wireless Communication System, European Union Conference
on Antennas and Propagation, EUCAP2006, Nice, France, 6-9 November,
2006.
A. Mohammed and T.Hult; Performance Evaluation of the Bluetooth Link for
Indoor Propagation by Measurement Trials and FEMLAB Simulations, Wireless Personal Multimedia Communications 2005, WPMC05, Aalborg, Denmark, 18-22 September, 2005.
T. Hult and A. Mohammed; Indoor Propagation Simulations Using FEM
for Short-Range Wireless Communication Systems Operating at 2.4 GHz,
MMWP05 - Conference on Mathematical Modelling of Wave Phenomena
2005, Växjö, Sweden , 14-19 August, 2005.
A. Mohammed and T. Hult; Evaluation of the Bluetooth Link and Antennas Performance for Indoor Office Environments by Measurement Trials and
FEMLAB Simulations , IEEE 61st Semiannual Vehicular Technology Conference, Stockholm, Sweden, May 30 - June 1, 2005.
Chapter 5 is published as:
A. Mohammed and T. Hult; The Effects of MIMO Antenna System Parameters and Carrier Frequency on Active Control Suppression of EM Fields,
Radioengineering Journal, Volume 16, Number 1, April, 2007.
T. Hult and A. Mohammed; Power Constrained Space-Time Processing for
Suppression of Electromagnetic Fields, Invited Paper, First Issue of Journal
of Communications Software and Systems (JCOMSS), Volume 1, Number 1,
September, 2005.
15
T. Hult and A. Mohammed; Suppression of EM Fields using Active Control Algorithms and MIMO Antenna System, Radioengineering Journal, Vol.
13, Number 3, pp. 22-25, September, 2004.
T. Hult and A. Mohammed; Active Signal Processing Algorithms for Controlling Electromagnetic Fields: A Tutorial, Invited Paper, 15th International
Congress on Sound and Vibration, ICSV15, Daejeon, Korea, 6-10 July, 2008.
T. Hult and A. Mohammed; Performance Evaluation of Adaptive Active Signal Processing Algorithms and MIMO Antenna System for the Reduction of
Electromagnetic Field Density, European Union Conference on Antennas and
Propagation, EUCAP2007, Edinburgh, UK, 11-16 November, 2007.
T. Hult and A. Mohammed; The impact of MIMO Antenna System and Carrier Frequency on Active Control Suppression of Electromagnetic Field, Wireless Networking Symposium 2004, WNCG2004, Austin, USA, 20-22 October,
2004.
T. Hult and A. Mohammed, Power Constrained Active Suppression of Electromagnetic Fields Using MIMO Antenna System, 12th International Conference
on Software, Telecommunications and Computer Networks, SoftCOM 2004,
Co-sponsored by IEEE Communications Society, Split, Croatia, 10-13 October, 2004.
T. Hult, A. Mohammed and S. Nordebo; Active Suppression of Electromagnetic Fields using a MIMO Antenna System, 17th International Conference on
Applied Electromagnetics and Communications, ICECom 2003, Co-sponsored
by IEEE Communications Society, Dubrovnik, Croatia, 1-3 October, 2003.
Chapter 6 is published as:
T. Hult, D. Grace and A. Mohammed; WCDMA Uplink Interference Assessment from Multiple High Altitude Platform Configurations, EURASIP Journal
on Wireless Communications and Networking: HAP Special Issue, Hindawi,
Special Issue, April 2008.
16
T. Hult, A. Mohammed and D. Grace; WCDMA Coverage Enhancement from
Multiple High Altitude Platforms, COST 297 - HAPCOS meeting and workshop, Nicosia, Cyprus, 7-9 April, 2008.
T. Hult, D. Grace and A. Mohammed; WCDMA Capacity and Coverage Enhancement from Multiple High Altitude Platform Configurations, European
Union Conference on Antennas and Propagation, EUCAP2007, Edinburgh,
UK, 11-16 November, 2007.
Chapter 7 is published as:
T. Hult and A. Mohammed; Cooperative Beamforming for Wireless Sensor
Networks, European Union Conference on Antennas and Propagation, EUCAP2007, Edinburgh, UK, 11-16 November, 2007.
17
Abbrevations and Acronyms
2D
3D
3G
AWGN
BER
BLER
BS
CAD
CDMA
CEFM
CP
DFT
DOA
DOD
DOF
EGC
ERS
FDM
FDMA
FEM
FSL
GSM
HAP
ISM
LEO
LHCP
LMS
LOS
MIMO
MISO
MRC
NLOS
OFDM
PD
PIFA
RHCP
Two Dimensional
Three Dimensonal
Third Generation
Additive White Gaussian Noise
Bit Error Rate
Block Error Rate
Base station
Computer Aided Design
Code Division Multiple Access
Combined Empirical Fading Model
Cyclic Prefix
Discrete Fourier Transform
Direction of Arrival
Direction of Departure
Degrees of Freedom
Equal Gain Combining
Empirical Roadside (model)
Frequency Divison Multiplexing
Frequency Division Multiple Access
Finite Element Method
Free Space Loss
Global System for Mobil telecommunication
High Altitude Platform
Industrial, Scientific and Medical (frequency band)
Low Earth Orbit
Left Hand Circular Polarized
Least Mean Square
Line of Sight
Multiple-Input Multiple-Output
Multiple-Input Single-Output
Maximum Ratio Combining
No Line of Sight
Orthogonal Frequency Division Multiplexing
Polarization Domain
Printed Inverted-F Antenna
Right Hand Circular Polarized
18
RSSI
RX
SAR
SC
SD
SIMO
SISO
SINR
SNR
STP
SVD
TD
TDM
TDMA
TX
UAV
UE
UMTS
WCDMA
WSN
XPD
XPI
Received Signal Strength Indicator
Receiver
Specific Absorption Rate
Selection Combining
Space Domain
Single-Input Multiple-Output
Single-Input Single-Output
Signal to Interference plus Noise Ratio
Signal to Noise Ratio
Space Time Polarization
Singular Value Decomposition
Time Domain
Time Division Multiplexing
Time Division Multiple Access
Transmitter
Unmanned Aerial Vehicle
User equipment
Universal Mobile Telephony System
Wideband CDMA
Wireless Sensor Networks
Cross Polar Discrimination
Cross Polar Isolation
19
Symbols and Notations
·
×
⊗
∗
R
C
x
x∗
x
xi
H
HT
HH
H−1
Hij
Tr(H)
diag {H}
||H||F
min x
w
CN (µ, σ 2 )
E {H}
r
E
∇
Jl (x)
jl (x)
nl (x)
hl (x)
Scalar product
Vector product
Kroenecker product (Tensor product)
Shur-Hadamard product (Elementwise product)
Convolution
Circular convolution
A set of real valued numbers
A set of complex valued numbers
Scalar variable
The complex conjugate of x
Data vector
Element i of vector x
Data matrix
Transpose of matrix H
Hermitian transpose, or complex conjugate
transpose of matrix H
Inverse of matrix H
Element in row i, column jof matrix H
Trace of matrix: Tr(H) = i Hii
Only the diagonal elements of H
The Frobenius norm of H: ||H||2F = Tr(HHH )
Minimize x with respect to w
Complex valued Gaussian distribution with
expected value µ and variance σ 2 E {H} or
Statistical expectation of H
Field position vector: r = (x, y, z)
Field data vector
∂
∂
∂
, ∂y
, ∂z
Vector gradient operator, ∇ = ∂x
Bessel function of the first kind, order l
Spherical
function of order l:
bessel
π
jl (x) = 2x
Jl+0.5 (x)
Spherical neuman
of order l:
function
π
nl (x) = (−1)l+1 2x
J−l−0.5 (x)
Spherical hankel function of order l:
hl (x) = jl (x) + ı · nl (x)
20
CHAPTER 1
INTRODUCTION
W
ireless communication networks are rapidly growing at an incredible
rate around the world and a number of emerging technologies are
seen to be critical to the improved economics and performance of these
networks. Among these technologies, the use of ’space-time processing’
in which time (the natural dimension of digital communication signals) is
complemented with the spatial dimension inherent in the use of multiple
spatially distributed antennas [10, 11], has appeared as a very promising
technology. The use of space-time signal processing can significantly improve
average signal power, mitigating fading, and reduce inter-symbol interference
and co-channel interference. This can in turn result in significant improvement
in energy efficiency, capacity, coverage and quality of wireless systems.
Space-time processing can be applied at the transmitter, the receiver or
both. Thus, the different antenna configurations used in defining spacetime systems can be classified as follows. Single-input single-output (SISO)
is the conventional wireless communication system configuration where the
transmitter and receiver utilize a single antenna only. Adding extra antennas
makes it possible to exploit the advantages of spatial dimension in the system.
A system where multiple antennas are employed at the transmitter only is
denoted as multiple-input single-output (MISO) and is said to utilize transmit
diversity. Similarly, a system where multiple antennas are employed at the
receiver only is denoted as single-input multiple-output (SIMO) and is said
to utilize receive diversity. On the other hand, a multiple-input multipleoutput (MIMO) system is enabled by the use of multiple transmit antennas
22
Chapter 1. Introduction
and multiple receive antennas in order to take full advantage of the spatial
dimension of the propagation channel. MIMO wireless links are important
since they improve link reliability through diversity advantage and increase
potential data rate through multiplexing gain. Thus, MIMO systems are seen
as a critical and promising technology for next generation wireless networks.
In this thesis we expand the scope of space-time processing by proposing
novel applications in wireless communications. These include enhancing
the capacity of satellite and high altitude platform (HAP) communication
systems, improving link quality for Bluetooth links in indoor office environments, reduction of the possibly harmful electromagnetic radiation from
mobile phones, enhancing the coverage and capacity of integrated multipleHAP 3G systems, and improving the energy efficiency of cooperative wireless
sensor networks (WSN).
1.1
Outline of the Thesis and Contributions
Chapter 2
In terrestrial wireless communications scenarios, where multipath propagation
and signal fading are important issues, the use of adaptive fading mitigation
techniques (channel assignment policies, adaptive modulation and coding,
equalizers, bit-loading, synchronizers, etc.) can represent fundamental means
of achieving a high service availability for critical applications, such as
real-time transmissions and broadband communications. In general, the
implementation of such adaptive techniques requires knowledge of the time
autocorrelation function of the channel. Moreover, since the use of smart
antennas is becoming a concrete possibility for both access points at base
stations and a wide range of user terminals (personal computers, fixed
collective wireless access terminals, laptops, etc.), the spatial autocorrelation
function of short-term signal variations has to be modeled as well.
As bandwidth is a paramount constraining factor on the number of channels it is possible to multiplex within a limited frequency range, traditionally
by using polarization diversity the number of channels can be doubled without
the need to increase the bandwidth. Recent research have shown that it is
possible to acquire even more channels by using a combination of spatial and
polarization diversity [8] in a scattering rich environment.
In chapter 2, we propose a novel multiple antenna channel model and
associated simulator that is taking into account the spatial, temporal and
1.1. OUTLINE OF THE THESIS AND CONTRIBUTIONS
23
polarization (STP) properties affecting signal transmission in wireless communications [14, 20–23]. In addition, we present the theoretical background,
features and properties, analysis and implementation of this STP channel
model and simulator. Further, we test the simulator for various propagation
conditions. Results show good correspondence between the simulated and
theoretical distributions and the adverse effect of depolarization on system
performance. The structure of the channel simulator is designed to maintain
affordable computational burden, through an efficient time-varying FIR filter
bank implementation.
Chapter 3
The need for high-speed, high-quality bandwidth efficient mobile communications is continuously growing. In chapter 3, we address the potential
gain of using MIMO antenna system in combination with OFDM (orthogonal
frequency division multiplexing) in order to enhance the capacity in satellite
[7, 14–18] and high altitude platform (HAP) [19–28] communication systems.
In particular, we consider the increase in channel capacity that is possible
by exploiting the platform (Satellite/HAP) and polarization diversity. In
addition, we investigate the effect of the various parameters (e.g. the
different compact MIMO antenna array configurations including a novel array
denoted as the MIMO-Octahedron, separation angles between platforms,
power control, mutual coupling and spatial correlation, cross-polarization
discrimination due to weather conditions) on the information theoretic
capacity of the total transmission channel of the satellite/HAP system.
Simulation results show that the platform diversity system provides superior
performance compared to the single platform system, and that the MIMOOctahedron and MIMO-Cube antenna arrays can access twice the number of
platforms as the MIMO-Tetrahedron and vector element antenna and thus
provide higher capacity.
Chapter 4
Over the last decade there has been an explosive growth in the use of wireless
mobile communications. Today we find users with mobile phones, wireless
PDA’s, MP3 players, and wireless headphones to connect to these devices.
In this chapter, we investigate the wave propagation effects of a short-range
wireless device, such as the Bluetooth technology. Specifically, we assess the
fading phenomenon for Bluetooth link in an indoor office environment by
24
Chapter 1. Introduction
simulation of different propagation scenarios [49–53], and use measurement
results to confirm our findings.
The spatial properties of wireless communication channels are extremely
important in determining the performance of wireless systems. Thus,
we apply space-time multiple antenna systems employing SIMO antenna
diversity system and MIMO antenna system using spatial diversity and
spatial multiplexing schemes to the Bluetooth system [51–53] and assess
their performance over fading radio channels in non-line of sight propagation
environment. Simulation results show a significant diversity and multiplexing
gain is achieved by the multiple antenna systems as compared to the SISO
antenna system.
Chapter 5
Several studies have been conducted on the effects of radiation on the human
body. This has been especially important in the case of radiation from hand
held mobile phones. The amount of radiation emitted from most mobile
phones is very small, but given the close proximity of the phone to the
head it might be possible for the radiation to cause harm. In chapter 5 of
this thesis we propose a new approach for the reduction of electromagnetic
field density at a certain volume in space (e.g. at the human head). The
suggested approach involves the use of adaptive active control algorithms and
a full space-time processing system setup (i.e. multiple antennas at both
the transmitter and receiver side or MIMO), with the objective of reducing
the possibly harmful electromagnetic radiation emitted by hand held mobile
phones [59–63]. In addition, we also investigate the impact of MIMO antenna
parameters, carrier frequency and power constraint on the performance of the
system. Simulation results show the possibility of using the adaptive control
algorithms and MIMO antenna system to attenuate the electromagnetic field
power density.
Chapter 6
Third generation mobile systems are gradually being deployed in many
developed countries in hotspot areas. However, owing to the amount of new
infrastructures required, it will still be some time before 3G is ubiquitous,
especially in developing countries. One possible cost effective solution for
deployments in these areas is to use High Altitude Platforms (HAPs).
1.1. OUTLINE OF THE THESIS AND CONTRIBUTIONS
25
In this chapter we investigate the performance of utilizing multiple HAPs
to provide coverage of a common cell area using a Wideband Code Division
Multiple Access (WCDMA) system [110–112]. In particular we study the
uplink system performance of the system. The results show that depending
on the traffic demand and type of service used, there is a possibility of
deploying 3-6 HAPs covering the same cell area. The results also show
the effect of cell radius on performance and the position of the multiple
HAP base stations which give the worst performance. In addition, we also
apply space-time receiver diversity techniques such as single-input multipleoutput (SIMO) or multiple-input multiple-output (MIMO) and compare their
performance with that obtained from a single-input single-output (SISO)
system. Simulation results show a superior performance is achieved using
these diversity techniques and that a practical 4x4 MIMO system provides an
optimal system performance.
Chapter 7
Wireless Sensor Networks (WSN) have been attracting great attention
recently due to the relatively low cost of deployed and usage in many
diverse and promising applications, such as biomedical sensor monitoring
(e.g., cardiac patient monitoring), habitat monitoring (e.g., animal tracking),
weather monitoring (temperature, humidity, etc.), low-performance seismic
sensing, environment preservation and natural disaster detection/monitoring
(e.g., flooding and fire). These applications have in common the need to
send their collected data to some central processing station. If the sensors
are located at a faraway distance from a processing node, an inefficient use of
bandwidth and transmitter power resources is the result if each wireless sensor
is transmitting its measurement data to the base station (processing station).
By using a coordinating cluster head, for each cluster of wireless sensor nodes,
we can use the combined transmitter power of the node cluster through the
use of beamforming or multipath diversity array processing to increase the
transmitter-receiver separation and/or to improve the signal-to-noise ratio
(SNR) of the communication link. The aim of this chapter is to investigate
and assess the beamforming performance of the randomly positioned wireless
sensor array and to compare its performance with different forms of diversity
array systems (SIMO, MISO and MIMO) [113]. Simulation results show that
the diversity systems are superior in performance to both the SISO link and
the traditional form of array beamforming.
26
Chapter 1. Introduction
CHAPTER 2
A NOVEL SPACE-TIME-POLARIZATION
CHANNEL MODEL FOR WIRELESS
COMMUNICATIONS
O
ne of the most common problems encountered in the analysis or design of
radio communications systems is the characterization of the propagation
channel, since a comprehensive knowledge of the channel features may help
the designers toward the selection of suitable solutions to establish reliable
communication links. Furthermore, the availability of realistic channel models
and effective simulators may be helpful in proving the effectiveness of the
selected solution.
In terrestrial wireless communications scenarios, where multipath propagation and signal fading are important issues, the use of adaptive fading
mitigation techniques (channel assignment policies, adaptive modulation and
coding, equalizers, bit-loading, synchronizers, etc.) can represent fundamental
means of achieving a high service availability for critical applications, such
as real-time transmissions and broadband communications. In general, the
implementation of such adaptive techniques requires knowledge of the time
autocorrelation function of the channel. Moreover, since the use of smart
antennas is becoming a concrete possibility for both access points at base
stations and a wide range of user terminals (personal computers, fixed
collective wireless access terminals, laptops, etc.), the spatial autocorrelation
function of short-term signal variations has to be modeled as well [36].
As bandwidth is a paramount constraining factor on the number of chan-
Chapter 2. A Novel Space-Time-Polarization
28
Channel Model for Wireless Communications
nels it is possible to multiplex within a limited frequency range, traditionally
by using polarization diversity the number of channels can be doubled without
the need to increase the bandwidth. Recent research have shown that it is
possible to acquire even more channels by using a combination of spatial and
polarization diversity [8] especially in a scattering rich environment. However,
the independent radio channels are sensitive to depolarizing effects which
might cause significant impact on system’s performance. The depolarizing
effect can be caused by interference due to weather conditions and from
interactions with physical objects that are present in the propagation medium.
In light of the above, and the vast interest in Multiple-Input MultipleOutput (MIMO) systems, multicarrier transmission employing Orthogonal
Frequency Division Multiplexing (OFDM) and compact MIMO antenna array
configurations, new and improved channel models are necessary to evaluate
the parameters and performance of these system. Thus, in this chapter we
propose a novel multiple antenna channel model and associated simulator that
take into account the spatial, temporal and polarization (STP) properties
affecting signal transmission in wireless communications. In addition, we
provide the theoretical background, features and properties, analysis and
implementation of this STP channel model and simulator. Further, we test
the simulator for various propagation conditions. The proposed channel
model and simulator are designed for link level simulations and is an
extension of the model presented in [36], where only the spatial and temporal
properties of the signals were implemented. The proposed channel simulator
provides a powerful tool for evaluating the performance of current and future
communication systems. However, it is designed to maintain an affordable
computational burden with the use efficient time-varying FIR filter bank
implementation.
The organization of this chapter is as follows. Section 2.1 presents the
theoretical background, features and properties, analysis and implementation
of the proposed space-time-polarization (STP) channel model. Section 2.2
present the simulation results and provide evaluations and performance
comparisons of the parameters for different propagation scenarios. Finally,
section 2.3 concludes this chapter.
2.1
Space-Time-Polarization Channel Model
In this section we present the theoretical background, features and properties,
analysis and implementation of the proposed space-time-polarization (STP)
2.1. SPACE-TIME-POLARIZATION CHANNEL MODEL
29
channel model and the associated simulator. Each object in the propagation
channel is modeled as a cluster of micro-scatterers [36], see figure 2.1,
in the local area (within a few hundred wavelengths) centered about the
center position of the cluster. This cluster is denoted as a macro-scatterer.
Furthermore, both the transmitter and the receiver can respectively be
positioned inside a local area surrounded by micro-scatterers. The clusters are
modeled in order to calculate the angle spreading effect and depolarization
due to reflection, diffraction, and scattering off objects in the non line-ofsight (NLOS) propagation environment plus the scintillation phenomena and
depolarization effects due to precipitation and Faraday rotation phenomena
in the direct line-of-sight (LOS) path as well [14, 21–23]. With the presence
of different polarizations, the attenuations, phase shifts and depolarizations
generated by the multipath cluster interaction can differ for different incident
polarization states and will therefore also generate a cross-polarization effect.
2.1.1
Space-Polarization Channel Model
The signals carried by the different sub-channels of a multiple-input multipleoutput (MIMO) communications system are written in a vector format as
T
i(t) i(1) (t), i(2) (t), · · · , i(Np )(t) ,
(2.1)
where i(p) (t) is the information signal transmitted with the pth sub-channel.
The transmitting antenna is assumed to be a linear transformation of the
input signal i(t) into the independent radio sub-channels s(t), according to
s(t) MTtx i(t),
(2.2)
At the receiver we have a similar transformation from the signals in
the independent radio sub-channels srx (t) into the output signal r(t) of the
system, i.e. the vector of the elementary signals received in each sub-channel,
T
r̂(t) r̂(1) (t), r̂(2) (t), · · · , r̂(Np )(t) = Mrx srx (t),
(2.3)
where s(t) and srx (t) are vectors containing the independent spatial-polarization sub-channels that are active for a specific antenna type and they are
related through
(2.4)
srx (t) = Hch ∗ s(t),
Chapter 2. A Novel Space-Time-Polarization
30
Channel Model for Wireless Communications
TX antenna
local area
Local area
Micro-scatterer
Doppler
angle
LOS path
Angle of
Departure
l-th Macro
scatterer
l-th LOS
Cluster
Depolarization
Depolarization
l-th Cluster
Angle of
Arrival
Angle spread
Local area
Micro-scatterer
RX antenna
local area
Figure 2.1: The cluster geometry for the space-time-polarization simulator.
2.1. SPACE-TIME-POLARIZATION CHANNEL MODEL
31
where the symbol ∗ indicates matrix convolution, as defined in [36]. The
channel Hch , from the transmitter sub-channel vector s(t) to the receiver
sub-channel vector srx (t), is the simulated propagation channel. Thus, the
sub-channel signal vector r̂(t) at the receiver can be rewritten using equations
2.2, 2.3 and 2.4 as a linear combination of all the transmitted sub-channel,
each of which is subjected to the effects of the propagation environment
r̂(t) = Mrx Hch ∗ MTtx i(t).
(2.5)
The coefficients of the linear combination represent the effect of the fading,
cross-correlation and depolarization induced by the channel environment.
Elementary channel matrix
In general, it is possible to assume that each sub-channel is transmitted by an
antenna array that uses a specific spatial processor (transmitter beamformer)
for each specific sub-channel. The pth transmitter beamforming weight
vector is then denoted as v(p) . The signals propagating through the wireless
channel are affected by several factors (e.g. spatial and temporal fast fading,
shadowing, etc.), in which the short-term fast effects are considered in [36].
In particular, the signals are affected by reflection, diffraction and scattering
phenomena, both at macroscopic and microscopic (scattering) scale that
generates attenuations, phase shifts and time delays. It also causes the signals
to arrive at the receiver from different Direction of Arrivals (DOA’s) of the
direct LOS path. This is characterized by a certain angular spread of the
signals. There is also the possibility of mobility at both transmitter and
receiver side, which contributes to the scattering phenomenon and give rise to
temporal fading processes. However, in the presence of different polarizations
the attenuations and phase shifts generated by the microscopic interactions
with the scattering structures may differ for different polarizations and could
generate cross-polar effects.
From equation 2.5 the elementary signal received in the pth sub-channel
can be written as
p
r̂ (t) = w
(p)H
arx (θ)
Np
γqp atx (ξ)v(q) h(ζ; t) ∗ i(q) (ζ),
(2.6)
q=1
where w(p) is the receiver beamforming weight vector used for the pth subchannel, atx (ξ) and arx (θ) are the transmitter and receiver array steering
Chapter 2. A Novel Space-Time-Polarization
32
Channel Model for Wireless Communications
vectors respectively. ξ and θ are the Direction of Departure (DOD) and
Direction of Arrival (DoA) expressed with respect to the transmitter and
receiver reference frame. h(ζ; t) is the time-domain elementary path impulse
response defined in [36], ∗ is the convolution operator, and γqp is the real
coefficient cross polarization discrimination (XPD), representing the fraction
of the q th polarization being scattered into the pth part
E
E⊥→
E
=
,
E⊥←
γqp =
(2.7)
γpq
(2.8)
where E is the amount of the signal that is still in the original transmitted
polarization state and E⊥→ is the the fraction of the transmitted signal that
has been rotated into the opposite orthogonal polarization state. Assuming
p ⊥ and q . Furthermore,
(2.9)
aTtx (ξ)v(p) = MTtx (q,q)
w(p)H arx (θ) = [Mrx ](p,p) ,
(2.10)
since from equations 2.2 and 2.3 it is possible to set the relationships
Mtx Dv ⊗ atx (ξ)
Mrx Dw ⊗ arx (θ),
where
⎡
0
0
..
.
v(2)
0
···
⎢
⎢
Dv ⎢
⎢
⎣
v(1)
···
..
.
(2.11)
(2.12)
⎤
0
.. ⎥
. ⎥
⎥ ∈ CN Np ,Np .
⎥
⎦
(2.13)
v(Np )
Dw ∈ CM Np ,Np is defined in a similar way and ⊗ indicates the Kronecker
product. The expression in equation 2.6 can then be rewritten in matrix
notation as
(2.14)
r̂p (t) = w(p)H arx (θ) γ (p)T ⊗ aTtx (ξ) Dv h(ζ; t) ∗ i(ζ),
where
γ (p) γ11 , γ21 , · · · , γNp ,1
T
.
(2.15)
2.1. SPACE-TIME-POLARIZATION CHANNEL MODEL
33
The vector of the received elementary sub-channels, i.e. the vector of the
elementary signals received in each sub-channel, can now be expressed as
T
(2.16)
r̂(t) r̂(1) (t), r̂(2) (t), · · · , r̂(Np ) (t) =
⎤
⎡
w(1)H arx (θ) γ (1)T ⊗ aTtx (ξ) Dv h(ζ; t) ∗ i(ζ)
⎥
⎢
..
=⎣
(2.17)
⎦=
.
(Np )H
(Np )T
T
arx (θ) γ
⊗ atx (ξ) Dv h(ζ; t) ∗ i(ζ)
w
H T
T
(2.18)
= Dw Γ ⊗ arx (θ)atx (ξ) Dv h(ζ; t) ∗ i(ζ),
where
Γ γ (1) , γ (2) , · · · , γ (Np ) =
⎡
⎤
γ11 γ12 · · · γ1Np
⎢
.. ⎥
⎢ γ21 γ22
. ⎥
⎢
⎥ ∈ RNp Np
=⎢ .
⎥
.
..
⎣ ..
⎦
γNp 1 · · ·
γNp Np
(2.19)
(2.20)
is the cross-polarization matrix. Thus, it is possible to define the multi
antenna space-polarization elementary path channel matrix as
ˆ
H(ζ,
t) ΓT ⊗ arx (θ)aTtx (ξ)h(ζ, t) ∈ CM Np Np .
(2.21)
This is also depicted as a block diagram in figure 2.2, where we can identify
the elementary-path channel matrix Ĥ(ζ, t) = arx (θ)aTtx (ξ)h(ζ, t) obtained
in [36]. Thus,
ˆ
H(ζ,
t) = ΓT ⊗ Ĥ(ζ, t),
(2.22)
and the received elementary sub-channel vector becomes
ˆ
r̂(t) = DH
w H(ζ, t) ∗ Dv i(ζ),
(2.23)
ˆ
T
which allows the equivalence, DH
w H(ζ, t)Dv ≡ Mrx Hch Mtx , as derived from
equation 2.5.
Global Multi Space-Polarization Channel Matrix
Following the analogy developed in [36], it is possible to identify the th
cluster multi antenna space-polarization channel matrix for each cluster of
Chapter 2. A Novel Space-Time-Polarization
34
Channel Model for Wireless Communications
Figure 2.2: The block diagram of the complete multiple antenna STP
simulator: (top figure) the signal from each transmitting antenna element is
filtered by a separate space-time-polarization FIR filter, and (bottom figure)
FIR filter block for each cluster.
2.1. SPACE-TIME-POLARIZATION CHANNEL MODEL
35
microscopic scattering elements in the physical channel. Thus, indicating
with D(χ) the multi-dimensional domain of the vector of the independent
T
channel variables χ [ξ, θ, ψtx , ψrx ] with its nominal value χ for each cluster
= 0, 1, · · · , LS . The th cluster channel matrix can then be computed as
ˆ
H (ζ, t)
H(ζ, t)dχ =
ΓT ⊗ arx (θ)aTtx (ξ)h(ζ, t)dχ.
(2.24)
D(χ )
D(χ )
The global multi space-polarization channel matrix can now be written as,
H(ζ, t)
LS
H (ζ, t).
(2.25)
=0
where H(ζ, t) is the total multi antenna space-time-polarization channel
simulator model.
We can now write the received signal vector r̂(t) using equations 2.2, 2.3
and 2.4, where we define Hch H(ζ, t), as a linear combination of all the
transmitted sub-channels:
r̂(t) = Mrx Hch ∗ MTtx i(t).
(2.26)
The coefficients of the linear combination represent the effect of the spatiotemporal fading, cross-correlation and depolarization induced by the channel
environment.
2.1.2
Statistical properties of the global channel matrix
From [36] we find that the characterization of the global channel matrix is a
stochastic process in order to take into account the statistical variations of
the physical effects of the micro-scatterers on the propagating signal.
Most of the assumptions and properties stated in [36] for the spatiotemporal channel matrices H (ζ, t) are still valid for the multiple space-timepolarization channel matrices H (ζ, t) and will briefly be analyzed in this
chapter. A few extra assumptions and properties are also discussed, related
to the specific structure of the cross-polarization matrices.
Assumption 1. Clusters are statistically independent to one another and
therefore there is no correlation between different multiple antenna spacepolarization cluster matrices H (ζ, t) and Hm (ζ, t), = m, nor is there
any correlation between their constituent multiple antenna space-polarization
elementary path sub matrices.
Chapter 2. A Novel Space-Time-Polarization
36
Channel Model for Wireless Communications
Assumption 2. The random part of the channels elementary path sub
matrices is characterized by:
1. the amplitude attenuation αSC and phase shift ejϕSC related to the
micro-scatterers, and behave in the same way for any polarization state.
2. the cross-polarization factors, γqp, , which represent the amount of the
q th polarization state that is rotated into the pth polarization state by
the th cluster.
The random variables γqp, , αSC and ϕSC are assumed to be statistically
independent and the random phase ϕSC is uniformly distributed in [0, 2π).
Furthermore, the random variables associated with different clusters are also
assumed to be independent.
As a consequence of the last assumption, the following properties can be
inferred.
Property 1. The cross-polarization matrix Γ consists of random variables,
whose probability distribution depends on the physical nature of the cluster.
Proof. Follows directly from Assumption 2.
Property 2. The multiple antenna space-time-polarization th cluster channel matrix can now be written as
ˆ
H (ζ, t) = Γ ⊗
H(ζ,
t)dχ.
(2.27)
D(χ )
Proof. Directly inferred from Property 1.
The structure of the th cross-polarization matrix Γ is described in
equation 2.19.
Assumption 3. The Doppler effect angles ψT X , ψRX are assumed to be
independent of each other and of any other stochastic variable in the channel
model.
Assumption 4. The extra time delay τ is a constant value for all the
elementary paths of a particular cluster.
Property 3. Each multiple antenna polarization cluster matrix H (ζ, t) is a
matrix of zero-mean circular complex Gaussian random variables, conditioned
by the cross-polarization factor.
2.1. SPACE-TIME-POLARIZATION CHANNEL MODEL
37
Proof. If we identify the constituent blocks of the multiple antenna polarization th cluster channel matrix,
⎡
[H ]11 (ζ, t)
⎢
⎢ [H ]21 (ζ, t)
H (ζ, t) = ⎢
⎢
..
⎣
.
[H ]12 (ζ, t)
···
[H ]22 (ζ, t)
..
···
[H ]Nq 1 (ζ, t)
.
⎤
[H ]1N p (ζ, t)
⎥
..
⎥
.
⎥,
⎥
⎦
(2.28)
[H ]Nq Np (ζ, t)
where
[H ]qp (ζ, t) γqp H (ζ, t).
(2.29)
Conditioned on γqp , the distribution of the matrix entries is circularly
complex Gaussian with zero mean.
Through applying the Central Limit Theorem to expressions in equation
2.24 and 2.25, we can infer that each matrix entry is a circularly complex
Gaussian random variable, since they are defined as a superposition of an
infinite number of stochastic contributions.
Furthermore, because of the uniformly distributed random phase ϕSC , the
statistical mean value of the cluster matrix is given by
ΓT ⊗ arx (θ)aTtx (ξ)E {h(ζ, t)} dχ =
(2.30)
E H (ζ, t) =
D(χ )
vT X
vRX
= αF S (τ )e−jω0 τ δ(ξ − τ ) ·
e−jω0 c t cos(ψT X ) e−jω0 c t cos(ψT X ) ·
D(χ )
·Γ ⊗
T
arx (θ)aTtx (ξ)E
jϕSC
e
(2.31)
dχ = 0,
(2.32)
where E {·} denotes statistical expectation.
Now we calculate the mutual correlation matrix of the entries of the
multiple antenna polarization th cluster matrix. To do this, we redefine
the vector h (ζ, t) as
(2.33)
h (ζ, t)
T
T
vec [H ]11 (ζ, t) , vec [H ]21 (ζ, t) , · · · ,
vecT [H ]Nq 1 (ζ, t) , vecT [H ]12 (ζ, t) , · · · , vecT [H ]Nq Np (ζ, t) .
Chapter 2. A Novel Space-Time-Polarization
38
Channel Model for Wireless Communications
It is now possible to reformulate this by inspecting the above expression
and rewriting it as
h (ζ, t) = vec {Γ } ⊗ vec {H (ζ, t)} ,
(2.34)
so that it is easy to see that the following properties are valid.
Property 4. Vectors h (ζ, t), hm (ζ, t), = m, are statistically independent.
Proof. Directly derived from Assumption 2.
Property 5. Vectors h (ζ, t), = 0, 1, . . . , LS are wide-sense stationary
(WSS) random processes with respect to the time variable t.
Proof. The vectors have zero mean, as shown in equation 2.30. Furthermore,
their stationarity with respect to the time variable t can be proved as follows.
(2.35)
R (ζ,t1 , t2 ) E h (ζ, t1 )hH
(ζ, t2 ) =
H
=E (vec {Γ } ⊗ vec {H (ζ, t)})(vec {Γ } ⊗ vec {H (ζ, t)})
=
H
H
=E vec {Γ } vec {Γ } ⊗ E vec {H (ζ, t)} vec {H (ζ, t)} ,
where we used the fact that the cross-polarization factors are statistically
independent from any other random variable, as stated in Assumption 2.
Thus, by defining the Polarization-Domain (PD) th cluster autocorrelation
matrix as
2
2
(2.36)
RP D, E vec {Γ } vecH {Γ } ∈ RNq ,Np ,
and using known results [36] about the Time and Space domain autocorrelation matrices, we can now write
R (ζ, t1 , t2 ) = RP D, ⊗ RT D, (ζ, t1 − t2 )RSD, = R (ζ, ∆t),
(2.37)
which demonstrates wide-sense stationarity with respect to time.
So far, we have presented the structure of the multiple antenna spacepolarization cluster channel matrix and its autocorrelation. We will now
define the structure of the simulator by implementing the channel model.
The separability of the polarization domain and the space and time domains,
as concluded from equation 2.37, preserves the validity of the spatial and
temporal characterizations, while it also allows the characterization of the
cross-polarization component as shown in equation 2.19.
39
2.1. SPACE-TIME-POLARIZATION CHANNEL MODEL
2.1.3
Numerical Implementation
The structure of the multiple antenna space-polarization simulator which
includes cross-polarization effects is that each transmitting antenna have Np
space-polarization sub-channels (i.e., Np signals) and the FIR filter structure
of [36], creates the spatio-temporal fading effects. In figure 2.2 we show
the simulator for which Np = 2 different space-polarization sub-channels are
(p)
presented for simplicity. Let sn [k] be the signal sample taken at the time
instant t = kTc , of the signal transmitted by the nth transmitting antenna
using the pth space-polarization sub-channel, according to
∗(p) (p)
(kTc ),
s(p)
n [k] vn i
(2.38)
(p)
where Tc is the sampling time used in the simulation and vn is the nth
element of the transmitting beamforming weight vector used for the pth space(p)
polarization sub-channel. Then, let xm,n [k] be the amount of the k th sample
generated by the contribution of the nth transmitting antenna of the signal
received at the mth receiving antenna through the pth space-polarization subchannel. It is then the faded and cross-polarized pth signal along the n−to−m
path of the channel, represented in figure 2.2. The effect of the multiple
antenna space-polarization channel on the n − to − m path, apart from the
additive noise, can now be written as
⎡
⎤
Np
LS
⎣bn,m, [k]
⎦
γqp, s(q)
δ0 = 0,
(2.39)
x(p)
m,n [k] =
n [k − δ ] ,
=0
q=1
where bn,m, [k] is the th filter tap at the time instant k and δ is the
associated time delay. In the above formulation it is worth to recognize
that the fading filter coefficients bn,m, [k] are multiplied every time by the
cross-polarization factors γqp, in matrix Γ . The complete multiple antenna
space-time-polarization simulator generates its filtering coefficients, including
the cross-polarization factors, in the following procedure.
Property 6. In order to guarantee that the coefficients of the FIR filtering
structure in figure 2.2 have the autocorrelation function expressed in equation
2.37, they are implemented as follows.
1. = 0.
2. begin loop
Chapter 2. A Novel Space-Time-Polarization
40
Channel Model for Wireless Communications
3. Generate (N × M ) independent zero-mean complex white Gaussian
processes G ∈ CN M,KS , where KS is the number of discrete samples to
be simulated.
4. Correlate the processes G in the temporal and spatial domain
• Design a time correlation shaping filter with transfer function
T (z), such that the time autocorrelation of the output process is
RT D, (ξ, δt).
• Then, filter each row of G with T (z), obtaining the matrix of timefiltered processes GT, .
• Compute the eigenvector decomposition of the spatial autocorrelation matrix
(2.40)
RSD, = USD, ΛSD, UH
SD, .
• Generate the matrix S USD, ΛSD, ∈ CN M,N M .
• Compute the matrix B S GT, ∈ CN M,Ks , containing all
the fading coefficients for the th cluster from each transmitting
antenna element to each receiving antenna element, and for the
time index, k = 0, 1, . . . , KS − 1.
to obtain the fading matrix B ∈ CN M,KS .
5. Generate Np2 independent zero-mean real white Gaussian stochastic
2
variables c ∈ RNp .
6. Compute the eigenvector decomposition of the polarization domain
autocorrelation matrix
RP D, = UP D, ΛP D, UH
P D, .
7. Generate the matrix XP D, UP D,
(2.41)
2
2
ΛP D, ∈ CNp Np .
8. Assign the proper correlation in the polarization domain to the vector
c , as
(2.42)
γ̂ XP D, c .
9. Assemble the estimated th cross-polarization matrix Γ̂ from γ̂ , using
(2.43)
γ̂ = vec Γ̂ .
2.2. SIMULATION RESULTS
41
10. = + 1.
11. repeat loop until = LS .
Proof. If we consider the filtering coefficient used at the time instant k, and
th tap, the space-time domain coefficients are written in the k th column of
the matrix B , i.e. bk, [B ]:,k . We can see that the coefficients of the
multiple antenna space-polarization simulator in figure 2.2 can be written as
Γ̃ ⊗bk, , or in a more convenient vector format as γ̃ ⊗bk, . Thus, the mutual
correlation function of these coefficient vectors can be computed as
E (γ̃ ⊗ bk, )(γ̃ ⊗ bk, )H = E γ̃ γ̃H ⊗ bk, bH
k, =
H
XP D, ⊗ E bk, bH
= XP D, E c cH
k, =
= UP D, ΛP D, UH
P D, ⊗ RT D, [k − t]RSD, =
= RP D, ⊗ RT D, [k − t]RSD, ,
(2.44)
H
= INp2 , from property 6 statement 5 and
where we used the fact that E cc
H
in equation 2.41, and E bk, bk, = RT D [0]RSD .
2.2
Simulation Results
In this chapter we present the simulation results showing some of the features
and capabilities offered by the proposed novel multiple antenna STP channel
simulator. In addition, we test the simulator performance under different
conditions, by considering both LOS and NLOS propagation scenarios. A
communication link operating at 2.4 GHz carrier frequency and Tc = 10µs
sampling time is simulated, where both the transmitter and receiver utilize
a twelve-element Cube shaped linear 3D array (MIMO-Cube antenna) [9].
The receiver is assumed to be moving, while the transmitter is stationary.
The long-term fading power values are normalized so that the total received
power in non-LOS (NLOS) propagation is 0 dBW, while, in the case of LOS
propagation, a Rice factor (K) of 10 dB is assumed. Only one reflection due
to a macro-scatterer is simulated, together with the direct path, with relative
delay of 600 ns.
In the LOS propagation scenario without cross-polarization, the normalized distribution of the channel coefficients is shown in figure 2.3, where a good
correspondence is achieved between the simulated LOS distribution, shown by
solid blue line, and the theoretical Rice distribution, shown by the solid red
Chapter 2. A Novel Space-Time-Polarization
42
Channel Model for Wireless Communications
0.45
Simulated LOS
K = 10 dB.
Theoretical Rice
distrib., K = 10 dB.
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
5
10
Normalized envelope r
15
20
Figure 2.3: The envelope distribution of the simulated received signals in a
LOS propagation environment with a Rice factor K = 10 dB, compared with
the theoretical Rice distribution.
43
2.2. SIMULATION RESULTS
0.4
Simulated LOS
original K = 10, XPD = 10dB
Theoretical Rice
distrib. K = 2.
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
5
10
15
20
Normalized envelope r
25
30
35
Figure 2.4: The envelope distribution of the simulated received signals in a
LOS propagation environment, with an original Rice factor K = 10 dB and
an XPD of 10 dB, compared with the theoretical Rice distribution.
line. Due to the high Rice factor (K = 10 dB), most of the received signal
power is concentrated along the direct LOS path.
Figure 2.4 show the probability distribution of the same signal as in
figure 2.3, but with a cross-polarization of XPD = 10 dB. It is evident from
comparing these figures that the depolarization between the two polarization
states is transforming the original signal with Rice distribution and Rice factor
K = 10 dB into a Rice distribution of K = 2 dB. The depolarization effect can
also be seen from the time series of the fading coefficients presented in figure
2.5 where deep fading dips are clearly observed for the case of XPD = 10
dB, and thereby adversely affecting the performance of the communications
channel. From this observation, we can also conclude that the XPD has similar
effect as ’blocking objects’ in the channel propagation environment.
Figure 2.6 shows the normalized distribution of the fading coefficients
envelope magnitude in a NLOS environment. As expected, it follows a
Chapter 2. A Novel Space-Time-Polarization
44
Channel Model for Wireless Communications
16
14
Normalized envelope r [dB]
12
10
8
6
4
2
0
ï2
with no depolarization
XPD = 10 dB
0
0.5
1
1.5
Time t [s]
2
2.5
3
ï3
x 10
Figure 2.5: The time series of the received signal in the LOS environment with
Rice factor K =10 dB: (blue) without XPD and (red) with XPD of 10 dB.
45
2.2. SIMULATION RESULTS
0.4
Simulated NLOS.
Theoretical Rayleigh
distribution.
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
Normalized envelope r
4
5
Figure 2.6: The envelope distribution of the simulated received signals
in a NLOS scattering environment compared with a theoretical Rayleigh
distribution.
Chapter 2. A Novel Space-Time-Polarization
46
Channel Model for Wireless Communications
0.4
Simulated NLOS
XPD = 10 dB.
Theoretical Rayleigh
distribution.
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
Normalized envelope r
4
5
Figure 2.7: The envelope distribution of the simulated received signals in a
NLOS propagation environment, with an XPD of 10 dB, compared with the
theoretical Rayleigh distribution.
Rayleigh distribution. The simulated distribution is shown by the blue solid
line, while the theoretical Rayleigh distribution analytically obtained from
the input parameters of the simulator is shown by the red solid line. A good
agreement between the simulated and theoretical data is observed.
Figure 2.7 shows the probability distribution of the same signal as in
figure 2.6, but with a cross-polarization of XPD = 10 dB. By comparing
these figures we can see that there is no difference in the distributions. In
addition, by observing the time series of the signal no effect on the fading
dips was noticed in this case, however an increase in attenuation of the total
signal was observed.
2.3. CONCLUSIONS
2.3
47
Conclusions
In this chapter we presented a novel multiple antenna channel model and
associated simulator which takes into account the spatial, temporal and
polarization (STP) properties affecting signal transmission in wireless communications. In addition, we have presented the theoretical background, features
and properties, analysis and implementation of the proposed STP channel
model and simulator. Further, we tested the simulator for various propagation
conditions, and the simulation results have shown good agreement with the
theoretical distributions. Finally, we investigated the impact of depolarization
on the probability distributions of the simulated signals and their adverse
effect on performance. The proposed channel model and simulator are
designed for link level simulations for various communication links where
both the transmitter and the receiver are equipped with with an array of
antennas. In the next chapter we will employ this simulator for investigating
the performance of satellite [7, 14–18] and high altitude platform [19–28]
communication links.
Chapter 2. A Novel Space-Time-Polarization
48
Channel Model for Wireless Communications
CHAPTER 3
SPACE-TIME-POLARIZATION
PROCESSING FOR CAPACITY
ENHANCEMENT IN HAP/SATELLITE
COMMUNICATION SYSTEMS
I
t has been widely recognized that the capacity in wireless communication
systems can be greatly increased by exploiting environments with rich
scattering such as urban areas or indoors. Classically, it is well understood
that the electromagnetic polarization of plane waves possesses two independent channels, or polarization states [2, 3]. However, it has been shown
that the existence of a scattering rich environment can increase the number
of combined spatial-polarization channel states and thus effectively increase
the channel capacity of the system [6–12]. Independent spatial-polarization
or frequency channels can be accessed by means of multiple antennas and
the use of orthogonal frequency division multiplexing (OFDM) at both the
transmitter and the receiver, thus the technique is referred to as multiple-input
multiple-output orthogonal frequency division multiplexing (MIMO-OFDM)
communication system. In this chapter we consider the MIMO-OFDM
technique as a means of achieving independent channels. In essence, the
MIMO technique achieves orthogonality over space and polarization domains
by employing the Singular Value Decomposition (SVD), and the OFDM
technique achieves orthogonality over the frequency domain by employing
the Discrete Fourier Transform (DFT) in conjunction with a Cyclic Prefix
Chapter 3. Space-Time-Polarization Processing for Capacity
50
Enhancement in HAP/Satellite communication systems
(CP) inserted to reduce the intersymbol interference (ISI) without losing
the orthogonality among the sub-carriers and therefore, equalization at the
receiver is relatively simple.
The aim is to study the theoretical potential of exploiting the spatialpolarization diversity provided by compact MIMO antenna array configurations (e.g., the vector element [7, 8], the MIMO-Cube [9], the MIMOTetrahedron [13] and the novel MIMO-Octahedron array antennas) to achieve
higher capacity in communication systems. For example, an application that
utilize the spatial-polarization channels is a high data rate transmission system
employing multiple satellites in designated orbits [14–18] or high altitude
platforms in the stratosphere [19–28].
Satellite communication systems today operate in a variety of frequency
bands, ranging from 100 MHz to 100 GHz. Low-Earth-Orbit (LEO) satellite
systems like ORBCOMM, E-SAT and LEO ONE [29] that operate in the
frequency range 100 to 400 MHz and with a bandwidth of a few MHz are
examples of low bit-rate systems that could benefit from the proposed MIMOOFDM multiple platform diversity technique.
High Altitude Platforms (HAPs), on the other hand, are quasi-stationary
aerial platforms consisting of either unmanned airships or planes that will
operate in the stratosphere, 17-22 km above the ground. This emerging
technology preserve many of the advantages of both satellite and terrestrial
systems [30–34] and has presently started to attract considerable attention
in Europe. Using narrow bandwidth repeaters on HAPs for high speed data
traffic have several advantages compared to using satellites, especially when
operating in a local geographical area. One of the main advantages is that the
received signal from the HAP is much stronger than a received signal of equal
transmitted power from a satellite. This allows for a much lower transmitter
power which would decrease the size and weight of the repeater equipment
carried by the HAP. In addition HAPs offer much easier deployment than
satellites and so high-speed connection can be made on demand for a specific
geographical area.
The proposed platform diversity system consists of virtual MIMO spatial
channels (created by a multiple relaying platform diversity) in conjunction
with the polarization and antenna pattern diversity (formed via special
compact MIMO antenna arrays). Various compact MIMO antenna array
configurations are investigated and their performance, in term of capacity,
is analysed. In addition, since these special compact MIMO antenna array
configurations depend on the array elements being positioned very closely
together, the effect of mutual coupling and spatial correlation will also be
3.1. PLATFORM DIVERSITY
51
analysed and taken into account when performing the simulation for this
combined diversity system. We also investigate the influence of the separation
angle between the multiple platforms on system performance, and determine
the optimal separation angles that maximize the total capacity of the system
for the various compact MIMO antennas. In the proposed scheme, we
aim to preserve the orthogonality of polarization states in order to achieve
the optimal theoretic capacity performance of the system. However, the
independent radio channels utilized in this system are sensitive to depolarizing
effects which might cause significant impact on system’s performance. The
depolarizing effect can be caused by interference at different layers of the
atmosphere. The signals suffer mainly tropospheric effects due to rain and
ice particles and ionospheric effects due to the Faraday rotation phenomena.
To reinforce the analysis, we present a novel multi-channel simulator that
produces realistic time-series of the fading process affecting signal transmission
in the proposed platform diversity system. The proposed simulator takes
into account the temporal, spatial and polarization properties affecting these
processes. Further, we will determine the impact on the total capacity of
the proposed application that utilizes the spatial-polarization channels for
high data rate transmission system using a multiple platform spatio-polarized
compact MIMO antennas system.
The organization of this chapter is as follows. Section 3.1 presents the
platform diversity system and the utilized channel models. Section 3.2
investigates the use of MIMO-OFDM and power control to further enhance
the system capacity. Section 3.3 present the structures of the various compact
MIMO antenna arrays. The depolarization analysis and definition of the
cross-polar discrimination and cross-polar isolation parameters and their effect
on system performance is presented in section 3.4. Section 3.5 present the
simulation results and provide evaluations and performance comparisons of
the different parameters. Finally, section 3.6 concludes the chapter.
3.1
Platform Diversity
In this chapter we propose an application for high data rate transmissions
using a system of multiple LEO-satellites [14–18] or High Altitude Platforms
(HAP) [19–28]. This system consists of virtually created MIMO channels in
the space domain using platform diversity in conjunction with 3D polarization
[4, 5] and radiation pattern diversity of a special MIMO antenna arrangement
[7, 8] and also through using the OFDM technique. The investigations are
Chapter 3. Space-Time-Polarization Processing for Capacity
52
Enhancement in HAP/Satellite communication systems
Scenario
1
2
3
4
5
6
7
8
Table 3.1: Platform Scenarios.
Platform Number of Platforms Type of Channel Model
Satellite
3
FSL
Satellite
6
FSL
Satellite
3
Multiple STP
Satellite
6
Multiple STP
HAP
3
FSL
HAP
6
FSL
HAP
3
Multiple STP
HAP
6
Multiple STP
HAP b
HAP a
HAP c
20 km
Tx
Rx
Figure 3.1: The MIMO-HAP diversity system with three HAPs (scenario 5)
and the channel paths from the transmitter to the receiver.
divided into eight scenarios, see Table 3.1.
The number of platforms used in the different scenarios is dependent on
the number of channels created by the employed antenna arrays. The antenna
arrays investigated in this chapter divide the scenarios into two groups which
utilize a platform diversity consisting of three or six relaying platforms.
Figure 3.1 and figure 3.2 show the diversity setup for scenarios 5 and 6,
respectively. In these two scenarios we assume that the HAPs are located
along a fixed line with the HAPs uniformly distributed and separated by the
angles θ.
A similar setup is produced for the LEO-satellite platforms in scenarios 1
and 2, where three or six satellites are used. These satellites are assumed to
53
3.1. PLATFORM DIVERSITY
20 km
Tx
Rx
Figure 3.2: The MIMO-HAP diversity system with six HAPs (scenario 6) and
the channel paths from the transmitter to the receiver.
be uniformly located along a fixed orbit with a constant angle of separation.
These two scenarios are shown in figure 3.3 and 3.4.
In the scenarios (1, 2, 5 and 6) the wave propagation channel Hch from
the N transmitter antenna array elements to the M receiver antenna array
elements is modeled as a free space loss (FSL) model [12], and is defined as a
transformation containing the space dependent decaying values of the signal
being transmitted
c
,
(3.1)
Hmn (r, f ) =
4πf |rm − rn |
where |rm − rn | is the distance along the path between transmitter array
element m and receiver array element n. In this propagation channel there
are no atmospheric or multipath interference and the noise in the system is
modeled as uncorrelated Gaussian noise.
For scenarios 3, 4, 7 and 8, a novel space-time-polarization (STP) multi
channel simulator model, proposed in chapter 2, is utilized. In these scenarios,
a signal transmitted through a propagation channel with physical objects
that generates multipath components of the transmitted signal, each with its
own attenuation, polarization, correlation, phase shift, delay and direction
of propagation. Depending on the material of the objects in the channel, a
frequency dependent stochastic scattering effects can also affect the received
signal.
Each object in the propagation channel is modeled as a cluster of microscatterers [36], see Figure 2.1 in chapter 2, in the local area (within a few
Chapter 3. Space-Time-Polarization Processing for Capacity
54
Enhancement in HAP/Satellite communication systems
Rx
Tx
qs qs
Figure 3.3: The MIMO-Satellite diversity system with three satellites
(scenario 1) and the channel paths from the transmitter to the receiver.
55
3.1. PLATFORM DIVERSITY
Rx
Tx
qs
Figure 3.4: The MIMO-Satellite diversity system with six satellites (scenario
2) and the channel paths from the transmitter to the receiver.
Chapter 3. Space-Time-Polarization Processing for Capacity
56
Enhancement in HAP/Satellite communication systems
hundred wavelengths) centered about the center position of the cluster. This
cluster is denoted as a macro-scatterer. Furthermore, both the transmitter
and the receiver can respectively be positioned inside a local area surrounded
by micro-scatterers.
In order to model the atmospheric angle spreading effect due to scintillation phenomena and depolarization effects due to precipitation and Faraday
rotation phenomena, clusters are added in the direct line-of-sight (LOS) path
as well [14, 21–23]. With the presence of different polarizations, attenuations,
phase shifts and polarizations generated by the multipath cluster interaction
with the signal can differ for different incident polarization states and will
therefore also generate a cross-polarization effect.
3.1.1
Space-Polarization Channel Model
The signals carried by the different space-polarization modes (or sub-channels)
are written in a vector format as
T
(3.2)
i(t) i(1) (t), i(2) (t), · · · , i(Np )(t) ,
where i(p) (t) is the information signal transmitted with the pth mode. The
transmitting antenna is assumed to be a linear transformation of the input
signal i(t) into the independent radio channels s(t), according to
s(t) MTtx i(t),
(3.3)
At the receiver we have a similar transformation from the signals in
the independent radio sub-channels srx (t) into the output signal r(t) of the
system, i.e. the vector of the elementary signals received in each mode,
T
r̂(t) r̂(1) (t), r̂(2) (t), · · · , r̂(Np )(t) = Mrx srx (t),
(3.4)
where s(t) and srx (t) are vectors containing the independent spatial-polarization modes that are active for a specific antenna type and they are related
through
(3.5)
srx (t) = Hch ∗ s(t),
where the symbol ∗ indicates matrix convolution, as defined in [36]. The
channel Hch , from the transmitter mode vector s(t) to the receiver mode
vector srx (t), is the simulated propagation channel developed in chapter 2.
3.2. THE MIMO-OFDM SYSTEM
57
Thus, the mode signal vector r̂(t) at the receiver can be rewritten using
equations 3.3, 3.4 and 3.5 as a linear combination of all the transmitted modes,
each of which is subjected to the effects of the propagation channel
r̂(t) = Mrx Hch ∗ MTtx i(t).
(3.6)
The coefficients of the linear combination represent the effect of the fading,
cross-correlation and depolarization induced by the channel.
3.2
The MIMO-OFDM System
Through the combination of MIMO and OFDM (Orthogonal Frequency Division Multiplexing), denoted as MIMO-OFDM, we also achieve orthogonality
over the frequency domain by using the Discrete Fourier Transform (DFT)
with a Cyclic Prefix (CP) to mitigate the effects of frequency selective
and Ts is
channels. Assuming a cyclic prefix CP ≥ τd · fs , where fs = T−1
s
the symbol time, we can write the received signals as a circular convolution
over the DFT-frame as
rm (t) =
N
hmn (t) sn (t) + vm (t),
(3.7)
n=1
where NDF T = 128 is the size of the DFT, m = 1, · · · , M are the receiving
antennas and vm (t) is AWGN. If we have a MIMO antenna system with N
transmitting antennas and M receiving antennas, we can then write the signal
for sub-channel k in the frequency domain between any pair of transmitting
and receiving antennas as
rm (k) =
N
hmn (k)sn (k) + vm (k),
(3.8)
n=1
where k denotes each separate subcarrier. If we write equation 3.8 in vector
notation we get
r(k) = H(k)s(k) + v(k),
(3.9)
where r(k) is an (M × 1) vector and s(k) is an (N × 1) vector of the received
and transmitted signals, respectively. H(k) is the (M ×N ) frequency response
matrix H(k) = hmn (k), m = 1, · · · , M and n = 1, · · · , N in 3.7 of the channel
between N transmitters and M receivers. The noise in the system v(k) is
Chapter 3. Space-Time-Polarization Processing for Capacity
58
Enhancement in HAP/Satellite communication systems
an (M × 1) vector assumed to be additive white Gaussian noise. Thus, the
correlation matrix of the noise vector v(k) is E{v(k)vH (k)} = σv2 · IM , where
σv2 is the variance of the noise and IM is the M × M identity matrix. Since
we are using the singular value decomposition (SVD) technique we can now
write the channel matrix H(k) as
H(k) = U(k)Σ(k)VH (k),
(3.10)
where Σ(k) is an (M × N ) matrix containing singular values that are larger
than zero σ1 (k) ≥ σ2 (k) · · · ≥ σr (k) > 0 where r is the rank of the
matrix H(k), and the (M × M ) matrix U(k) and the (N × N ) matrix V(k)
contain the corresponding eigenvectors as matrix column vectors. To obtain
a diagonalized system we then define
y(k) = Σ(k)x(k) + n(k),
(3.11)
⎧
⎨ y(k) = UH (k)r(k)
s(k) = V(k)x(k)
(3.12)
⎩
n(k) = UH (k)v(k)
Since the MIMO-OFDM channels in equation 3.10 are uncorrelated and
the correlation of the noise n(k) is E{n(k)nH (k)} = σn2 · IM then we can write
the theoretical maximum information capacity of the system [10] as
NDF
r
T −1
2
σm
(k)
2
,
(3.13)
log2 1 + σxm (k)
C=
σn2
m=1
where
k=0
where σx2m is the variance of the separate uncorrelated input signals in vector
x(k). The capacity in equation 3.13 is constrained by the total radiated power
from the transmitting antennas, defined as
Prad =
NDF
T −1
r
k=0
m=1
σx2m (k).
(3.14)
To maximize the total sum of capacities in all the sub-channels we use
the so called water-filling technique in which we allocate more power to the
sub-channels with high eigenvalues. The optimal water-filling solution [37] is
then given by
⎧
2
σn
σ2
2
⎪
if γ − σ2 n(k) ≥ 0
2 (k) ,
⎨ σxm (k) = γ − σm
m
(3.15)
⎪
2
⎩ 2
σn
σxm (k) = 0, if γ − σ2 (k) ≤ 0
m
59
3.3. COMPACT ANTENNA ARRAYS
where k = 0, · · · , NDFT − 1, m = 1, 2, · · · , r and γ is a pre-defined threshold
level of the signal-to-noise ratio in the system and it is dependent on the total
transmitted power Prad in equation 3.14. The average signal-to-noise ratio
SNRavg in the simulations is calculated as
SNRavg = 10 log10
1
Nactive
NDF
T −1
k=0
r
σ 2 (k)
σx2m (k) m 2
σn
m=1
,
(3.16)
where Nactive is the number of active channels used for which the variance of
the input signals σx2m > 0.
3.3
3.3.1
Compact Antenna Arrays
Array Configurations
The Compact MIMO Antenna Array Configurations each transmit and receive
antenna arrangement of the system consists of a special compact MIMO
antenna array configuration, which possess a structure of different designs
and complexities as shown in figure 3.5. The tested antennas shown in this
figure are: the vector element antenna, MIMO-Cube, MIMO-Tetrahedron and
MIMO-Octahedron. The detailed description of the structure and analysis of
these antennas is presented in the next section.
3.3.2
The Space-Polarization Domain
The polarization and antenna radiation pattern of the electromagnetic field
can be expressed as a multipole expansion [2, 3] of the field emanating from
a virtual sphere enclosing the antenna that is being analyzed. This series
expansion consists of weighted orthogonal base functions on the surface of the
virtual sphere and allow for a solution to Maxwell’s equations that can be
written as (see Appendix A.1),
⎧
j
⎪
⎪
⎨ E = l,m k aE (l, m)(∇ × fl (kr)Xlm ) + aM (l, m)gl (kr)Xlm
(3.17)
⎪
⎪
j
= 1
⎩ H
l,m aE (l, m)fl (kr)Xlm − k aM (l, m)(∇ × gl (kr)Xlm )
η0
where η0 is the intrinsic impedance of free space. The base functions
lm (ϕ, θ) are orthogonal vector functions of the spherical field
lm (ϕ, θ) = LY
X
Chapter 3. Space-Time-Polarization Processing for Capacity
60
Enhancement in HAP/Satellite communication systems
Figure 3.5: The structure of various compact MIMO antenna array
configurations: (top left) vector element antenna, (top right) MIMO-Cube,
(bottom left) MIMO-Tetrahedron and (bottom right) MIMO-Octahedron.
3.3. COMPACT ANTENNA ARRAYS
61
in ϕ and θ directions when the far-field of the antenna is projected onto the
= j
r×∇ is
virtual sphere. Ylm is the scalar spherical harmonic functions and L
the angular momentum operator. The radial functions gl and fl in equation
3.17 are spherical Hankel functions representing an outgoing (transmitted)
wave or an incoming (received) wave. The weights aE and aM are the
corresponding real valued coefficients and will give the gain of each orthogonal
function (mode) for a particular electromagnetic far-field pattern, as shown
by equation 3.18,
⎧
1
k
⎪
∗
dΩ
⎪
Ylm
(θ, φ) r · E
⎪
⎨ aE (l, m) ≈ η0 · l(l + 1) fl (kr)
(3.18)
k
⎪
∗
⎪
⎪
g
(l,
m)
≈
−
(kr)
Y
(θ,
φ)
r
·
H
dΩ
a
M
l
⎩
lm
l(l + 1)
By using equation 3.18, we can calculate which modes are active on any
arbitrary antenna enveloped by a virtual sphere by knowing the current
the charge distribution ρ and the intrinsic magnetization M
of
distribution J,
the antenna structure. These modes are theoretically orthogonal to each other
and therefore represent independent ports of the antenna. The transmitting
channel Htx is then assumed as the linear transformation of the input signal x
into the mode domain atx according to atx = Htx x. For the receiving channel
we have a similar transformation from the mode domain arx into the output
signal y of the system following y = Hrx arx , where atx and arx are vectors
containing the mode gains for a specific antenna type.
To separate these modes into uncorrelated channels we use singular value
decomposition
(3.19)
H = UΣVH ,
where U and V are matrices containing the eigenvectors of the antenna and
Σ comprise of the antenna gains for independent MIMO subchannels.
The orthogonalization of the channel into the independent subchannels is
done by multiplying the signal to be transmitted x with the matrix V on
the transmitter side of the channel and multiply the received signal y on the
receiver side of the channel with the matrix UH
y = UH H (Vx) ,
(3.20)
where y is a vector containing the decoded signal from the independent MIMO
subchannels and x is a vector of the separate signals to be transmitted through
the MIMO channel.
Chapter 3. Space-Time-Polarization Processing for Capacity
62
Enhancement in HAP/Satellite communication systems
Figure 3.6: The theoretical antenna pattern when the six channels of the
vector element antenna are activated. The three omnidirectional antenna
beams at elevation angle 0 degrees and azimuth 0 and 90 degrees have both
vertical and horizontal polarization.
The first compact MIMO antenna array we investigated is known as the
vector element antenna [7, 8], see figure 3.5. This antenna consists of three
orthogonal electric dipoles forming an electric tripole together with a magnetic
tripole formed by three orthogonal loop antennas (magnetic dipoles), which
will give a maximum of six independent antenna ports as shown in figure 3.6.
The singular values contained in matrix Σ in equation 3.19 for the vector
element antenna array are shown in figure 3.7. It can be clearly seen from
this figure that we have one very good channel (> -2 dB), four fairly good
channels (> -30 dB) and one weak channel (< -40 dB).
The second antenna type is the MIMO-Cube [9], which consists of twelve
electric dipoles positioned on the twelve edges of a cube as shown in figure
3.5. It can been seen from figure 3.8 that this antenna array has theoretically
twelve independent antenna ports.
Figure 3.9 show the singular values
63
3.3. COMPACT ANTENNA ARRAYS
0
ï5
relative channel gain [dB]
ï10
ï15
ï20
ï25
ï30
ï35
ï40
ï45
1
2
3
4
Channel number
5
6
Figure 3.7: The theoretical antenna gain for each of the six orthogonalized
sub channels in the vector element anttena.
Chapter 3. Space-Time-Polarization Processing for Capacity
64
Enhancement in HAP/Satellite communication systems
Figure 3.8: The theoretical antenna pattern when all twelve channels of the
MIMO-Cube antenna are activated. The four antenna beams at elevation
angle 0 degrees have vertical linear polarization and the eight beams at
elevation ± 45 degrees have horizontal linear polarization.
65
3.3. COMPACT ANTENNA ARRAYS
0
ï10
relative channel gain [dB]
ï20
ï30
ï40
ï50
ï60
ï70
ï80
ï90
ï100
1
2
3
4
5
6
7
8
9
Channel number
10
11
12
Figure 3.9: The theoretical antenna gain for each of the twelve orthogonalized
sub channels of the MIMO-Cube antenna array.
Chapter 3. Space-Time-Polarization Processing for Capacity
66
Enhancement in HAP/Satellite communication systems
Figure 3.10: The theoretical antenna pattern when all six channels of the
MIMO-Tetrahedron antenna are activated. The three antenna beams at
elevation angle 30 degrees have vertical linear polarization and the three beams
at elevation -30 degrees have horizontal linear polarization.
contained in matrix Σ in equation 3.19 for the MIMO-Cube antenna array.
We can clearly see that we have eight fairly strong channels (> -50 dB), one
weak channel (< -60 dB) and one very weak channel (< -90 dB).
The third compact antenna that we investigated is known as the MIMOTetrahedron [13] as shown in figure 3.5. This antennas has six electric
dipoles placed at the six edges of a tetrahedron, and so has theoretically
six independent ports as can be seen in figure 3.10.
The singular values
contained in matrix Σ in equation 3.19 for the MIMO-Tetrahedron antenna
array asre shown in figure 3.11. It can be clearly seen from this figure that we
have one very good channel (> -2 dB), four fairly good channels (> -32 dB)
and one weak channel (< -40 dB). Comparing the sub channel gains of the
MIMO-Tetrahedron with the gains of the vector element antenna we can see
that the MIMO-Tetrahedron have slightly higher gain in the three strongest
67
3.3. COMPACT ANTENNA ARRAYS
0
ï5
relative channel gain [dB]
ï10
ï15
ï20
ï25
ï30
ï35
ï40
ï45
1
2
3
4
Channel number
5
6
Figure 3.11: The theoretical antenna gain for each of the six orthogonalized
sub channels of the MIMO-Tetrahedron antenna array.
Chapter 3. Space-Time-Polarization Processing for Capacity
68
Enhancement in HAP/Satellite communication systems
Figure 3.12: The theoretical antenna pattern when all twelve channels of the
MIMO-Octahedron antenna are activated. The six antenna beams at elevation
angle 30 degrees have both vertical and horizontal linear polarization and the
six beams at elevation -30 degrees also have both vertical and horizontal linear
polarization.
sub channels than is achieved by the vector element antenna.
Finally, the fourth compact antenna we proposed and investigated is a
novel array configuration, which we denoted as the MIMO-Octahedron. This
antenna consists of twelve electric dipoles positioned in a double tetrahedron
geometry, as can be seen in figure 3.5. This design is created by taking two
MIMO-Tetrahedron arrays and placing them with one tetrahedron vertex
facing a vertex of the other tetrahedron and then rotating one of the
tetrahedrons 60 degrees around the axis going through both vertices and
finally displace one of the tetrahedron so that they both have the same central
point. Theoretically this will give twelve independent ports as can be seen
from 3.12. The singular values contained in matrix Σ in equation 3.19 for the
MIMO-Octahedron antenna array are shown in figure 3.13. We can clearly
69
3.3. COMPACT ANTENNA ARRAYS
0
ï10
relative channel gain [dB]
ï20
ï30
ï40
ï50
ï60
ï70
ï80
ï90
ï100
1
2
3
4
5
6
7
8
Channel number
9
10
11
12
Figure 3.13: The theoretical antenna gain for each of the twelve orthogonalized
sub channels of the MIMO-Octahedron antenna array.
Chapter 3. Space-Time-Polarization Processing for Capacity
70
Enhancement in HAP/Satellite communication systems
see from this figure that we have eigh fairly strong channels (> -50 dB) and
four weak channels (< -70 dB). If we compare the MIMO-Octahedron with
the MIMO-Cube, we can see that the overall average gain is about the same,
however there exist an extremely weak channel in the MIMO-Cube. This
observation regarding the MIMO-Cube was also noted in [9].
3.3.3
Mutual Coupling and Spatial Correlation
Assuming that we have a MIMO antenna system with N transmitting antennas
and M receiving antennas, the complex envelope of the received signal rm (t)
at the receiving compact array after matched filtering can be expressed as the
linear convolution
rm (t) =
N
hnm (t)sn (t − τ ) + vm (t),
(3.21)
n=1
where m = 1, . . . , M . vm (t) is assumed to be AWGN. Rewriting 3.21 in vector
notation results in
r = Hs + v,
(3.22)
where s is the (N × 1) vector containing the transmitted signals from the N
transmitting antenna elements and v is the corresponding (N × 1) zero-mean
AWGN vector. H in 3.22 is the normalized (N × M ) channel matrix modelled
as
1/2
1/2
Zrx (Rrx ) H0 (Rtx ) Ztx
,
(3.23)
H=
Crx Ctx
where H0 is the channel response without spatial correlation and mutual
coupling. Rrx and Rtx are the spatial correlation matrices on the receiving
and transmitting side, respectively. The mutual coupling between the
elements of the compact antenna array is denoted as Zrx and Ztx normalized
by Crx and Ctx , respectively. The mutual coupling is calculated from
⎧
tx
−1
⎨ Ztx = Ztx
0 Z0 + ZL
(3.24)
⎩
−1
Zrx = ZL (Zrx
+
Z
)
L
0
where Z0 represents the impedance matrix of the transmitting and receiving
compact arrays, ZL is a diagonal matrix containing the source impedance
which has been chosen as the complex conjugate of the self impedance given
3.4. DEPOLARIZATION ANALYSIS
71
by the diagonal impedance matrix Z0,ii , and Crx and Ctx are normalizing
factors [35].
The spatial correlation matrices Rtx and Rrx are calculated between the
antenna element positions and polarization states according to [6]
ϕ θ
ρp,q = !
ζ
κ
ϕ θ
aq (Θ)a∗p (Θ) sin θp(Θ)dκdζdθdϕ
ζ
κ
|aq (Θ)| sin θp(Θ)dκdζdθdϕ
(3.25)
1
×!
ϕ θ
ζ
κ
|ap (Θ)| sin θp(Θ)dκdζdθdϕ
where the element p, q of matrix R is the correlation between antenna element
p and q. ϕ and θ are the spherical coordinates expressing the spatial domain
and ζ and κ are the polarization angle and phase difference, respectively, that
account for the effects in polarization domain [6]. In equation 3.25, a(Θ) is
the steering vector and p(Θ) is the joint probability distribution function of
T
the parameter vector Θ = [θ ϕ ζ κ ] , where T denotes a transpose operator.
It is assumed that all the parameters are independent of each other and that
p(ζ) = u {0, π} and p(κ) = u {−π, π} are uniformly distributed.
3.4
Depolarization Analysis
The polarization of a time-harmonic plane-wave is assumed to be the
alignment of the electric field component of the TEM plane-wave, which can
then be represented by the x− and y−components of the electric field vector
as
E
= (Exex + Ey ey ) ejωt .
(3.26)
E
Propagation of a linearly polarized high frequency wave in the ionosphere
will experience a rotation of the polarization plane. Depending on the
frequency and the length of the path, the amount of rotation can vary from
negligible (above 10 GHz) to several rotations (below 1 GHz) [38]. This
effect is known as Faraday rotation and is caused by the combined effect
of a high electron density and the earth’s magnetic field. In the troposphere,
depolarization can be caused by precipitation. All rain drops in a given cloud
are affected by similar forces within the cloud which cause a certain degree of
alignment between the rain drops [38, 39].
Chapter 3. Space-Time-Polarization Processing for Capacity
72
Enhancement in HAP/Satellite communication systems
The polarization of an electromagnetic wave traveling through anisotropic
media (e.g. a cloud containing rain and ice particles) is generally altered.
Consequently a polarized wave might emerge with some component that
is orthogonal to the original polarization state (e.g. vertically polarized
signal containing a horizontal component or a Right-Hand Circular Polarized
(RHCP) signal containing a component of Left-Hand Circular Polarization
(LHCP)). The relationship between these polarization components of the
electromagnetic wave is measured by the cross-polar discriminatio (XPD) or
the cross-polar isolation (XPI) [38, 39].
E
(3.27)
XPD = 20 log10
E⊥→
E
,
(3.28)
XPI = 20 log10
E⊥←
where E is the amount of the signal that remain in the same polarization state
as before, and E⊥→ is the amount of the signal that has scattered out into the
opposite orthogonal polarization state. E⊥← is the amount of the opposite
orthogonal signal that has scattered into the original signals polarization state.
Depolarization from rain is strongly correlated with the rain attenuation
and can be calculated from the following empirical formula [38, 39],
XPD = a − b log(L),
(3.29)
where a=35.8 and b=13.4 are reasonable values for frequencies about 10 GHz,
and L is the rain attenuation [38, 39].
3.5
Simulation Results
In this section we investigate the capacity improvement resulting from the use
of multiple HAP or satellite system employing compact MIMO antenna arrays
and compare the results to that obtained from a system without diversity
(denoted single-input single-output SISO). In addition, we will also show the
effects of mutual coupling and spatial-polarization correlation (calculated by
the Finite Element Method) on the capacity of the system. The simulation
results are divided according to the used multiple platform (HAP or satellite)
and type of channel model employed (referring to table 3.1) for the different
scenarios.
73
3.5. SIMULATION RESULTS
8000
Ideal MIMOïCube or ideal MIMOïOctahedron,
12 independent channels and 6 satellites.
Ideal Vect. elem. ant. or ideal MIMOïTetrahedron,
6 independent channels and 3 satellites.
Single satellite system (SISO),
2 independent channels.
7000
Capacity C [bps]
6000
5000
4000
3000
2000
1000
0
5
10
15
20
Average SNR [dB]
25
30
Figure 3.14: The capacity of the multiple satellite system for the ideal (no
mutual coupling or spatial correlation) compact MIMO arrays in figure 3.5.
First we compare the capacity for different ideal (no mutual coupling or
spatial correlation) compact antenna arrays using satellites in scenarios 1 and
2 (figure 3.14) and HAPs in scenarios 5 and 6 (figure 3.15).
The capacity results shown in figure 3.14 are obtained for scenarios 1 and
2 for a system of satellites operating at an altitude of 1200 km and with a
separation angle of 20 degrees, and plotted against the average signal-to-noise
ratio (SNR) of the system. The elevation angle at both the transmitting
and the receiving ground base stations is held at 10 degrees throughout the
investigations.
Figure 3.15, on the other hand, show the results obtained for scenarios 5
and 6 for a system of HAPs operating at an altitude of 20 km and with a
separation angle of 20 degrees, and also plotted against the average signal-tonoise ratio of the system. The elevation angle is held at 10 degrees throughout
this investigations as well.
It is evident from figure 3.14 and 3.15 that the multiple satellite or multiple
HAP diversity system provides superior performance as compared to the
Chapter 3. Space-Time-Polarization Processing for Capacity
74
Enhancement in HAP/Satellite communication systems
8000
Ideal MIMOïCube or ideal MIMOïOctahedron,
12 independent channels and 6 HAPs.
Ideal Vect. elem. ant. or ideal MIMOïTetrahedron,
6 independent channels and 3 HAPs.
Single HAP system (SISO),
2 independent channels.
7000
Capacity C [bps]
6000
5000
4000
3000
2000
1000
0
5
10
15
20
Average SNR [dB]
25
30
Figure 3.15: The capacity of the multiple HAP system for the ideal (no mutual
coupling or spatial correlation) compact MIMO arrays in figure 3.5.
3.5. SIMULATION RESULTS
75
single satellite or single HAP case. It is also apparent that the MIMO-Cube
antenna or MIMO-Octahedron antenna provides a better capacity than both
the MIMO-Tetrahedron and the vector element antenna due to the higher
number of acquired platforms (independent channels). Due to the longer
distance to the satellites compared to the HAPs the capacity is consequently
lower for the satellite system.
For example, let us compare the performance of the multiple platform
systems (using 3 and 6 platforms) together and with that of the single platform
case at an SNR of 20 dB. We can observe that in the multiple satellite system
(figure 3.14) that the capacity of 6 satellites is 107% higher than the single
satellite system and 59% higher than the 3 satellite system, which in turn is
30% higher than the single satellite system. Performing the same comparison
for the multiple HAP system (figure 3.15) yields a capacity of the 6 HAP
system that is 158% higher than the single HAP system and 85% higher than
the 3 HAP system, which in turn is 39% higher than the single HAP system.
Next we investigate the effect of different separation angles between
platforms on the capacity for different compact antenna arrays. The maximum
capacity, calculated in accordance with equation 3.13, is achieved when there is
a spatial-polarization alignment between the modes of the transmitting array
and the receiving array. Since the spatial-polarimetric radiation pattern is
dependent on the geometrical shape of the compact array, the separation angle
where the maximum capacity of the system occurs is also dependent of the
geometry of the array and therefore it differs for the different arrays depicted
in figure 3.5. For example, figure 3.16 show the effect of the separation angles
between platforms on the capacity of the HAP system employing the vector
element antenna array. In order to simplify the comparison and show the effect
of the separation angle on the performance, we plot the capacity for a fixed
SNR of 20 dB for various separation angles (ranging from 0 to 120 degrees in
steps of 5 degrees) as shown in figure 3.17. It is clear from this figure that the
separation angle between HAPs has a great impact on the system capacity.
It is also evident that the optimal separation angle that maximizes the total
capacity of the system for an SNR of 20 dB is found to be 20 degrees for the
simulated HAP system employing the vector element antenna.
Performing similar simulations for the other compact MIMO array configurations (MIMO-Tetrahedron, MIMO-Octahedron and the MIMO-Cube)
yield the results shown in figure 3.18 for a fixed SNR of 20 dB and multiple
HAPs system (employing 3 or 6 HAPs). From this figure, it is clear that
the MIMO-Cube and the vector element antenna array have their maximum
capacity at separation angles of 15 and 20 degrees, respectively, while both the
Chapter 3. Space-Time-Polarization Processing for Capacity
76
Enhancement in HAP/Satellite communication systems
4000
20°
30°
10°
40°
50°
60°
70°
80°
90°
100°
110°
3500
Capacity C [bps]
3000
2500
2000
1500
1000
500
0
5
10
15
20
Average SNR [dB]
25
30
Figure 3.16: The capacity of the HAP system for various separation angles
using the ideal vector element antenna array.
MIMO- Tetrahedorn and MIMO-Octahedron have their maximum capacity
at 10 degrees. The agreement in optimal separation angle in the MIMOTetrahedorn and MIMO-Octahedron arrays is due to the similar geometry of
the arrays, since the MIMO-Octahedron can be seen as two co-located MIMOTetrahedron arrays. It is also clear from figure 3.18 that both the vector
element antenna and the MIMO-Cube array are more robust in situations
where the platforms are widely spread, and that the MIMO-Tetrahedron and
MIMO-Octahedron arrays have better performance in situations where the
platforms are positioned close together. We can also observe in figure 3.18
that if the separation angle tends toward 0 degrees the spatial diversity will
collapse into a SISO (single platform system). Similar observations were noted
for the multiple satellite system.
Next, we show the effects of mutual coupling and spatial-polarization
correlation (both calculated by the Finite Element Method) on the capacity
of the system, and the results are plotted in figures 3.19 and 3.20 for various
compact antennas of the multiple satellite system. It is evident from these
figures that although the capacity is degraded by correlation and mutual
coupling, we still achieve significant gain compared to the single antenna case.
77
3.5. SIMULATION RESULTS
2900
2800
Capacity C [bps]
2700
2600
2500
2400
2300
2200
2100
2000
0
20
40
60
80
100
Separation angle between HAPs e [degrees]
120
Figure 3.17: The capacity for different separation angles using the ideal vector
element antenna array at an SNR of 20 dB.
Chapter 3. Space-Time-Polarization Processing for Capacity
78
Enhancement in HAP/Satellite communication systems
Vector elem. ant.
3 HAPs
MIMOïCube ant.
6 HAPs
MIMOïTetrahedron ant.
3 HAPs
MIMOïOctahedron ant.
6 HAPs
6000
5500
5000
Capacity C [bps]
4500
4000
3500
3000
2500
2000
1500
0
10
20
30
40
Separation angle e [degrees]
50
60
Figure 3.18: The capacity of the multiple HAP system for different separation
angles using the ideal compact antenna arrays in figure 3.5, at an SNR of
20 dB.
3.5. SIMULATION RESULTS
79
For example, if we compare the performance in figure 3.19 for an average SNR
of 20 dB, we get a 108% higher capacity from the ideal MIMO-Cube antenna
than from the ideal MIMO-Tetrahedron antenna, and a 225% higher capacity
compared with the non-diversity single HAP system. If we take into account
the correlation and the mutual coupling the MIMO-Cube antenna still has a
106% higher capacity than the MIMO-Tetrahedron antenna and a 172% higher
capacity than the ideal non-diversity single HAP system. Similar observations
were noted for the multiple HAP system.
So far, the investigations have been performed with ideal free space loss
(FSL) channel model. In scenarios 3, 4, 7 and 8 we use the proposed spacetime-polarization (STP) channel model simulator described in section 3.1.1
to analyze the atmospheric propagation effects on the performance of the
multiple platform diversity systems. In the following simulations we set up
a multi channel model dominated by LOS components and with weak NLOS
components, with a Rice factor of 10, which corresponds to a rural type of
environment.
For scenarios 3 and 4, the satellites are randomly positioned according
to a uniform distribution at altitudes between 1200 and 1500 km and within
an angular sector from -60 to +60 degrees. The satellites are moving with a
speed of 500 m/s, and the ground stations are stationary. Since this system
is using linear polarization the Faraday rotation effect of the ionosphere will
have a devastating effect on the polarization de-correlation of the modes if
the carrier frequency is below 2 GHz (see chapter 3.4). This could result
in total loss of the signal being transmitted. Therefore, a carrier frequency
of 10 GHz has been chosen to avoid excessive Faraday rotation. Selecting a
10 GHz carrier frequency then results in a system that is mainly affected by
tropospheric effects (see chapter 3.4).
Figure 3.21 show the impact on the capacity for different cross-polar
discrimination (XPD) values. An XPD = ∞ represents a channel with no
depolarization effects and is comparable to scenarios 1 and 2. With moderate
precipitation in the troposphere we have an XPD value of 26 dB (calculated
according to equation 3.29) which, for example, results in a 23% drop in
capacity for an average SNR of 20 dB. With a worse precipitation value
(XPD = 16 dB), would result in a 54% drop in capacity. From these results,
We can see that precipitation in the troposphere can cause severe degradation
in system performance due to the loss of several communication sub channels.
At an XPD of 0 dB, we have a total loss of the signal.
The corresponding multiple HAP system in scenarios 7 and 8 are setup
with a uniform random positioning of the HAPs at altitudes between 17 and
Chapter 3. Space-Time-Polarization Processing for Capacity
80
Enhancement in HAP/Satellite communication systems
5000
Ideal Vect.elem.ant.
Vect.elem.ant. with
mutual coupling.
Vect.elem.ant. with mutual
coupling and spatial correlation.
Ideal single satellite system.
4500
4000
Capacity C [bps]
3500
3000
2500
2000
1500
1000
500
0
5
10
15
20
Avergae SNR [dB]
25
30
25
30
8000
Ideal MIMOïCube ant.
MIMOïCube with mutual coupling.
MIMOïCube with mutual
coupling and spatial correlation.
Ideal single satellite system.
7000
Capacity C [bps]
6000
5000
4000
3000
2000
1000
0
5
10
15
20
Average SNR [dB]
Figure 3.19: The effect imposed on capacity by mutual coupling between the
array elements and by spatial-polarization correlation of the radiation patterns
of the array for: (top figure) the vector element antenna array and (bottom
figure) MIMO-Cube antenna array. The single antenna system is added in
the graph for comparison purposes.
81
3.5. SIMULATION RESULTS
5000
Ideal MIMOïTetrahedron.
MIMOïTetrahedron with mutual coupling.
MIMOïTetrahedron with mutual coupling and spatial correlation.
Ideal single satellite system
4500
4000
Capacity C [bps]
3500
3000
2500
2000
1500
1000
500
0
5
10
15
20
Average SNR [dB]
25
30
25
30
8000
Ideal MIMOïOctahedron.
MIMOïOctahedron with mutual coupling.
7000
MIMOïOctahedron with mutual coupling
and spatial correlation.
Ideal single satellite system.
6000
Capacity C [bps]
5000
4000
3000
2000
1000
0
5
10
15
20
Avergae SNR [dB]
Figure 3.20: The effect imposed on capacity by mutual coupling between
the array elements and by spatial-polarization correlation of the radiation
patterns of the array for: (top figure) the MIMO-Tetrahedron antenna array
and (bottom figure) MIMO-Octahedron antenna array. The single antenna
system is added in the graph for comparison purposes.
Chapter 3. Space-Time-Polarization Processing for Capacity
82
Enhancement in HAP/Satellite communication systems
8000
MIMOïCube with mutual coupling
and spatial corr. , XPD = '
MIMOïCube with mutual coupling
and spatial corr., XPD = 26 dB
MIMOïCube with mutual coupling
and spatial corr., XPD = 16 dB.
Single satellite system
7000
Capacity C [bps]
6000
5000
4000
3000
2000
1000
0
5
10
15
20
Average SNR [dB]
25
30
Figure 3.21: The effect of depolarization on the MIMO-Cube satellite diversity
system compared to the ideal vector element antenna array and ideal single
satellite system.
83
3.5. SIMULATION RESULTS
8000
MIMOïCube with mutual coupling
and spatial corr. , XPD = '
MIMOïCube with mutual coupling
and spatial corr. , XPD = 20 dB
MIMOïCube with mutual coupling
and spatial corr., XPD = 10 dB
Ideal Vect. elem. ant. with
3 HAPs
Single HAP system
7000
Capacity C [bps]
6000
5000
4000
3000
2000
1000
0
5
10
15
20
Average SNR [dB]
25
30
Figure 3.22: The effect of depolarization on the MIMO-Cube HAP diversity
system compared to the ideal vector element antenna array and ideal single
HAP system.
22 km and within an angular sector from -60 to +60 degrees. Performing
a similar simulation for a multiple HAP system, we set up a multi channel
model dominated by LOS components and with weak NLOS components,
with a Rice factor of 10, which corresponds to a rural type of environment.
Since HAPs are positioned in the stratosphere below the ionospheric layers
there is no Faraday rotation effect. Therefore, a lower carrier frequency of
2.5 GHz has been chosen since the results are only affected by tropospheric
effects (see chapter 3.4).
Figure 3.21 show the impact on the capacity for various XPD values.
As in the satellite scenario, an XPD = ∞ represents a channel with no
depolarization effects and is comparable to scenarios 5 and 6. For example,
with a fairly-harsh precipitation in the troposphere (XPD = 20 dB) would
results in a 30% drop in capacity for an average SNR of 20 dB. With a worse
precipitation (XPD 10 dB), would result in a 59% drop in capacity. Thus, it is
clear that precipitation in the troposphere can also cause severe degradation
in system performance due to the loss of several communication sub channels.
In extreme cases, e.g. XPD of 0 dB, will yield a total loss of the signal.
Chapter 3. Space-Time-Polarization Processing for Capacity
84
3.6
Enhancement in HAP/Satellite communication systems
Conclusions
In this chapter we have investigated the capacity enhancement resulting from
the use of different compact MIMO antenna arrays in a multiple HAP or
multiple satellite in order to enhance the capacity in these systems. Simulation
results show that the multiple platform diversity systems utilizing compact
MIMO antenna arrays outperform that of a single platform system. It was
also shown that the MIMO-Cube and MIMO-Octahedron antenna arrays are
superior to the MIMO-Tetrahedron antenna array and the vector element
antenna since they have twice the number of independent channels which will
result in a higher capacity.
Further, a small degradation in capacity is resulted due to the effects of
spatial correlation and mutual coupling between the separate antenna array
elements of the compact antenna arrays. We have also shown the effects of the
separation angle between platforms on system performance, and determined
the optimal separation angle that maximizes the total capacity of the system.
It has also been shown that MIMO-Cube and vector element antenna arrays
are preferred when the platforms are widely separated (> 15 degrees) and that
the novel MIMO-Octahedron and MIMO-Tetrahedron are preferred when the
platforms are closely positioned (< 15 degrees).
We have also presented a novel multi-channel simulator that is taking
into account the temporal, spatial and polarization properties affecting the
signals. In addition, we have also determined the impact on the total capacity
of the proposed platform diversity system. Simulation results have shown
that the depolarization will have a severe impact on the performance. Since
the compact MIMO-antenna arrays used here only utilizes linear polarization
it will experience a devastating depolarization at frequencies lower than 2
GHz, due to Faraday rotation. At frequencies above 10 GHz the Faraday
rotation will be negligible, but there is still degradation in performance due
to depolarizing precipitation.
CHAPTER 4
SPACE-TIME PROCESSING FOR QUALITY
IMPROVEMENT OF SHORT RANGE
WIRELESS COMMUNICATION LINKS
O
ver the last decade the world has witnessed explosive growth in the
use of wireless mobile communications. Looking around we find users
with mobile phones, wireless PDAs, pagers, MP3 players, and wireless
headphones to connect to these devices - a small testament of the impact
of wireless communications on our daily lives. In addition the burst of new
technologies such as Bluetooth and other short-range wireless communications
are encouraging the further development of a wide variety of distributed
wireless devices [40].
Bluetooth is one of those short range wireless communication technology
systems which aims at replacing many proprietary cables that connect one
device with another with one universal short-range radio link. Recently, many
mobile devices (e.g., mobile phones, PDAs, computer mice) with integrated
Bluetooth modules have been introduced. Their wireless technology is used
to transfer any kind of data onto these devices. Bluetooth devices operate
in the industrial, scientific and medical (ISM) band at 2.4 GHz, and use 79
channels each occupying 1 MHz. The reader is refereed to [41–43] for further
information about this technology.
Propagation of radio waves inside buildings is a very complicated issue,
and it depends significantly on the indoor environment (home, office, factory)
and the topography (LOS: line of sight and NLOS: non-line of sight). The
Chapter 4. Space-Time Processing for Quality Improvement
86
of Short Range Wireless Communication Links
statistics of the indoor channel varies with time due to movements of people
and equipment [45]. A survey of indoor propagation measurement and models
can be found in [44], and electromagnetic propagation effects in [47]. There
are limited investigations in the open literature on the measurements and
simulations of multipath wave propagation effects on the performance of live
Bluetooth links.
In this chapter we present measurement campaigns (signal power, bit
error rate and data rate) in indoor office building for LOS and NLOS
propagation scenarios and access their effects on the Bluetooth link. These
measurements were carried out using various antennas (omni-directional and
directive antennas), and we will present comparative analysis to access the
potential improvement in system performance gained from the use of directive
antennas. We will also show the effect of antenna parameters (gain and
efficiency) on the results and the overall impact on the quality and coverage
of the Bluetooth link. In addition, in this chapter we will also assess
the fading phenomenon by FEM simulation modelling (carried out in the
software package COMSOL Multiphysics) [48] of LOS and NLOS propagation
scenarios, and use the measurement results and theoretical analysis [49, 50]
to confirm our findings. A simple path loss model is derived for the indoor
environment and the simulations are also used for assessing the impact on
propagation when doors are opened or closed.
The spatial properties of wireless communication channels are extremely
important in determining the performance of the systems. Thus, there
has been great interest in employing space-time signal processing schemes
since they can offer a broad range of ways to improve wireless systems
performance. For instance, techniques such as Single-Input Multiple-Output
(SIMO) and Multiple-Input Multiple-Output (MIMO) can enhance link
quality through diversity gain or increase the potential data rate or capacity
through multiplexing gain. In the final part of this chapter, we apply these
techniques to a Bluetooth system operating over a fading radio channel in a
NLOS propagation environment and assess their impact on performance via
simulations [51–53].
The organization of this chapter is as follows. In section 4.1 we provide a
brief description of the building in the tested indoor office environment and
the various types of antennas used in the measurement trials and their related
parameters. In section 4.2 we present the results of these measurements. The
FEM simulations of the tested environment and the application of space-time
processing is featured in section 4.3. Finally, section 4.4 concludes the chapter.
4.1. THE TESTED INDOOR OFFICE ENVIRONMENT
4.1
87
The Tested Indoor Office Environment
The measurement trials were performed indoors in typical office environments.
In this section we will describe the building structure and material where
the measurements took place and later in the results section we show the
sensitivity of the Bluetooth link, employing different antenna types, in these
indoor environments. Figure 4.1 shows a typical example of office environment
which is quite common all over the world. The dimensions of the hallway of
the building in this figure are (45 x 1.85 x 2.30) meters. Most doors are
mainly made of wood except of the two outer doors, one at each end of the
hallway, which are made of metal. The inner walls in the hallway consist of
a large single pane window in a wooden frame. The walls between the rooms
consist of two plasterboards supported by two vertical steel crossbars and
the plasterboards are nailed to vertical wooden crossbars that are situated
at regular intervals inside the wall. Mostly all the furniture in the office
are made of wood and plastic. The outer walls of the building are made of
concrete isolated with thermal material and dual pane windows surrounded
by wooden/metal frames.
4.1.1
The Used Antennas
The antenna is the interface between the transmitter and the receiver and the
propagation medium, and it therefore is a deciding factor in the performance
of a radio communication system. To improve and develop the design of
Bluetooth antenna, the Bluetooth Special Interest Group (SIG) has left the
antenna part as an open door for the antenna manufacturers. In the past few
years, the designs of Bluetooth antennas have been developed significantly and
since then many companies have entered the Bluetooth antenna market and
others had already left it. The Bluetooth radio module has to be connected
to an antenna to transport the electromagnetic energy from the radio module
to the antenna (transmitter), or from the antenna to the radio module
(receiver). In addition, there are three important parameters concerning both
the propagation of electromagnetic waves and the definition of the coverage
of the wireless devices. These parameters are the receiver sensitivity, output
power and antenna gain.
The radiation pattern of an antenna could be omnidirectional (a circular
pattern with the same radiation in every direction in one plane) or directional.
Therefore the radiation pattern in a particular direction determines if the
antenna has a directive gain or not. Fixed network devices such as LAN
Chapter 4. Space-Time Processing for Quality Improvement
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of Short Range Wireless Communication Links
Figure 4.1: Description of the indoor office environment used in the
measurement scenarios for: NLOS (top figure) and LOS (bottom figure).
4.1. THE TESTED INDOOR OFFICE ENVIRONMENT
89
Access Points (LAP) could use antennas that are directed as they are installed.
Conversely, mobile devices such as cellular phones, laptops, cameras, etc. need
to transmit and receive at any direction and angel. As a consequence, in the
choice of an antenna for a product, its position as well as its parameters (gain,
efficiency and radiation pattern) should be taken into account and investigated
properly.
In this chapter, both omnidirectional and directive antenna types have
been used and tested. The range of the Bluetooth antenna is much different
in practical measurements than the theoretically anticipated range especially
in an office environment; this observation will be also revealed in the
measurement results section. The popular antenna types for Bluetooth devices
are the external dipole, microstrip and planar inverted-F antenna (PIFA).
In this chapter the Bluetooth Application Tool Kit has been used in the
measurements as we have mentioned above. In order to connect and measure
with different antennas by using the Bluetooth Application Tool Kit module
which has an originally microstrip PIFA antenna printed on a Printed Circuit
Board (PCB) board, a cable with SMA connector has been connected to a
feeding point with impedance of 50 Ω as a requirement for each Bluetooth
antenna when it would be mounted on the board. The different antenna
types used in these test are presented below; the operational frequency range
for all antennas is 2.4-2.5 GHz and their nominal feeding impedance is 50 Ω.
It is worth mentioning at this point that generic names have been given to
the different antennas used in these measurements rather than their specific
names. The various tested antennas and their radiation patterns are presented
in the appendix. The PIFA antenna used in the Master Bluetooth device has
two galvanic contacts, one to the earth and the other as a feeding point with
impedance of 50 Ω. The structure of the PIFA antenna is optimized for small
size requirements, large bandwidth and efficient gain. The size of the PIFA
antenna is (25 × 7) mm.
The Half Wave Model 1 antenna (Appendix figure B.1) relies on a
reflection formed wave between the active element and a conductive plane.
It is a big directional antenna. The gain value of this antenna is 9.2 dBi
and its efficiency is 95%. Because of its large size, this antenna can be
used as an external antenna for some applications like a printer server and
measuring instruments. The return loss, which has been measured with a
network analyzer, is 14.4 dB.
The Half Wave Model 2 antenna (Appendix figure B.2) is an external
antenna which was supplied with an adjustable radiator angle. This antenna
could take different positions (vertical, horizontal, etc.). The Half Wave Model
Chapter 4. Space-Time Processing for Quality Improvement
90
of Short Range Wireless Communication Links
2 antenna is characterized by a radiation pattern which is almost the same
at all directions (omnidirectional). The gain value of this antenna is 1.6 dBi,
the efficiency is 75% and the return loss is 15 dB.
The Quart Wave Model 1 antenna (Appendix figure B.5) has a small size
of (18.2 × 3.9 × 1.6) mm, and it has surface-mounted embedded antenna. It
can be integrated into PC cards, mobile phones, access points and Bluetooth
enabled devices. It is a linearly polarized antenna with a peak gain of 2 dBi.
The Quart Wave Model 2 antenna (Appendix figure B.4) is also small in
size (21 × 4 × 3) mm and can be used as an embedded antenna for Bluetooth
enabled devices. The gain value of this antenna is 4.1 dBi, its efficiency value
is 68% and the return loss is 10.784 dB. The radiation pattern of the Quart
Wave Model 2 antenna is not omnidirectional.
The Half Wave Model 3 antenna (Appendix figure B.3) has relatively small
size (27 × 8 × 3) mm and can be used both as an embedded antenna and
an external antenna for Bluetooth enabled devices. The radiation pattern
of this antenna indicates that the Half Wave Model 3 antenna is not an
omnidirectional antenna. The gain value of this antenna is 4.0 dBi, its
efficiency is 62% and the return loss is 13.46 dB.
4.1.2
The Measurements Setup
Measurement campaigns were conducted so that we can get an understanding
of how the signal power, BER and the data rate are affected by NLOS and LOS
propagation scenarios for the different Bluetooth antennas that have been used
in the indoor office environment. The antennas used in these measurement
trials and their parameters have been described in the previous section.
One room (back room marked with a dot) and part of the hallway were
used in the measurements to provide NLOS and LOS scenarios between the
two Bluetooth devices/antennas, respectively, as shown in figure 4.1. A PC
is connected to a Bluetooth device with PIFA antenna, have been used as a
stationary Bluetooth device (Master). Another PC with a Bluetooth device
(Slave), was rolled along the hallway in 1 m interval following the dotted line
in figure 4.1. The various used antennas, which are described in the previous
section, were replaced alternately on the Slave side. In this chapter, the
Receiver Signal Strength Indicator (RSSI) is used in the measurements; this
term and signal power has been used interchangeably here. The Bluetooth
RSSI measurement compares the received signal power with two threshold
levels, which define the Golden Receive Power Range [41]. Note that all the
results for signal power measurements were registered after measuring it 10
4.2. RESULTS OF THE MEASUREMENTS
91
times to ensure that a stable signal is being measured. For the fast fading dip
identification, the measured return value of RSSI was flickering (or hopping)
from 0 dB to -20 dB and back again to 0 dB and so on (i.e., a stable result
couldn’t be measured).
Note that the door in the back room, where the master was placed for
NLOS scenario, was open and other doors in the hallway were also open during
the measurements. In addition, people in the office were allowed to move
freely during the measurements, and the results of these measurements were
registered after a successful data transmission. For the NLOS measurement
scenario all the measurements have been started at the range of 3 meters (see
figure 4.1) in order to avoid the direct LOS path.
4.2
Results of the Measurements
Antennas that are able to direct the transmitted and received signals’
energy are of great interest for future wireless communication systems.
The directivity implies reduced transmit power and interference and hence
potential for increased capacity, quality and range. In this section we present
the measurement trails using different directive antennas and compare with
isotropic antenna for NLOS and LOS propagation scenarios described in the
previous section. The results of tree types of measurement trails (signal power,
bit error rate and data rate) will be presented in this section.
The RSSI or signal power measurement results are shown in figure 4.2.
It is evident from this figure that a significant reduction in signal power
is achieved with the gradual increase of both the distance and the number
of the obstacles between the Master and the Slave along the dotted line in
figure 4.1. Increasing the distance ever further will ultimately produce a break
in transmission; that is a disconnection between the radio modules at different
distances depending on the parameters (gain and efficiency) of the different
used antennas and the propagation scenario. This is the reason why the Half
Wave Model 1 antenna (9.2 dBi, 95%) has the highest signal power and best
range (19 meters) while the Half Wave Model 3 antenna (4 dBi, 62%) has the
lowest signal power and range (9 meters). The results of the other antennas
are intermediate between the results of the above two mentioned antennas.
Note that a successful data transmission was impossible after the coverage
range of each antenna shown in figure 4.2. The most important distance in
this scenario is at 10 meters which is the anticipated range of the Bluetooth
class 3 modules used in these measurements.
Chapter 4. Space-Time Processing for Quality Improvement
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of Short Range Wireless Communication Links
An interesting observation in NLOS scenario is the reception of stable (or
constant) signal power level (in some distances for all the used antennas) in
spite of increasing the distance between the Master and the Slave. This can
be clearly seen from the RSSI results in figure 4.2 for example at the distance
from 9-12 meters, and will be verified to a certain extent by the FEM model
although in the simulation we can observe some fluctuations.
An important observation that can be made from figure 4.2 regarding LOS
scenario is that the signal still exists in the hallway much farther beyond the
operating range of 10 meters (see for example Half Wave Model 1 ). This
phenomenon could be explained by the tunnelling effect where the hallway
acts as a waveguide to the reflected radio waves from the walls along the
hallway. Hence the increased coverage ranges as compared to NLOS scenario.
In figure 4.3 we show the results of BER measurements for the different
antennas. BER is defined as the number of errors in the system that occurs
within a given sequence of bits. For example, a BER of 10−4 means that
in average one bit out of 10000 bits is corrupted. Generally, the BER
becomes higher by increasing the distance between the transmitter and the
receiver, and by increasing the number of obstacles in the communications
path. However, the effect of fast fading on the measurement results is evident
from the rapid fluctuation of the measured BER values for all antennas as
shown in figure 4.3. Again, the Half Wave Model 1 antenna provided the best
results (lowest BER values) among the other used antennas, which is clearly
related to its high gain and efficiency parameters.
For NLOS scenario in figure 4.3a, the highest BER value of 1.964% was
obtained by the Half Wave Model 3 antenna at a distance of 12 m, while
the lowest BER value of 0.378% (at the same distance) was obtained by the
Half Wave Model 1 antenna, see figurefig:BER. The BER results of the other
antennas were in between the above mentioned values. On the other hand,
for LOS scenario in figure 4.3b, the results of BER measurements show a
minimum value of 0.0% (no errors) and a maximum value of 0.905%, see
figure 4.3. In other words, the BER is lower in LOS as compared to NLOS
scenario as expected. Again, the Half Wave Model 1 antenna has the best
results (lowest BER values) among the other used antennas, which is clearly
related to its high gain and efficiency parameters.
Finally, the results of the data rate measurements are plotted in figure 4.4.
From these plots we notice only a very slight reduction of the Bluetooth link
data rates with increasing the distance. The data rate results are also in
agreement with the pattern of the BER results in figure 4.3; that is the higher
the BER value, the lower data rate that can be achieved and vice versa. This
4.2. RESULTS OF THE MEASUREMENTS
93
Figure 4.2: The signal power measurements results for: NLOS (top figure) and
LOS (bottom figure). The RSSI generally drops with increasing the distance
between the Master and the Slave.
Chapter 4. Space-Time Processing for Quality Improvement
94
of Short Range Wireless Communication Links
Figure 4.3: The BER measurement results for: NLOS (top figure) and LOS
(bottom figure). The BER increases with distance and the rapid fluctuations
are due to fast fading.
4.3. FEM SIMULATIONS
95
can be clearly seen in the distance of 12 m for NLOS scenario, where the
highest data rate value of about 172.2 kbps, see figure 4.4 was obtained by
the Half Wave Model 1 antenna and the lowest data rate value of 169.4 kbps,
see figure 4.4 was obtained by the Half Wave Model 3 antenna. The results
of the Quart Wave Model 2, Quart Wave Model 1 and Half Wave Model 3
antennas has followed a similar pattern by giving intermediate data rate values
as was the case for RSSI and BER scenarios. A similar pattern of results (not
shown) were obtained from LOS scenario.
Figure 4.4: The data rate measurement results for NLOS. Only a slight drop
in data rates is obtained with increasing distance between the transmitter and
receiver.
4.3
4.3.1
FEM Simulations
The Simulated Indoor Model
The simulation of the radio waves is done using the Finite Element Method
(FEM) which is numerically solving Maxwell’s field equations for the electromagnetic field. Here we are using the software package COMSOL Multiphysics
Chapter 4. Space-Time Processing for Quality Improvement
96
of Short Range Wireless Communication Links
for the finite element calculations. In a macroscopic environment we can write
Maxwell’s field equations as:
= − ∂B
∇×E
∂t
= J + ∂ D
∇×H
∂t
ρ
∇·D =
ε
=0
∇·B
(4.1)
Fourier transforming these equations and solving for either the electric E
field or the magnetic H field we obtain the time-harmonic Helmholtz equation:
(here is shown the solution of the electric field E)
= jωµJ
+ ω 2 εµE
∇2 E
(4.2)
For simplicity, the vector arguments (r, ω) and the term e j ωt are omitted here
and for the remainder of this chapter.
The field in our model is source-free everywhere except inside the
transmitting antenna element where we have the current Iz from the
transmitter with an even distribution over the cross-section area Aant of the
r, ω):
antenna element giving the current density J(
⎧
⎨ ẑ · Iz (r, ω) , inside the antenna element
Aant
(4.3)
J(r, ω)
⎩
0, elsewhere
Assuming that the model does not contain any material with magnetic
properties we can describe the electric properties of the different materials as
a complex valued dielectric parameter εc defined as:
σ
(4.4)
εc = ε r − j
ωε0
where εr is the relative permittivity and σ is the conductivity of the material
for a specific angular frequency ω. In table 4.1 is shown the different materials
with corresponding permittivity and conductivity used in our model [48]. In
this model we assume that these parameters are independent of time.
4.3. FEM SIMULATIONS
Material
Glass
Plaster board
Brick
97
Table 4.1: Material properties.
Dielectric constant εr Conductivity σ [mS/m]
4.2
1 · 10−11
2.27
0.18
4.44
1
The full 3D model of the office environment, used in the simulations, is
shown in figure 4.5 and in figure 4.6 the 2D projection of this partial building
can be viewed and compared to the real floor plan of the office building shown
in figure 4.1.
Figure 4.5: The simplified office model obtained from transferring the real
floor plan in figure 4.1 into a CAD (Computer Aided Design) program.
4.3.2
FEM Simulation Results
In this section we present the FEM simulations of the indoor office environment. The simulations were performed at the frequency 2.402 GHz. The
simulations are divided into four cases which differ in the position of the
transmitting antenna and whether or not the doors along the hallway are
opened or closed. The antenna is either placed in the corridor or in the
top right office room as shown in figure 4.1. In order to obtain a complete
comparison between the FEM simulation results and the measurements data,
we have divided the simulations into a line of sight (LOS) environment
(figure 4.7) and a non line of sight (NLOS) environment (figure 4.8). The
Chapter 4. Space-Time Processing for Quality Improvement
98
of Short Range Wireless Communication Links
Figure 4.6: The 2D projection of the model in figure 4.5.
collection of data from the simulated model has been done along the same
path that the real measurements (figure 4.1) were done. These paths can be
seen in figures 4.1, 4.7 and 4.8 marked by dashed arrows. In figures 4.7 and 4.8
the simulation results are shown as the two dimensional power distribution
of the transmitted signal.
" calculated as the time averaged magnitude
" This is
"
"
of the Poynting vector "S (r, ω)", where r = (x, y, z). The rapid change in
power over a very short distance in space is caused by superposition of the
reflected, diffracted, refracted and scattered components of the wave with
itself. This power level variation is shown by the two dimensional fading
pattern in figures 4.7 and 4.8, for LOS and NLOS propagation scenarios,
respectively. These figures clearly illustrate the tunneling effect phenomenon
along the hallway and give an indication about the range of operation. In
addition, the figures also confirm the predominance of the tunneling effect
and the extended range in LOS as compared to NLOS propagation scenario.
These observations are in agreement with the measurement results presented
in the previous section.
If we collect signal power data (by measurements or simulations) along the
path indicated by the arrows in figures 4.7 and 4.8 we obtain an average signal
power or received signal strength indicator (RSSI) as shown in figures 4.10
and 4.9 for NLOS and LOS, respectively. Since the FEM simulations were
done assuming an omnidirectional antenna, the power profile should be
4.3. FEM SIMULATIONS
99
Figure 4.7: FEM simulations showing the two dimensional power distribution
inside the office environment for a LOS scenario with all the doors along the
hallway closed (top figure) or opened (bottom figure). The transmitter is
positioned at the coordinate (x=5m; y=2m).
Chapter 4. Space-Time Processing for Quality Improvement
100
of Short Range Wireless Communication Links
Figure 4.8: FEM simulations showing the two dimensional power distribution
inside the office environment for a NLOS scenario with all the doors along
the hallway closed (top figure) or opened (bottom figure). The transmitter is
positioned at the coordinate (x=7.5m; y=26.5m).
4.3. FEM SIMULATIONS
101
compared with measurement results using an omnidirectional antenna as
presented in figures 4.9 and 4.10. It is evident from these figures that the
real measurements and simulation results show reasonable agreement for both
propagation scenarios.
Since the simulated model is experimentally confirmed, and this is a weakstationary problem with a narrow band time-harmonic signal, it is in this case
sufficient to describe the channel parameters as a Ntx × Nrx complex-valued
matrix H
⎤
⎡
H12
···
H1Nrx
H11
⎢ H21
H22
H2Nrx ⎥
⎥
⎢
⎥
⎢
.
..
⎥
H
H
H
H=⎢
(4.5)
31
32
3Nrx
⎥
⎢
⎥
⎢
..
..
..
⎦
⎣
.
.
.
HNtx 1 HNtx 2 · · · HNtx N rx
These complex-valued numbers Hij describe the amplitude and phase
due to the distance between the different combinations of transmitting and
receiving antennas.
In order to validate the results presented above we compare these results
with the theoretical statistics of the signal as shown in figure 4.11. It can
be seen that the probability distribution (density function) of the signal in
the NLOS scenario is close to a Rayleigh distribution (top plot in figure 4.11)
which is to be expected in a NLOS environment. On the other hand, we obtain
a Rice probability distribution (bottom plot in figure 4.11) with a Rice-factor
K ≈ 1.4 for LOS scenario.
By inspecting figures 4.9 and 4.10 and observing the changes in the signal
strength, we can assess the impact on propagation when the doors along
the hallway are either opened or closed. An interesting observation from
these simulations is that we have a change in power levels when the doors of
the offices are opened compared to when they are closed; this observation of
”door state” is also confirmed by real measurements done in [54]. This effect
however, does not seem to be as prominent in the NLOS scenario since the
signal strength is only less affected by the status of the doors.
To model the NLOS path loss of the office environment, we sample
the simulated received signal strength along paths leading away from the
transmitting antenna. The NLOS paths (a, b and c) that have been analyzed
are shown in figure 4.12.
A power-distance law [55] is developed using a regression model fitted to
the sampled data from the simulation (see figure 4.13). The path loss exponent
Chapter 4. Space-Time Processing for Quality Improvement
102
of Short Range Wireless Communication Links
4
Simulated RSSI (Doors opened)
Simulated RSSI (Doors closed)
Measured RSSI (Doors opened)
2
0
Average power [dB]
ï2
ï4
ï6
ï8
ï10
ï12
ï14
ï16
0
5
10
15
Distance [m]
20
25
Figure 4.9: Power profile for LOS scenario using: measurement data for an
omnidirectional antenna and simulated data when doors along the hallway
are opened or closed.
103
4.3. FEM SIMULATIONS
0
Simulated RSSI (Doors opened)
Simulated RSSI (Doors closed)
Measured RSSI (Doors opened)
ï2
Average power [dB]
ï4
ï6
ï8
ï10
ï12
ï14
ï16
0
2
4
6
8
Distance [m]
10
12
14
Figure 4.10: Power profile for NLOS scenario using: measurement data for
an omnidirectional antenna and simulated data when doors along the hallway
are opened or closed.
Chapter 4. Space-Time Processing for Quality Improvement
104
of Short Range Wireless Communication Links
Distribution of signal
simulated NLOS data
theoretical Rayleigh distribution
0.6
Probability
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
Signal strength
5
6
7
Distrbution of signal
simulated LOS data
theoretical Rice distribution
0.45
0.4
Probability
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1
2
3
4
Signal strength
5
6
7
Figure 4.11: (top plot) The probability distribution of the simulated NLOS
data and the theoretical Rayleigh distribution, and (bottom plot) the
probability distribution of the simulated LOS data and the theoretical Rice
distribution with a Rice factor of approximately 1.4.
4.3. FEM SIMULATIONS
105
a
b
c
Figure 4.12: NLOS propagation scenario where the arrows show the three
analyzed paths: a) path going through the upper office walls, b) path along
the corridor, and c) path going through the lower office walls.
β is estimated using the least squares method. The model is described as
the logarithmic loss L(d) at the distance d from the transmitting antenna
according to
(4.6)
L(d) = L(d0 ) − 10β log10 (d)
where d0 is a distance of reference. The path loss exponent β is then compared
between different scenarios to discern the behaviour of the propagating field
in different indoor environments. As a reference, β = 2, represents the wellknown free space exponent value. By taking the mean value of 100 estimated
values of β simulated along the corridor (see figure 4.12) we find β ≈ 1.71
with a standard deviation of σ ≈ 0.05 which is due to the tunneling effect of
the corridor. For the path following the upper arrow in figure 4.12, the same
analysis yields β ≈ 4.43 with a standard deviation of σ ≈ 0.02 and for the
lower path we have β ≈ 3.14 with a standard deviation of σ ≈ 0.02. These
estimates of the path loss exponent β are consistent with findings chaptered
in the literature [39, 55].
Next, we investigate the improvement in system performance resulting
from diversity gain and multiplexing gain in NLOS scenarios of a system
employing multiple transmit/receive antennas with different combining techniques. The simulations of the single-input multiple-output (SIMO) and
Chapter 4. Space-Time Processing for Quality Improvement
106
of Short Range Wireless Communication Links
ï95
Simulated data
Regression model
ï100
Received Power [dBW]
ï105
ï110
ï115
ï120
ï125
ï130
ï135
0
5
10
15
20
Distance from the transmitter [m]
25
Figure 4.13: An example of a regression model (red) fitted to the sampled
data from the simulations (blue).
107
4.3. FEM SIMULATIONS
multiple-input multiple-output (MIMO) system were done along the same
paths of the indoor office building shown in figure 4.12 and at a high signal
to noise ratio (SNR) of 50 dB in order to get a fair comparison.
Multiple-antenna channels provide spatial diversity, which can be used
to improve the reliability of the link. The basic idea is to supply to the
receiver multiple independently faded replicas of the same information symbol,
so that the probability of all signal components fading simultaneously is
reduced. To illustrate this point for a SIMO system, we show in figure 4.14
the simulated received signal power from five receiver antennas separated by
half a wavelength. These five received signals are combined to give an overall
improvement of the system by taking advantage of the diversity gain achieved
through multiple receiving antennas, as shown in figure 4.15. This figure
shows the diversity gain for a SIMO system (employing 1 transmitting antenna
and 5 receiving antennas) for three different types of combining methods:
Selection Combining (SC), Equal Gain Combining (EGC) and Maximum
Ratio Combining (MRC) [52, 53]. Compared with the single antenna system
we can see that SC will give around 1-2 dB gain, EGC results in about 2-3
dB while MRC improves the signal by 6-8 dB.
5
0
Rx Power level [dB]
ï5
ï10
ï15
ï20
ï25
ï30
0
5
10
15
20
Distance from transmitter along xïaxis [m]
25
30
Figure 4.14: The power profile from five receiving antenna elements separated
by half a wavelength.
To further show that multiple antennas provide a robust source of diversity
Chapter 4. Space-Time Processing for Quality Improvement
108
of Short Range Wireless Communication Links
10
Seletion combining
Equal combining
Maximum ratio combining
Single antenna
Received Power level [dB]
5
0
ï5
ï10
ï15
ï20
ï25
ï30
0
5
10
15
20
25
Distance from transmitter along xïaxis [m]
30
Figure 4.15: Improvement of the received signal due to different receiver
diversity combining methods.
109
4.3. FEM SIMULATIONS
gain in NLOS channels, we perform simulations using an increasing number
of antenna elements at the receiver. From figure 4.16 we can clearly see that
even a few extra antennas at the receiver will result in a noticeable increase
the diversity gain (e.g. two extra antennas will give a 0.65, 1.87 and 3.23 dB
diversity gain respectively for the three examples of combining methods).
These results suggest that using multiple receiver antennas will improve the
indoor coverage of the transmission, especially if we use the Maximum ratio
or Equal gain combining methods.
Antenna receive diversity (SIMO)
14
Theoretical
Maximum Ratio
Equal gain
Selection
Diversity gain Gdiv [dB]
12
10
8
6
4
2
0
0
5
10
15
Number of receiver antennas N
20
Figure 4.16: The receiver diversity gain obtained by a SIMO system with
three different combining methods.
Finally, we consider the use of diversity (or multiple antennas) at both
the transmitter and receiver, respectively, giving rise to a MIMO system.
The MIMO system simulation has been analyzed for both spatial diversity
and spatial multiplexing schemes. That is to say, a MIMO system can
provide two types of gain: diversity gain and spatial multiplexing gain. In
the case of spatial diversity, the procedure is the same as for the SIMO
system described above and a MRC of the antennas output is used to provide
maximum diversity gain. In the case of spatial multiplexing, we create
separate uncorrelated sub channels to send data in parallel data streams
Chapter 4. Space-Time Processing for Quality Improvement
110
of Short Range Wireless Communication Links
which can then be interpreted as an increase of the total channel capacity
or an SNR improvement of the total channel. In this analysis we use the
SNR and compare it with the SNR enhancement resulting from the diversity
gain. If the SNR of the channel is improved the path loss exponent β will
accordingly decrease.
5
4.5
Path loss exponent `
4
3.5
3
2.5
2
1.5
1
2
3
4
5
6
7
8
9
10
Number of antennas at the transmitter and receiver respectively [Ntx × Nrx]
Figure 4.17: Showing the decrease of β in proportion to the size of the
Ntx × Nrx MIMO antenna system. In this analysis we have the same number
of antennas both on the transmitting and receiving side.
Figure 4.17 shows the path loss exponent versus the size of the antenna
array for the three paths shown in figure 4.12. The blue, red and green data
points and graphs corresponds to path a, b and c, respectively, in figure 4.12.
From this figure it is clear that increasing the number of antennas will result
in a decrease of the path loss exponent for the MIMO diversity system (solid
lines and for data points). The decrease in β is in the order of -0.14 per each
added antenna except in path c where the decrease is -0.52 per each added
antenna. In the case of spatial multiplexing (dashed lines and for data
points) we have a decrease in β by -0.78 per each added antenna except along
path a where we only have a decrease of -0.34 per each added antenna. The
spatial multiplexing system offers at least a 50% improvement in the path loss
4.4. CONCLUSIONS
111
exponent compared to the diversity system.
It should also be stressed that the number of antenna elements to be
used would depend on many factors such as the physical size of the different
devices, power requirements, complexity and cost restrictions imposed by
manufacturing.
4.4
Conclusions
In this chapter we investigated the wave propagation effects of a shortrange wireless device operating at 2.4 GHz in an indoor office environment.
The investigations were carried out using measurement trials and FEM
propagation modelling for NLOS and LOS propagation scenarios. The
measurement trails and simulations have shown good agreement. This was
also confirmed by comparison with the theoretical statistical probability
distribution of the signal in both scenarios. A power-distance exponential
propagation law was found to be sufficient to describe the propagation both
for corridors (propagation exponent β ≈ 1.66 − 1.76) and through office walls
(propagation exponent β ≈ 3.12 − 4.45). The FEM simulations were also used
for assessing the influence on propagation when doors are opened or closed.
The simulation results have shown a power loss in LOS scenario when the
doors of the offices are opened compared to when they are closed and that
this effect does not appear to be prominent in the NLOS scenario.
We have also investigated a SIMO antenna diversity system utilizing
different combining techniques and a MIMO antenna system using spatial
diversity and spatial multiplexing schemes to improve the performance over a
fading radio channel in a NLOS propagation environment. Our results show a
substantial gain would be achieved using a MIMO spatial multiplexing system.
It also shows that even a SIMO scheme would offer a considerable diversity
gain and improvement in system performance. However, more investigations
are necessary to better understand the path loss behaviour in a multiple
antenna system.
Chapter 4. Space-Time Processing for Quality Improvement
112
of Short Range Wireless Communication Links
CHAPTER 5
POWER CONSTRAINED SPACE-TIME
PROCESSING FOR SUPPRESSION OF
ELECTROMAGNETIC FIELDS
T
here have been several studies done, with conflicting results, on the effects
of cell-phone radiation on the human body [56–58]. The amount of
radiation emitted from most cell phones is very minute. However, given
the close proximity of the phone to the head, it is entirely possible for the
radiation to cause harm. If you want to be on the safe side, the easiest way
to minimize the radiation you are exposed to is to position the antenna as far
from your head as possible. Utilizing a hands-free kit, a car-kit antenna or a
cell phone whose antenna is even a couple of inches farther from the head can
do this most effectively. This chapter makes a contribution to that discussion
by proposing a new approach employing adaptive active control algorithms
combined with a Multiple-Input Multiple-Output (MIMO) antenna system to
suppress the electromagnetic field at a certain volume in space.
Active methods for attenuating acoustic pressure fields have been successfully used in many applications. In this paper we investigate if these methods
can be applied to an electromagnetic field in an attempt to lower the power
density at a specified volume in space.
The cancelling out of a signal can be achieved by employing the principle
of superposition. For example, if two signals are superimposed, they will
add either constructively or destructively. The objective of our study is
to investigate the possibility of applying adaptive active control algorithms
Chapter 5. Power Constrained Space-Time Processing
114
for Suppression of Electromagnetic Fields
with the goal of reducing the electromagnetic field power density at a specific
volume using the superposition principle and MIMO antenna system. Initially,
the application we evaluate is a model of a mobile phone equipped with
one ordinary transmitting antenna and a number of actuator-antennas which
purpose is to cancel out the electromagnetic field at a specific volume in space
(e.g. at the human head) [59–63]using power level information obtained by an
sensor antenna array. Later, we investigate the effects of the size and number
of MIMO antenna elements on the performance of the system [59, 61].
It is worth stressing at this point that the purpose of this MIMO system is
not to improve the capacity or quality of transmission between the mobile unit
and base station, but to predict the channel response or sense the radiated
field which can then be controlled by using the active control algorithms. For
this purpose, a class of algorithms called Filtered-X [76, 77, 80], which are
well known from the area of acoustic noise cancellation are employed and
evaluated to assess their behaviour and performance in this electromagnetic
type of environment. By constraining these adaptive algorithms we also try
to make the total output power level transmitted by the antenna elements,
locked to a predefined value. This power constraint is achieved through the
use of a quadratic constraint on the active control algorithms [60–63].
The modelling of the antenna elements and the electromagnetic field
calculations are performed using the simulation package FEMLAB (currently
COMSOL Multiphysics) [64, 65]. This software is also used in combination
with MATLAB to implement and test the adaptive algorithms used to control
the electromagnetic field. The operating carrier frequency used in the initial
investigation is 900 MHz (a wave length λ of approximately 0.33 m). Later,
we test the algorithms at different carrier frequencies (e.g., other GSM bands
and UMTS) [59].
The organisation of this chapter is as follows. In section 5.1, we present the
FEMLAB MIMO antenna model. In section 5.2, the different unconstrained
adaptive algorithms used to suppress the power density of the electromagnetic
field are presented. Simulation results comparing these different algorithms
are shown in section 5.3. The constrained solution of the output power is
presented in section 5.4. Simulation results investigating the effects of the
different MIMO antenna system parameters including the operating frequency
are analysed and presented in section 5.5. Finally, section 5.6 concludes the
chapter and presents further research ideas.
5.1. THE MODEL
5.1
5.1.1
115
The Model
The FEM model
The application used in this chapter is a three-dimensional (3D) model of
a physical system consisting of eight vertical antenna elements and of a
human head, a two-dimensional representation of the 3D model is shown
in figures 5.1 and 5.2, respectively. The simulation of the radio waves is
performed numerically by using the finite element method (FEM) in COMSOL
Multiphysics software package for solving the electromagnetic field equations.
Figure 5.1: 2D model representing the tested physical system.
In a simple medium where we have no external sources except inside the
transmitting antenna elements, we can write Maxwell’s equations in timeharmonic form as:
= j ωB
∇×E
= µJ − j ωµD
∇×B
=ρ
∇·D
(5.1)
=0
∇·B
(5.4)
(5.2)
(5.3)
where the vector arguments and the term e −j ωt are omitted for simplicity.
To solve the electric field with the current density in the antenna as the
from equation 5.2 and
input source we eliminate the magnetic flux field B
get:
= j ωµJ
− ω 2 εµE
(5.5)
∇× ∇×E
Chapter 5. Power Constrained Space-Time Processing
116
for Suppression of Electromagnetic Fields
meter
Boundary
meter
Figure 5.2: The FEM representation of the 2D model in figure 5.1. The outer
boundary is set to a radius of 1 meter to limit the FEM solution.
= 0 and we get
If it is assumed that there are no free charges, then ∇ · E
the inhomogeneous Helmholz’s equation:
= −j ωµJ
+ ω 2 εµE
∇2 E
(5.6)
The parameters denoted by ε (permittivity), µ (permeability)and σ
(conductivity) define the electromagnetic properties of the different materials
in the model.
To model materials that contain both conductive and dielectric properties,
a complex valued permittivity εc is defined:
σ
(5.7)
εc = ε r − j
ωε0
where σ is the conductivity and εr is the relative permittivity of the material
when there is an incident time-harmonic wave with an angular frequency ω.
Several authors have suggested permittivity and conductivity values of
the human brain tissues as a function of frequency (examples in [72–74]). The
5.1. THE MODEL
117
data have been assessed through measurements or by deriving values from
the intensity levels of magnetic resonance images (MRI) and thermographies,
or by theoretical analysis. This variety of methods give a wide range of
geometrical and dielectric properties of the brain tissue. The most common
data was published 1957 by Schwan [71]. Schwan and other authors validated
these values up to microwave frequencies [72, 73], and proposed analytical
expressions derived from Debye’s model of molecular dipole moment in
dispersive materials. The standardization seems to converge on data published
by Gabriel [74].
For simplicity an average of the electric properties of the brain and skull
is used here; for example at a frequency of 900 MHz the following parameters
are used
εr =45.805496
σ =0.766504[S/m]
(5.8)
(5.9)
These values are based on the 4-Cole-Cole equation as described in [74].
The antenna elements are assumed to be made out of copper and will have
the following electric properties
εr =1, since this is no dielectric material
σ =5.99 · 10 .[S/m]
7
(5.10)
(5.11)
If we assume that there are no ferromagnetic materials in this FEM model,
it will be sufficient to set the permeability equal to the free space permeability
µ = µ0 .
The finite element method requires that the modelled area is finite and
therefore it needs an outer boundary as is clearly shown in figure 5.2. In order
to simulate an electromagnetic wave travelling out towards infinity using this
model, it is necessary to define the outer boundary of the modelled area so that
it does not reflect any signal back towards the antennas (i.e. total absorption
at the outer boundary):
outside = 0
inside − D
(5.12)
n · D
where n is the normal vector of the boundary pointing outwards, and since it
is a virtual boundary there are no surface charges or currents. This will then
lead to a Neuman type of boundary condition:
∂D
= −j (n · k) D
∂n
(5.13)
Chapter 5. Power Constrained Space-Time Processing
118
for Suppression of Electromagnetic Fields
√
where k = ω εµ.
In the model created here the wave will be very close to orthogonal against
the boundary in all directions so there will be no significant reflection of the
= εE
we will get the boundary equation:
wave. Since D
!
=0
− ω n2x + n2y + n2z εµ E
(5.14)
n · ∇E
When the time-harmonic solution of the electric field components E(x,
y, z)
is calculated (see figure 5.3), COMSOL Multiphysics solves the other fields
the magnetic
automatically using Maxwell’s equations to get the magnetic H,
flux density B and the electric displacement D fields, respectively.
Figure 5.3: The numerical solution to the electric field problem.
y, z) and
The E(x,
y, z) is then used to calculate the Poynting vector S(x,
the time averaged power density. In this case with a stationary wave, this
5.1. THE MODEL
vector can be defined as [68]:
%
&
# $
= 1E
×H
∗ ,
S
2
119
(5.15)
where · denotes a time average.
Figure 5.4: A surface plot showing the calculated magnitude of the power
density based on the electric field solution.
The best way to visualize the power density
# $ is by using a two-dimensional
in decibels as illustrated in
surface plot to show the magnitude of S
figure 5.4.
Further, from the numerical FEM solution E(x,
y, z) we can also calculate
the maximum specific absorption rate (SAR) value according to
SAR = σ ·
2
|E|
ρ
(5.16)
where σ is the conductivity and ρ is the density of the material. The SAR
value calculated in the simulations is the maximum SAR value in each point
Chapter 5. Power Constrained Space-Time Processing
120
for Suppression of Electromagnetic Fields
inside the human head. This value is not the same as the value used in the
standards for mobile telephones, which is the mean value of equation 5.16
taken over 10 gram of tissue.
The SAR limit recommended by the International Commission of NonIonizing Radiation Protection (ICNIRP) is 2 W/kg averaged over 10 gram of
tissue. Thus to fulfill this limit with certainty we need to have a maximum
SAR below 2 W/kg.
5.1.2
The MIMO model
To reduce the electromagnetic field within a certain volume in the FEMmodelled space, a MIMO radio channel is modelled in order to compensate
for the spatial displacement. In this chapter, the FEM simulation program
”COMSOL Multiphysics” is used to simulate the physical MIMO antenna
system, which (initially in this Section) consists of 3 transmitting antennas
and 5 receiving antennas as shown in figure 5.1. The spacing between the
antenna elements used in this application is 0.02m λ; thus this arrangement
can not be seen as an ordinary beamformer as the antenna elements are
working in the radiated near-field. The input signals to this system are
three separate currents in a complex-valued phasor notation, one for each
transmitting antenna. The simulated output current from the 5 receiving
antennas form a complex-valued data vector denoted as the error signal vector
of the system. The centre antenna T2 (see figure 5.1) is transmitting the
signal that we want to cancel (it acts as the antenna on any ordinary mobile
telephone) and the two flank transmitter antennas T1 and T3 (see figure 5.1)
are denoted as actuator-antennas, which will be used to reduce the signal from
the antenna T2 at some specified volume.
By changing the amplitudes and phases of the currents assigned to the
three transmitting antennas it is possible to control the transmitted power
from the separate antenna elements.
The calculated time-harmonic electromagnetic wave in the model will then
generate a current density inside the receiving antenna elements. According
to Ampere’s law for a time-harmonic wave in a simple conductive media we
have the following equation:
= j ωµεc E
∇×B
(5.17)
The total output current Iout from each receiving antenna element can
be calculated by integrating both sides over the cross section area S of the
121
5.1. THE MODEL
antenna element:
Iout = jωε0
σ
εr − j
ε0 ω
dS
E
(5.18)
S
The result from each antenna element is then stored in a complex-valued
data vector e. If we have a system of three transmitter antennas and five
receiver antennas the transmitter antenna in the middle (T2 ) (see figure 5.1)
is the one we want to cancel, then the two flanking transmitter antennas are
denoted as the actuator-antennas (T1 , T3 ).
Since the simulated model is experimentally confirmed to be linear, and
this is a weak-stationary problem with a monochromatic time-harmonic signal,
it is in this case sufficient to describe the parameters as a 5×3 complex-valued
matrix H:
⎤
⎡
H11 (ω) H12 (ω) H13 (ω)
⎢ H21 (ω) H22 (ω) H23 (ω) ⎥
⎥
⎢
⎥
(5.19)
H=⎢
⎢ H31 (ω) H32 (ω) H33 (ω) ⎥
⎣ H41 (ω) H42 (ω) H43 (ω) ⎦
H51 (ω) H52 (ω) H53 (ω)
These complex-valued numbers Hij describe the amplitude and phase
due to the distance between the different combinations of transmitting and
receiving antennas. The general mathematical MIMO model is shown in
figure 5.5.
Figure 5.5: The general mathematical MIMO model of the entire antenna
system.
Chapter 5. Power Constrained Space-Time Processing
122
for Suppression of Electromagnetic Fields
Each column in H represents the time-harmonic frequency response
functions between one of the transmitting antennas and each of the receiving
antennas. The superimposed signals received by the antenna array, constitutes
a vector e with five complex-valued elements:
T
(5.20)
e = e1 e2 e3 e4 e5
If we divide the matrix H is into two separate complex-valued matrices (F
and g) as shown in figure 5.6, we get:
'
F = [H1 H3 ] =
and
g = H2 =
F11
F12
g1
F21
F22
g2
g3
F31
F32
F41
F42
g4
g5
F51
F52
T
(T
(5.21)
(5.22)
The two columns in F represent the frequency response functions of the
actuator -antennas and are denoted as the forward channels. The vector g is
denoted as the direct channel and represents the frequency response function
of the antenna with the signal we want to cancel out. The total noise of the
model is described by vector v, and can be modelled as a complex-valued
additive white Gaussian noise vector. The vector e is the combined signals
and noise received from the antenna array as shown in figure 5.6.
Figure 5.6: Block diagram of the antenna system described as two channels.
If the carrier signal transmitted through the direct channel g is to be
suppressed at the receiving antenna array, a phase-shifted and amplified copy
of the same carrier signal could be transmitted through the forward channels
123
5.1. THE MODEL
to superimpose the signal in the direct channel. This could be achieved by
incorporating a filter w which would allow control over the signals going
through the forward channels as shown in figure 5.7.
v
s
g
x
w
+
e
Control
F
Algorithm
Figure 5.7: Model of the direct channel g, and the forward channels F
controlled by the filter w.
To achieve the best possible attenuation in energy sense, the total energy
output ξ of the signal e at the receiving antennas must be as low as possible.
The minimum energy with respect to the filter w is:
2
(5.23)
min ξ = min E |e| = min E eH e
w
w
w
where H denotes a conjugate transpose. With the noise v included in the
system, the residual error signal e in equation 5.20 is given by:
e = sg + sFw + v
(5.24)
If the input signal s and the noise v are assumed to be uncorrelated, then
the mean energy can be written as:
ξ = rd + wH p + pH w + wH RF w + rv
(5.25)
where RF is the covariance matrix of the forward channels, p is the crosscorrelation between the direct channel and the forward channels, rd and rv
are the signal power of the direct channel and the noise, respectively.
The minimum energy ξmin is found by differentiating ξ with respect to
the complex conjugate of filter coefficients w∗ and then setting the derivative
equal to zero:
(5.26)
∇w∗ ξ = 0 ⇔ p + RF w = 0
Chapter 5. Power Constrained Space-Time Processing
124
for Suppression of Electromagnetic Fields
wopt = −R−1
F p
(5.27)
This is the Least Mean Square (LMS) solution to the problem and is the
optimal solution in mean energy sense. Figure 5.9 shows the surface plot of the
power density solution when the filter coefficients controlling the signals going
through the forward channels are the optimal least mean square coefficients
wopt obtained from equation 5.27.
Figure 5.8: The power density in the model with no optimization.
5.2. THE ADAPTIVE ALGORITHMS
125
Figure 5.9: The power density in the model when the optimal filter coefficients
wopt are used.
5.2
The Adaptive Algorithms
The least mean square solution in equation 5.25 describes a quadratic form
in the complex valued w-domain, and there is only one optimum point. The
gradient of the quadratic performance surface will be evaluated with respect
to the conjugate filter coefficients: −∇w∗ ξ . This will give the local steepest
descent direction towards the minimum point of the performance surface. To
give some idea of how these complex valued filter coefficients move toward
the minimum point, the magnitude of the filter coefficients are plotted in
figure 5.10 and in figures 5.11-5.14 and figure 5.18 for the other different
adaptive algorithms.
If the point (w0 , w1 ) in figure 5.10 has the energy value ξ, then a new point
in direction of the negative gradient vector must be closer to the minimum
point of the surface. So this will give an iterative update equation of the
filter-coefficients as:
(5.28)
wn+1 = wn + (−∇w∗ ξ(n))
The mean-energy ξ of the error function can according to equations 5.23
Chapter 5. Power Constrained Space-Time Processing
126
for Suppression of Electromagnetic Fields
Figure 5.10: The quadratic performance surface where the energy ξ is depicted
as equivalued closed contour-curves.
and 5.24 be expressed as:
= E eH e =
H
E (sg + sFw + v) e
ξ=E
|e|
2
(5.29)
If we differentiate equation 5.29 with respect to the conjugate of the filter
coefficients w∗ we get the gradient of the mean energy:
(5.30)
−∇w∗ ξ = −E FH s∗ e
Define FH s∗ ≡ XH , we get:
−∇w∗ ξ = E −XH e
(5.31)
The expected value is generally unknown, so this can be estimated by a
sample mean instead; that is:
ˆ w∗ ξ = −XH e
−∇
ˆ denotes the estimated gradient.
where ∇
(5.32)
127
5.2. THE ADAPTIVE ALGORITHMS
If this is substituted into the weight-updating equation 5.28 we get:
wn+1 = wn + µ (∇w∗ ξ(n)) = wn − µXH e
(5.33)
This is the so-called Filtered-X LMS [76, 80] (FX-LMS), since X is the
input signal filtered through the forward channels F. The step-length µ in
FX-LMS is a constant value and therefore the stability range and convergence
rate will change with the change of input power as:
0<µ<
2
Tr (RF )
(5.34)
To get around the change of convergence rate, consider that:
(
' 5
5
2
∗
|F |
Fm1
Fm2
2
m=1
RF = s∗ FH Fs = |s| · 5m=1 m1 ∗
5
2
m=1 Fm1 Fm2
m=1 |Fm2 |
(5.35)
Then the trace of the matrix RF will be:
2
Tr (RF ) = |s|
5
2
|Fm2 | |Fm1 |
2
(5.36)
m=1
where m designates the five different receiving antennas. The above range for
convergence (equation 5.34) can then be written as:
0<µ<
2
|s|
2
5
2
m=1
|Fm2 | |Fm1 |
2
(5.37)
If we introduce a new step-length parameter β (0 < β < 2) and normalize
by the trace of the matrix RF , we get:
µ=
2
|s|
5
m=1
β
2
|Fm2 | |Fm1 |
2
(5.38)
Then the range of the step-length will be fixed within the range 0 < β < 2.
If this substitution is made in the FX-LMS weight-updating algorithm
(equation 5.33), we get the Normalized FX-LMS algorithm:
XH
n
e
(5.39)
wn+1 = wn + β
α + Tr (RF )
where α is a noise regulating parameter if the elements of RF are small [76,80].
Chapter 5. Power Constrained Space-Time Processing
128
for Suppression of Electromagnetic Fields
Another approach to an adaptive algorithm is by using the optimal least
mean square solution from equation 5.27 in combination with the gradient
vector of the quadratic performance surface [76, 80]:
∇ξ = RF w + p
(5.40)
If we multiply both sides of the gradient by R−1
F , we get:
R−1
F ∇ξ = w − wopt
(5.41)
Rearrange equation 5.41 into an iterative equation where wn = w is the
present position (or iteration) and wn+1 = wopt is the next position, we get:
wn+1 = wn − R−1
F ∇n ξ
(5.42)
If the expression of the gradient vector is inserted into equation 5.42 we
obtain:
(5.43)
wn+1 = wn − R−1
F (RF wn + p) = wopt
This is the FX-Newton algorithm and its iterative equation moves from
any arbitrary point wn on the performance surface to the minimum point in
one single step. This can be clearly seen in figure 5.11 for a signal-to-noise
ratio (SNR) of 30 dB.
If the noise level is high (i.e., low SNR), this can give a very erratic search
of the minimum point with a large misadjustment (i.e. noise) as illustrated
in figure 5.12.
One approach to smooth the misadjustment noise is by using a step-length
variable µ as a smoothing regulator:
wn+1 = wn − µR−1
F (RF wn + p)
(5.44)
where 0 < µ < 1.
This solution is still going to give an erratic search with a large
misadjustment, unless a very small step-length is used which will also slow
down the rate of convergence. However, if the gradient vector (RF wn + p)
is estimated by the sample mean as was done in the FX-LMS algorithm [76],
we get:
ˆ w∗ ξ = Ê XH e = XH e
(5.45)
−∇
whereˆdenotes an estimation.
5.2. THE ADAPTIVE ALGORITHMS
129
Figure 5.11: The Newton algorithm finds the minimum point in one step.
SNR = 30 dB.
Using equation 5.45, the new weight update equation is given by:
ˆ wH ξ (n) = wn − µR−1 XH
∇
(5.46)
wn+1 = wn − µR−1
n e
F
F
n
This is the so-called FX-Newton/LMS algorithm, which is a compromise
between the two adaptive approaches. This will result in a greatly enhanced
smoothing of the gradient-noise as can be seen from figure 5.13.
The main problem with both the FX-Newton and the FX-Newton/LMS
algorithms is the need to calculate the inverse of the covariance matrix,
which is computationally inefficient. However, if the diagonal elements of
the covariance matrix RF are large compared to the off-diagonal values, then
the covariance matrix can be estimated from:
R̂F ≈ diag {RF }
(5.47)
By inserting this estimate into the weight updating equation and using a
separate step-length for each matrix element, we get:
wn+1 = wn − MXH
n e
(5.48)
Chapter 5. Power Constrained Space-Time Processing
130
for Suppression of Electromagnetic Fields
Figure 5.12: The erratic search of the Newton algorithm when the noise level
is high. SNR = 10 dB.
)
where
M=
5µ1
|s|2 ·
m=1 |Fm1 |
0
*
0
2
5µ2
|s|2 ·
m=1 |Fm2 |
2
Equation 5.48 is known as the Actuator Individual Normalized FX-LMS
algorithm [77].
If the eigenvalues of RF are disparate, then the Actuator Individual
Normalized FX-LMS will outperform the Normalized FX-LMS since each filter
weight will be controlled and normalized separately. On the other hand, if
the eigenvalues of the covariance matrix roughly have the same value, then
the Normalized FX-LMS and the Actuator Individual Normalized FX-LMS
behave in a similar way as can be seen from figure 5.14.
5.3
Simulation Results
In the previous section we presented the different adaptive algorithms to
suppress the power density of the electromagnetic field and thereby decreasing
the maximum SAR value inside the human head. These algorithms are
5.3. SIMULATION RESULTS
131
Figure 5.13: This plot clearly shows why the Newton/LMS algorithm (the
green trace) is preferable to the ordinary relaxed Newton algorithm (the red
trace) when a high noise level is present in the estimation of the gradient
vector. SNR = 10 dB.
unconstrained; that is there is no control over the total output power from
the mobile phone. In chapter 5.4, the constrained solution will be presented.
In this section we evaluate and compare the different unconstrained adaptive
algorithms.
The ordinary FX-LMS algorithm is the simplest to implement of the
evaluated algorithms, but this algorithm has some disadvantages when the
input signal is non-stationary. The Normalized FX-LMS algorithm normalizes
the input signal with its signal power, resulting in a more robust algorithm
at the expense of higher computational complexity. Another approach to the
adaptive search is Newton’s method where it is possible to solve the problem
in one single step under ideal conditions. This single-step algorithm, however,
is very sensitive to noise and is therefore impractical. To improve the noise
insensitivity of the Newton algorithm, a gradient vector estimate is used to
smooth the algorithm. This algorithm is called the FX-Newton/LMS. Both
the FX-Newton and FX-Newton/LMS algorithms require a matrix inversion
of the covariance matrix, resulting in high computational complexity. The
Chapter 5. Power Constrained Space-Time Processing
132
for Suppression of Electromagnetic Fields
Figure 5.14: A comparison between the Actuator Individual Normalized FXLMS and the FX-Newton/LMS. Since the eigenvalues of RF and of diag (RF )
are roughly the same the two algorithms will behave in a similar fashion.
Actuator Individual Normalized FX-LMS algorithm only uses the diagonal of
the covariance matrix to simplify the problem of calculating the inverse of the
covariance matrix.
From the above discussion and by testing the algorithms by simulations,
it was concluded that the Normalized FX-LMS and the Actuator Individual
Normalized FX-LMS are the preferred algorithms since they are both robust
and noise-insensitive. Figure 5.15 shows the calculated maximum SAR level
inside the human head relative to the maximum SAR level of a single
transmitting antenna for both adaptive algorithms. The figure also show
the corresponding maximum SAR level attained by employing a passive five
element reflector and the least mean square solution which is used as a
benchmark for comparisons.
The amount of SAR attenuation achieved by the least mean square solution
is approximately 12 dB relative to the maximum SAR level produced by a
single antenna system (i.e., by using the direct transmitting antenna only, as
shown in figure 5.1). It is clear from figure 5.15 that the adaptive algorithms
after convergence give about 10 dB more attenuation compared to using the
133
5.4. POWER CONSTRAINTS
maximum Specific Absorption Rate SAR [W/kg]
4
a
3.5
3
2.5
b
2
1.5
1
d
c
0.5
e
0
0
10
20
30
40
50
Iterations
Figure 5.15: The maximum SAR level inside the human head. Plots (from top
to bottom): a) One transmitting antenna only. b) 5 passive sensor elements
as a passive reflector. c) FX-LMS. d) Actuator Individual FX-NLMS. e) Least
Mean Square solution.
five receiving antenna elements as a passive reflector. It can also be seen that
the Actuator Individual FX-NLMS converges about 40% faster than the FXNLMS towards the least mean square solution, since each diagonal element of
the covariance matrix is normalized separately.
Finally, in figure 5.16 we show the power density field for one transmitting
antenna with five passive reflector elements, and in in figure 5.17 three
transmitting antennas tuned to the least mean square solution (i.e., the
adaptive algorithms after convergence), respectively. It is clearly evident from
this surface plot that the electromagnetic power density field inside the head
is lower in the adaptive algorithms case.
5.4
Power Constraints
In the previous sections we presented the different unconstrained adaptive
algorithms to suppress the power density of the electromagnetic field and their
respective simulation results. There is however a major drawback with these
Chapter 5. Power Constrained Space-Time Processing
134
for Suppression of Electromagnetic Fields
Figure 5.16: Power density surface plot inside the human head (referring to
figure 5.1) using one active transmitting antenna with five passive reflector
elements (plot b in figure 5.15).
adaptive algorithms: that is although the SAR is attenuated by approximately
5 dB (as shown in plots c-e in figure 5.15) inside the human head, there is no
control over the total output power from the mobile phone. This means that
the total output power changes when the filter adapts, which is unfortunate
since the magnitude of the total output power from the mobile phone depends
on the distance from the base station. For example, if we take the case of
three transmitting antennas and five receiving antennas, this would result in
an increase of the total output power by approximately 20% (although this
still gives a suppression of 5 dB inside the human head). However, with some
other antenna spacing the mobile phone might lose the connection when the
adaptive suppression filter converges towards the optimum value.
To alleviate this problem, some form of power constraint [60] could be
used on the minimization process; that is:
(5.49)
min rd + wH p + pH w + wH RF w + rv
wH
2
2
subject to: |sw| + |s| = C,
C∈
135
5.4. POWER CONSTRAINTS
where the symbol denotes a real number. This optimization problem can
then be solved by forming a Lagrange equation [81] defined as:
(5.50)
L (w, λ) = wH RF w + wH p + pH w − λ C − s∗ wH ws − s∗ s
By differentiating this Lagrange equation and setting it to zero, we get a
suboptimal solution of w which is dependent on the variable λ:
∇wH L (w, λ) = 0
2
⇔
RF wco + p + λ |s| wco = 0
2
RF + λ |s| I wco = −p
(5.51)
(5.52)
where wco denote the constrained values of the filter coefficients. If we
multiply equation 5.52 by R−1
F we get:
2
I + λ |s| R−1
wco = −R−1
(5.53)
F
F p
The right hand side of equation 5.53 is the unconstrained optimal solution
wopt which was derived earlier in this chapter (see equation 5.27). Using this
information and rearranging equation 5.53, we get:
−1
2
wopt
(5.54)
wco = − I + λ |s| R−1
F
It can be clearly seen from equation 5.54 that it is now possible to adjust
the unconstrained solution by using a diagonal loading of the covariance
matrix. The parameter λ can be chosen so that equation 5.54 satisfies the
constraint. Unfortunately there are no closed form solutions for the optimal
value of the loading variable λ. However, equation 5.54 can be simplified
by employing a Maclaurin expansion of the first term on the right hand
side, for values of λ that are close to zero. If we use the first two terms
of the MacLaurin expansion (see equation 5.55), it is possible to derive
an approximate expression where we only need to perform a single matrix
inversion operation:
−1
2
2
≈ I − λ |s| R−1
(5.55)
I + λ |s| R−1
F
F
When this approximation is substituted into the solution of the constrained
minimization, we get the constrained values of the filter coefficients as:
wco = −wopt − λ |s| R−1
F wopt
2
(5.56)
Chapter 5. Power Constrained Space-Time Processing
136
for Suppression of Electromagnetic Fields
To find out which value of λ we need, the constraint (equation 5.57)
should be solved for the value of the constrained filter coefficients wco and
the required power constraint level C:
2
2
|swco | + |s| = C
(5.57)
This will yield a quadratic equation which has the following solution:
+
H 2
H
C
H w
2 · wopt
q ±
q
− 4 · qH q wopt
+
1
−
−2 · wopt
opt
|s|2
λ=
2 H
2 · |s| q q
(5.58)
where q = R−1
w
.
opt
F
So, by setting the constraining power level C and using the unconstrained
optimal values of the filter coefficients wopt , we can now use equation 5.58
to calculate what the value of λ should be. This value is then inserted into
equation 5.56 in order to calculate the constrained filter coefficients wco , which
(for convenience) is re-stated again here:
wco = −wopt − λ |s| R−1
F wopt
2
(5.59)
As an example, if the constrained filter coefficients of equation 5.59 are
used in the iterative FX-LMS adaptive algorithms, it can be seen in figure 5.18
that it will converge at the non-optimal solution that satisfy the constraint
and has the shortest distance to the unconstrained optimal point. The
convergence of this non-optimal constrained least square solution for the
Actuator Individual FX-NLMS can also be observed in figure 5.19 and in
figure 5.20 is shown the maximum specific absorption rate (SAR) inside the
human head when the Actuator Individual FX-NLMS algorithm have reached
the constrained least square solution.
In figure 5.20 and figure 5.21 we show the effect of using an adaptive
algorithm with a power constraint imposed on the solution. The purpose
of this constraint is to allow for the minimum SAR value inside the human
head while keeping the radiated power from the antenna system at a level
consistent with the specified radiated output power from a mobile phone.
The adaptive algorithm used in figures 5.20, figure 5.21 and figure 5.19 is
the Actuator Individual Normalized FX-LMS algorithm with an imposed
constraint according to equation 5.59.
5.5. THE EFFECTS OF MIMO ANTENNA PARAMETERS AND CARRIER FREQUENCY
137
5.5
The Effects of MIMO Antenna Parameters
and Carrier Frequency
The Least Mean Square solution obtained in chapter 5.3 is the optimal solution
in energy sense for this problem. This particular solution (figure 5.4) is only
valid assuming the position of each element does not change. However, there
might be positions of the antenna elements that are more favorable with
respect to the power density and SAR level inside the head. By changing the
spacing of the antenna elements during calculations of the attenuated SAR
level inside the human head we will investigate if there exist some optimal
spacing between the different antenna elements.
In this FEM model setup we assume three degrees of freedom (DOF), as
shown in figure 5.22. The spacing between the sensor elements, denoted ∆y,
the distance (d) between the sensor element array (the receiving elements)
and the actuator element array (the transmitting elements). The third DOF
is the spacing between the actuator elements, denoted ∆a. In the first analysis
we look at how the spacing of the sensor elements and the distance between
the transmitter and receiver antennas affect the SAR level inside the head,
see figure 5.23.
It is clear from figure 5.23 that the farther apart the transmitter and
receiver antennas are located the lower the SAR level is inside the head. This is
due to the increase of the distance (d) (see figure 5.22) between the transmitter
and receiver antennas. An increase of this distance will also increase the
distance between the transmitter antennas and the head which will decrease
the SAR level inside the head. By analyzing figure 5.23 we can see that the
two-dimensional cost function J (∆y, d) is flattening out at a distance d of
approximately 25 cm. The spacing between the sensor elements (receiving
elements) at the distance d=25 cm should be approximately 5 cm. With this
spacing the sensor element array will cover a larger portion of the head. By
using these values as a good approximation of the optimal displacement of the
actuator elements and the distance between the sensor elements this would
result in an SAR attenuation of approximately 7 dB. Using these values as
a starting point, figure 5.24 is showing how the separation of the actuator
antenna elements ∆a affects the SAR level of the cost function J (∆y, d)
inside the head.
From figure 5.24 we can see that the attenuation inside the head will
increase as the spacing between the actuator elements decrease. This is a
consequence of the electromagnetic waves being transmitted from almost the
Chapter 5. Power Constrained Space-Time Processing
138
for Suppression of Electromagnetic Fields
same point in space. The theoretical extreme of this is to place all actuator
antennas in the exact same position, which will give a complete cancellation
of the waves and would give a zero power and SAR level inside the head.
According to this analysis we need a MIMO antenna system that has a spacing
of 5 cm between the sensor elements and a spacing of 3 cm between the
actuator elements. The distance between the sensor elements and actuator
elements should be about 25 cm or more. This would result in a MIMO
antenna system with a size of approximately 25 by 20 cm which is not practical
to place on top of a mobile phone. However, we foresee many applications
where this size would be practical. Studying figure 5.23 and figure 5.24 we
observe that if the original positions of the antenna elements, with an actuator
antenna spacing of 2 cm is used and we increase the spacing of the sensor
elements from 2 cm to 3 cm we would get an extra 2 dB SAR attenuation
inside the head compared to the original positioning of the antenna elements
in figure 5.1. We have also investigated the impact on the systems performance
as a result of changing the number of antenna elements in the actuator and
sensor arrays. In these simulations we have calculated the least mean square
solution as a function of the number of antenna elements in the actuator array
M and the sensor array N.
Figure 5.25 shows, as expected, a decrease in the SAR level inside the head
as long as every new added sensor element cover more of the head. Although,
when the sensor array extends outside the length of the human head we attain
no further improvement in the attenuation. Another interesting observation
from figure 5.25 is that if the number of actuator elements is larger than the
number of sensor elements the system becomes unstable.
Finally, we investigate the effect of the carrier frequency on the system
performance. The suppression of the electromagnetic field inside the head so
far in this chapter has been analyzed at the GSM frequency band centered at
900 MHz. Therefore, it would be interesting to investigate the effect of using
this system at higher carrier frequencies in order to evaluate its performance
at other GSM bands and the UMTS frequency band. In this experiment, we
sweep the carrier frequency of the simulated system between 500 MHz and
2.5 GHz and the results can be viewed in figure 5.26. From this figure it can
be clearly seen that we have a minimum point at the carrier frequency of
950 MHz. This optimum frequency is dependent on the type and size of the
different antenna elements. It can also be noted from figure 5.26 that the SAR
attenuation of the power level at GSM/UMTS frequencies does not differ by
more than 1-2 dB’s.
5.6. CONCLUSIONS
5.6
139
Conclusions
In this chapter we have presented a FEM model which solves the partial
differential equation of an electromagnetic field and simulated the physical
MIMO antenna system which is controlled by various adaptive signal processing algorithms in order to suppress the field at a certain volume in space. We
have also presented the solution for constraining the total output power of
the system to a predefined level. In addition, we have investigated the effects
of the size and number of MIMO antenna elements on the performance of the
system and also tested the algorithms at different carrier frequencies. The
SAR attenuation levels achieved from these simulations suggest the possibility
of using an active antenna system for the reduction of electromagnetic field
density. However, our result also show some limitations associated with
implementing these antenna arrays in mobile phones, for which further
research is needed to find practical solutions. In addition, we foresee other
applications where this array size and arrangement would be suitable for
practical implementation.
Chapter 5. Power Constrained Space-Time Processing
140
for Suppression of Electromagnetic Fields
Figure 5.17: Power density surface plot inside the human head (referring to
figure 5.1) using three transmitting antennas tuned to the least mean square
solution (plot e in 5.15).
141
5.6. CONCLUSIONS
The Quadratic Performance Surface
0.8
Absolute Value of Weight w0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.1
0.2
0.3
0.4
0.5
0.6
Absolute Value of Weight w1
0.7
0.8
Figure 5.18: An example of using the power constraint in combination with the
FX-LMS algorithm. The red trace shows the convergence of the unconstrained
filter coefficients. In the green trace we have a constraint that allows for half
the power needed to reach the optimal point.
Chapter 5. Power Constrained Space-Time Processing
142
for Suppression of Electromagnetic Fields
maximum Specific Absorption Rate SAR [W/kg]
4
a
3.5
3
2.5
b
2
1.5
1
d
f
c
0.5
e
0
0
10
20
30
40
50
Iterations
Figure 5.19: The maximum SAR level inside the human head. Plots (from top
to bottom): a) One transmitting antenna only. b) 5 passive sensor elements
as a passive reflector. c) FX-LMS. d) Actuator Individual FX-NLMS. e) Least
Mean Square solution. f) Actuator Individual FX-NLMS with constraint.
The average total power level
inside the human head -35 dB
Minimum without constraint
The average total power level
inside the human head -26 dB
Minimum with constraint
}
Total antenna output
at optimal attenuation
with a constraint ~0.26 dB
Figure 5.20: Power density suface plots inside the human head. Comparing the attenuation of electromagntic
energy inside the human head and the radiated power from the antenna system without constraint (bottom
left figure) and with a constraint (bottom right figure). All three figures have the distance in x and y
directions measured in meters.
{
}
Total antenna output
at optimal attenuation
~1.1 dB
Total antenna output
power normalized to
0 dB
Before minimization
5.6. CONCLUSIONS
143
for Suppression of Electromagnetic Fields
144
Chapter 5. Power Constrained Space-Time Processing
Figure 5.21: The same results as in figure 5.20, but the three plots are zoomed out to show more of the
far-field. Comparing the attenuation of electromagntic energy inside the human head and the radiated
power from the antenna system without constraint (bottom left figure) and with a constraint (bottom right
figure). All three figures have the distance in x and y directions measured in meters.
145
5.6. CONCLUSIONS
R1
T1
Dy
R3
T2
T3
R2
Da
R4
R5
TM
RN
d
Figure 5.22: The MIMO system showing the three variables of the antenna
displacement.
Chapter 5. Power Constrained Space-Time Processing
146
for Suppression of Electromagnetic Fields
Distance between Tx and Rx antenna elements d [cm]
SAR
50
45
2
40
35
1.5
30
25
1
20
15
0.5
10
5
2
4
6
8
10
12
14
16
Spacing of sensor elements 6y [cm]
18
20
Figure 5.23: The maximum SAR level inside the head as a 2-dimensional cost
function J (∆y, d) with respect to the spacing between the sensor elements
and the distance between the transmitting and receiving antennas. These
SAR levels refer to a system with N=5 sensor elements and M=2 actuator
elements.
147
5.6. CONCLUSIONS
1.4
Specific Absorption Rate SAR [W/kg]
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0
5
10
15
Spacing of sensor elements 6y [cm]
20
Figure 5.24: The effect of increasing the spacing ∆a between the actuator
antenna elements. This result was calculated with a sensor array spacing of
∆y = 5 cm and a separation between the sensor array and the actuator array
of d = 25 cm.
Chapter 5. Power Constrained Space-Time Processing
148
Specific Absorption Rate SAR [W/kg]
for Suppression of Electromagnetic Fields
10
8
6
4
2
0
2
0
4
5
6
10
8
10
15
Number of Sensor array eleme
Number of Actuator array elements
Figure 5.25: The maximum SAR level inside the human head as a function
of the number of elements in the actuator and sensor array.
149
5.6. CONCLUSIONS
5.5
Specific Absorption Rate SAR [W/kg]
5
4.5
4
3.5
3
2.5
2
1.5
1
500
1000
1500
Frequency f [MHz]
2000
2500
Figure 5.26: The change in SAR level inside the human head at different
carrier frequencies. This simulation was done with a sensor array spacing of
∆y = 3 cm and a distance between the sensor array and the actuator array
of d = 3 cm.
Chapter 5. Power Constrained Space-Time Processing
150
for Suppression of Electromagnetic Fields
CHAPTER 6
SPACE-TIME PROCESSING FOR
INTERFERENCE MITIGATION IN HAP
WCDMA SYSTEMS
T
hird generation mobile systems are gradually being deployed in many
developed countries in hotspot areas. However, owing to the amount of
new infrastructures required, it will still be some time before 3G is ubiquitous,
especially in developing countries. One possible cost effective solution for
deployments in these areas is to use High Altitude Platforms (HAPs) [82–90]
for delivering 3G (WCDMA) communications services over a wide coverage
area [36, 91, 92, 94, 95]. HAPs are either airships or planes that will operate
in the stratosphere, 17-22 km above the ground. This unique position offers
a significant link budget advantage compared with satellites and much wider
coverage area than conventional terrestrial cellular systems. Such platforms
will have a rapid roll-out capability and the ability to serve a large number of
users, using considerably less communications infrastructure than required by
a terrestrial network [82]. In order to aid the eventual deployment of HAPs
the ITU has allocated spectrum in the 3G bands for HAPs [96], as well as in
the mm-wave bands for broadband services at around 48GHz worldwide [97]
and 31/28GHz for certain Asian countries [98].
Spectrum reuse is important in all wireless communications systems.
Cellular solutions for HAPs have been examined in [99, 100] , specifically
addressing the antenna beam characteristics required to produce an efficient
cellular structure on the ground, and the effect of antenna sidelobe levels on
Chapter 6. Space-Time Processing for Interference
152
Mitigation in HAP WCDMA Systems
channel reuse plans [100]. HAPs will have relatively loose station-keeping
characteristics compared with satellites, and the effects of platform drift on
a cellular structure and the resulting inter-cell handover requirements have
been investigated [101]. Cellular resource management strategies have also
been developed for HAP use [102].
Configurations of multiple HAPs can also reuse the spectrum. They can
be used to deliver contiguous coverage and must take into account coexistence
requirements [36, 92]. A technique not widely known is their ability to serve
the same coverage area reusing the spectrum to allow capacity enhancement.
Such a technique has already been examined for TDMA/FDMA systems
[34,103,104]. In order to achieve the required reduction in interference needed
to permit spectrum reuse, the highly directional user antenna is used to
spatially discriminate between the HAPs. The degree of bandwidth reuse
and resulting capacity gain is dependent on several factors, in particular the
number of platforms and the user antenna sidelobe levels. An alternative
method of enhancement is to apply space-time diversity techniques, such
as Single-Input Multiple-Output (SIMO) receive diversity or Multiple-Input
Multiple-Output (MIMO) diversity, to improve the spectrum reuse in the
multiple HAP scenario.
In the case of many 3G systems the user antenna is either omni-directional
or at best low gain, so in these cases it cannot be used to achieve the same
effects. The purpose of this chapter is to examine how the unique properties
of a WCDMA system can be exploited in multiple HAP uplink architectures
to deliver both coverage and capacity enhancement (without the need for the
user antenna gain).
In addition to the spectral reuse benefits, there are three main benefits for
a multiple HAP architecture:
• The configuration also provides for incremental roll-out: initially only
one HAP needs to be deployed. As more capacity is required, further
HAPs can be brought into service, with new users served by the newly
deployed HAPs.
• Multiple operators can be served from individual HAPs, without the
need for complicated coexistence criteria since the individual HAPs
could reuse the same spectrum.
• HAPs will be payload power, volume and weight constrained, limiting
the overall capacity delivered by each platform. Capacity densities can
be increased with more HAPs. Moreover, it may be more cost effective
6.1. MULTIPLE HAP SYSTEM SETUP
153
to use more lower capability HAPs [105] (e.g., solar powered planes),
rather than one big HAP (e.g., solar powered airship), when covering a
large number of cells.
The chapter is organized as follows: in section 6.1 the multiple HAP
scenario is explained. The interference analysis is presented in section 6.2.
In section 6.3 we examine the completely overlapping coverage area case,
different numbers of platforms, and simulation results showing the achievable
capacity enhancement are presented. Finally, conclusions are presented in
section 6.4.
6.1
Multiple HAP system setup
In this chapter we use a simple geometric positioning of the high altitude
platforms to create signal environments that can easily be compared and
analyzed. In each constellation, the HAPs are located with equal separation
along a circular contour, as shown in figure 6.1.
R
qm
dm
Figure 6.1: An example of a system simulation setup with N = 2 HAPs with
overlapping cells of radius R. dm is the distance on the ground between the
cell centre and the vertical projection of the HAP on the ground and θm is
the elevation angle towards the HAP.
The separation distance dm along the line from the vertical projection of
the HAP on the ground to the cell centre is varied from 70 km to zero (i.e., all
the HAPs will be located on top of each other in the latter case). All HAPs
in this chapter are assumed to be flying in the stratosphere at an altitude of
20 km. The size of the coverage area assigned to each HAP is governed by the
Chapter 6. Space-Time Processing for Interference
154
Mitigation in HAP WCDMA Systems
shape of the base station antenna pattern. If we assume that we only have
one cell per HAP, then the coverage area is also synonymous with the total
cell area of the HAP.
6.1.1
User Positioning Geometry
Each UE (User Equipment) is positioned inside the cell according to an
independent uniform random distribution over the cell coverage area with
radius R, as shown in figure 6.2. The position of each UE inside each cell
is defined relative to the HAP base station that it is connected to, and
also relative to every other HAP borne base station. This is necessary in
order to evaluate the impact of interference between the different UE-HAP
transmission paths.
BS 1
BS 2
BS 3
Cell boundary
Figure 6.2: A plot showing a sample distribution of 150 UE, where 50 UE are
assigned to each of the three base stations (BS1, BS2 and BS3).
6.1.2
Base station antenna pattern
The base station antenna pattern for the simulations were chosen to be simple
but detailed enough to show the effects of the main and side lobes, especially in
155
6.1. MULTIPLE HAP SYSTEM SETUP
the null directions, as illustrated in figure 6.3. A simple rotationally symmetric
pattern based on a Bessel function is used for this purpose, and is defined by [1]
⎛
G(ϕ) ≈ 0.7 · ⎝
2 · J1
⎞2
sin(ϕ)
⎠ ,
sin(ϕ)
70π
ϕ3dB
(6.1)
where J1 (·) is a Bessel function of the first kind and order 1, ϕ3dB is the 3
dB beam width in degrees of the main antenna lobe. The 3 dB beam width
of the antenna is computed from the desired cell radius according to
cell radius
.
(6.2)
ϕ3dB = 2 · arctan
HAP altitude
0
Normalized antenna gain G [dB]
ï10
ï20
ï30
ï40
ï50
Cell radius 10 km
Cell radius 5 km
Cell radius 2 km
ï60
ï70
ï100
ï50
0
Eïplane e [degrees]
50
100
Figure 6.3: HAP base station antenna patterns for different cell radii.
6.1.3
User equipment antenna pattern
In this analysis we assume that each UE employs a directive antenna
and communicates with its corresponding HAP basestation. Using this
Chapter 6. Space-Time Processing for Interference
156
Mitigation in HAP WCDMA Systems
assumption we only need to set the desired maximum gain of the UE antenna
we want to use, as shown Table 6.1. The antenna pattern of the directive
antennas is calculated according to 6.1, but with a fixed maximum gain instead
of a fixed main beam width, the beamwidth is then ϕ(Gmax ) .
User Equipment
Mobile phone
Data terminal
Max. ant. Gain [dBi]
0
2,4,12
Table 6.1: Antenna gains used in the simulation setup.
6.1.4
UE-HAP radio propagation channel model
In this chapter we use the Combined Empirical Fading Model (CEFM)
together with the Free Space Loss (FSL) model. CEFM combines the results
of the Empirical Roadside Shadowing (ERS) model [106] for low elevation
angles with the high elevation angle results from [107] for the L and S Bands.
Using the FSL model the path loss from UE n to HAP base station m, is
given by
2
(4π · dm
n)
F SL
= tx
,
(6.3)
lm,n
2
Gm,n · Grx
m,n · λ
where dm,n is the line of sight distance between the UE n and HAP m. The
rx
receiver Grx
m,n and transmitter Gm,n antenna gain patterns are calculated
using 6.1 and 6.2. The carrier frequency fc used in the simulation is 1.9
GHz which gives a wavelength λ of 0.1579 meters. The CEFM fading loss
associated to HAP m is calculated as
Lf (θm ) = a · loge (p) + b
[dB],
(6.4)
where p is the percentile outage probability, and the data fitting coefficients
a and b are calculated according to [106]
0
2
− 0.15 · θm − 0.7 − 0.2 · fc
a = 0.002 · θm
,
(6.5)
b = 27.2 + 1.5 · fc − 0.33 · θm
157
6.1. MULTIPLE HAP SYSTEM SETUP
where θm is the elevation angle of HAP m. The total channel gain from UE
n to HAP m is then given by
L (θ ) −1
f m
F SL
10
.
(6.6)
gm,n (θm ) = lm,n · 10
6.1.5
WCDMA Setup
The different service parameters used in this chapter are collected from the
3GPP standard [108] and are summarized in Table 6.2. In order to account
for the relative movement between the UE and the base stations, a fading
propagation channel model based on equation 6.6 is simulated. This results
in a Block Error Rate (BLER) requirement of 1 % for the 12.2 kbps voice
service and a BLER of 10 % for 64, 144 and 384 kbps data packet services,
respectively.
Parameters
Chip rate
Data rate
Req. Eb /N0
Max. Tx. Power
Voice activity
Voice
12 kbps
11.9 dB
125 mW
0.67
Type of service
Data
Data
3.84 Mcps
64 kbps 144 kbps
6.2 dB
5.4 dB
125 mW 125 mW
1
1
Data
384 kbps
5.8 dB
250 mW
1
Table 6.2: WCDMA service parameters employed in the simulation.
6.1.6
Space-Time Processing Techniques
The spatial properties of wireless communication channels are extremely
important in determining the performance of the systems. Thus, there has
been great interest in employing space-time signal processing schemes since
they can offer a broad range of ways to improve wireless systems performance.
For instance, receiver diversity techniques such as Single-Input MultipleOutput (SIMO) and Multiple-Input Multiple-Output (MIMO) can enhance
Chapter 6. Space-Time Processing for Interference
158
Mitigation in HAP WCDMA Systems
link quality through diversity gain or increase the potential data rate or
capacity through multiplexing gain. In this section, we apply these techniques
to HAPs and in the next section we determine their impact on performance
via simulations.
In this scenario, we assume that the link between the UE and the HAP
BS is setup according to the previous sections in this chapter. The total
spatio-temporal and polarization degrees of freedom is, in an Orthogonal User
Multiple Access SIMO system, restricted by the number of users and the
number of receiving antennas. If Es is the average transmit energy per symbol,
the received signal r is given by [109]
r = Es · wH hs + wH n,
(6.7)
where s is the transmitted signal, h is the channel response vector, hn =
|hn |ejφn , n = 1, 2, · · · , Nrx , for all receiving antennas, in which |hn | is defined
as the inverse of the channel gain in equation 6.6 assuming that the separate
channels are independent. The received noise vector n for all receiving
antennas is assumed to be AWGN and w are the combining weights at the
receiver. Choosing the combining weights w to be equal to the channel
response vector h will result in the Maximum Ratio Combining (MRC)
method, which can be represented as
(6.8)
r = Es · ||h||2 s + hH n.
The SNR for the received signal can now be written as
2
√
&
%
Es · ||h||2
||h||4
s · Es
SNRM RC =
= SNRn ·||h||2 = SNRn ·Nrx ,
=
·E
2
2
2
H
σ
||h||
(h n)
n
(6.9)
where SNRn is the signal to noise ratio in each receiving antenna and Nrx is
the number of receiving antennas.
A similar combining method as in the SIMO receiver diversity is used
in the MIMO diversity method. MIMO diversity utilize Ntx transmitting
antennas and Nrx receiving antennas and assumes the channel response matrix
Hnm = |Hnm |ejφnm , n = 1, 2, · · · , Nrx , m = 1, 2, · · · , Ntx . |Hnm | is the inverse
of the channel gain from equation 6.6, and provided that the separate channels
are independent then H is a diagonal matrix. The noise is AWGN and the
received signal from the MIMO diversity system can then be expressed as [109]
H
H
Hwtx s + wrx
n,
(6.10)
r = Es · wrx
159
6.2. INTERFERENCE ANALYSIS
The SNR for the received signal is then given by
2
√
&
%
Es · ||H||2F
||H||4F
s · Es
= SNRn ·Ntx ·Nrx , (6.11)
=
·E
SNRM RC =
2
σn2
||H||2F
(HH n)
where SNRn is the signal to noise ratio in each receiving antenna and Nrx
is the number of receiving antennas and Ntx is the number of transmitting
antennas.
6.2
Interference analysis
Assuming that we have a setup of M different HAPs covering the same cell
area and N users connected to each HAP, we can denote each UE position
as (xm,n , ym,n ), where n = {1, 2, . . . , N } and m = {1, 2, . . . , M }. An example
of a scenario setup with N = 50 and M = 3 is shown in figure 6.2. The
maximum power ptx
m,n that the user in location (xm,n , ym,n ) is transmitting
dependent of the type of service used and can be obtained from Table 6.2. In
WCDMA systems, power control is a powerful and essential method exerted
in order to mitigate the near-far problem. The power received at base station
(HAP) m from user n is
tx
prx
m,n (θm ) = pm,n · gm,n (θm ),
(6.12)
where gm,n (θm ) is the total link gain, as defined in 6.6, between UE
transmitter n and its own cell’s BS receiver m. To be able to maintain a
specific quality of service we need to assert that we maintain a good enough
SINR (Signal to Interference plus Noise Ratio) level. From Table 6.2 we can
see the required Eb /N0 values for different services, and we can express the
required SINR, γm,n for user n at HAP base station m as
Eb
R
req
·
,
(6.13)
γm,n =
W
N0 req
where R is the data rate of the service and W is the Chip-rate of the system.
The required SINR can then be expressed as
req
=
γm,n
prx
m,n
= M N
Itot
m =1 n =1
n =n
ptx
m,n
ptx
m,n ·
pw
gm ,n (θm )
+
gm,n (θm )
gm,n (θm )
,
m = {1, 2, . . . , M }
n = {1, 2, . . . , N }
(6.14)
Chapter 6. Space-Time Processing for Interference
160
Mitigation in HAP WCDMA Systems
which can be formulated as
γireq =
ptx
i
K
k=1
n =n
ptx
k
,
pw
gk (θm )
+
·
gi (θm )
gi (θm )
m = {1, 2, . . . , M }
n = {1, 2, . . . , N }
i = 1 + (n − 1) + N (m − 1)
(6.15)
with K = M · N as the total number of users in all cells and pw is the additive
req
→ γireq , gm ,n (θm )
white Gaussian noise (AWGN) at the receiver, γm,n
tx
tx
→ gk (θm ), gm,n (θm ) → gi (θm ), pm ,n → pk are performed according to
the index mapping rules in equation (6.15). To solve for the transmitter power
ptx
k of each of the K individual UE simultaneously 6.14 can be reformulated
into a matrix form (see appendix C) as
ptx = (I − A)
−1
b,
(6.16)
where the calculated vector ptx contains the necessary transmitter power level
assigned to each of the K UE to fulfil the SINR requirement and where matrix
[A]K×K and vector [b]K×1 are defined as
[aik ]K×K = γireq ·
gk (θm )
gi (θm )
pw
,
gi (θm )
n = {1, 2, . . . , N } , i = 1 + (n − 1) + N (m − 1)
[aik ] = 0 for n = n,
m = {1, 2, . . . , M } ,
m = {1, 2, . . . , M } ,
for n = n and
[bi ]K×1 = γireq ·
n = {1, 2, . . . , N } ,
k = 1 + (n − 1) + N (m − 1)
(6.17)
Using the prx = g ptx , where denotes an elementwise multiplication
and g is the total channel gain vector [gk ]K×1 for all k = {1, 2, . . . , K} users,
then all elements in the vector prx for each block that contain the UE of each
of the M cells are balanced. The total cell interference can then be calculated
as
N
own
prx
m = {1, 2, . . . , M }
(6.18)
Im (θm ) =
m,n (θm ),
n=1
oth
(θm ) =
Im
M
N
m =1
m =m
n=1
prx
m ,n (θm ) + pw ,
m = {1, 2, . . . , M }
(6.19)
6.3. SIMULATION RESULTS
161
own
where pw is the thermal noise at the receiver, Im
(θm ) is the interference
oth
from the UE within the own cell m and Im (θm ) is the interference from the
UE in the M − 1 other cells where M is the total number of cells. We can
now calculate iU L (θm ) which defines the other to own interference ratio for
the uplink to HAP m and is given by
iU L (θm ) =
oth
Im
(θm )
.
own
Im (θm )
(6.20)
This is a performance measure of the simulated system capacity at a
specific elevation angle θm towards the HAP (see figure 6.1). If iU L (θm ) is
between zero and one there is possibility to have multiple HAP base stations
covering the same coverage area. The actual number of users that can access
the HAP base stations is also dependent of which data rate each user is using
for transmission.
6.3
Simulation Results
In this simulation we assume M HAPs uniformly located along a circular
boundary, with the centre of the circular boundary acting as the pointing
direction of the HAPs base station antennas which simulate several overlapping cells, see figure 6.1. The beamwidth of these base station antennas are
determined by the radius of the cell coverage area (see figures 6.1 and 6.3).
These results are acquired through running Monte Carlo simulations of
the multiple HAP system. The aim of the simulation is to assess the effect of
adding more HAPs on the system’s capacity and of the impact of using spacetime diversity techniques. The distance dm between the cell centre and the
vertical projection of the HAP on the earth’s surface is denoted as ”distance
on the ground” and is varied from 0 to 70 km with a fixed cell position,
as shown in figure 6.4. The distance to the cell centre is also changing the
elevation angle θm towards the HAP base station m as seen from the user.
The cell radius has been set to 10 km and 30 km, and the HAP altitude is 20
km. Each HAP base station serves 100 users within each corresponding cell.
From figure 6.5 it is clear that with the smaller cell radius (10 km) the
worst case scenario will occur when all the HAPs are stacked on top of each
other at 90 degrees elevation angle from the cell centre (i.e., at a distance dm
on the ground of 0 km). In the larger cell radius case (30 m) the worst case
scenario happens approximately at 30 km which is at the edge of the cell.
Chapter 6. Space-Time Processing for Interference
162
Mitigation in HAP WCDMA Systems
R
qm
dm
Figure 6.4: A plot illustrating the change of HAP position dm to create
different elevation angles θm .
Comparing the bottom diagram in figure 6.5 with the two diagrams in
figure 6.6, we can see that if we utilize a maximum allowed other-to-own
interference ratio equal to one, then as the service data rate decreases, the
number of possible HAP base stations covering the same area can increase
from 2-4 HAPs (depending on the distance dm between the cell centre and
the vertical projection of the HAP on the ground) for the combined service
(12 kbps and 384 kbps) to 6 HAPs with the same service (12 kbps on all
HAPs).
Next, we analyze the impact of different space-time diversity techniques
(SIMO and MIMO) on the possible number of HAPs that can coexist within
the same cell area and compare them to a single-input single-output (SISO)
system. From figure 6.7 it is obvious that using a space-time diversity
technique will enhance the interference mitigating capability and improve the
overall performance of the multiple HAP system. This interference mitigation
technique can also be interpreted as a capacity improvement, which is clearly
seen in figure 6.7 for a three HAP system and in figure 6.8 for a seven HAP
system. In both of these figures we can observe a decrease in the other-toown interference ratio as we use an increasing number of antennas at the
transmitter and receiver, which in turn will allow more HAPs to provide
wireless service to more users by utilizing the remaining degrees of freedom
of the system.
Comparing the graphs in figure 6.8, we can observe that a seven HAP
6.3. SIMULATION RESULTS
163
Figure 6.5: The performance of the voice service (12 kbps) from one HAP in
combination with the data service (384 kbps) on the remaining HAPs for cell
radius of 10 km (top) and 30 km (bottom). The distance on the ground dm
is varied from 0 to 70 km.
Chapter 6. Space-Time Processing for Interference
164
Mitigation in HAP WCDMA Systems
1.1
5 HAPs
4 HAPs
3 HAPs
2 HAPs
Other to Own interference ratio iul
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10
20
30
40
50
Distance on the ground [km]
60
70
1.4
6 HAPs
5 HAPs
4 HAPs
3 HAPs
2 HAPs
7 HAPs
Other to Own interference ratio iul
1.2
1
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
Distance on the ground [km]
60
70
Figure 6.6: The other to own interference ratio obtained for a 30 km cell
radius for: (top) the performance of the voice service (12 kbps) from one
HAP in combination with the data service (144 kbps) on the remaining HAPs
and (bottom) the performance when we have voice services (12 kbps) on all
HAPs. The distance on the ground dm is varied from 0 to 70 km.
165
6.3. SIMULATION RESULTS
1
SISO
1x2 SIMO
1x4 SIMO
2x2 MIMO
2x4 MIMO
4x4 MIMO
8x8 MIMO
Other to own interference ratio iUL
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
Distance on the ground dm [km]
70
80
Figure 6.7: The other to own interference ratio obtained for a 30 km cell
radius for: the performance of the voice service (12 kbps) from one HAP in
combination with the data service (384 kbps) on the remaining two HAPs and
utilizing different SISO, SIMO and MIMO space-time diversity systems. The
distance on the ground dm is varied from 0 to 70 km.
Chapter 6. Space-Time Processing for Interference
166
Mitigation in HAP WCDMA Systems
SISO
1x2 SIMO
2x2 MIMO
4x4 MIMO
8x8 MIMO
Other to own interference ratio i
UL
1.5
1
0.5
0
0
10
20
30
40
50
60
Distance on the ground d [km]
70
80
m
Figure 6.8: The other to own interference ratio obtained for a 30 km cell
radius for: the performance of the voice service (12 kbps) from one HAP in
combination with the data service (384 kbps) on the remaining six HAPs and
utilizing different SISO, SIMO and MIMO space-time diversity systems. The
distance on the ground dm is varied from 0 to 70 km.
6.4. CONCLUSIONS
167
system using SISO would not be possible due to the interference. However,
a SIMO diversity system (utilizing two receiving antennas at the HAP base
station) would make a seven HAP system possible. Adding more antennas at
the receiver and transmitter respectively will increase the number of possible
HAPs that can be used in the multiple HAP system. However, the benefit of
the diversity system will diminish even with increasing the number of antennas
beyond a certain limit. From figure 6.7 and figure 6.8 it is obvious that
this limit is obtained at approximately a 4x4 MIMO system, beyond which
diversity gain is negligible as is evident from the graph of the MIMO 8x8
system.
It is also clear from figure 6.6 that the worst case distance (highest
interference level) is at approximately 30 km, and consequently a worst case
elevation angle of 34 degrees. This maximum interference level depends on the
cell radius chosen for the HAP base station as shown in figure 6.9. Simulation
results show that for cell radii larger than 10 km the maximum interference
level will occur at the cell boundary.
6.4
Conclusions
In this chapter we have investigated the possibility of multiple HAP coverage
of a common cell area in WCDMA systems with and without space-time
diversity techniques and in particular we have studied the uplink. From
these simulations it is shown that as the service data rate decreases, the
number of possible HAP base stations that can be deployed to cover the same
geographical area increases. It has further been shown that this increment in
number of HAP base stations can be enhanced to some extent by using spacetime diversity techniques. We have also shown that the worst case position
of the HAPs is in the centre of the cell if the cell radius is small (≤ 20 km)
and at the cell boundary for large cells (≥ 20 km). We can conclude that
there is a possibility of deploying 3-5 (SISO), or 5-8 (1x2 SIMO, 2x2 MIMO
and 4x4 MIMO) HAPs covering the same cell area in response to an increase
in traffic demands, depending on the type of service used. There also appear
to be a limit on the number of HAPs that could be deployed using spacetime diversity techniques. Simulation results have shown that the maximum
number of HAPs that could be sustained is approximately eight when using
the voice services with 4x4 MIMO on all HAPs and users.
Chapter 6. Space-Time Processing for Interference
168
Mitigation in HAP WCDMA Systems
1
50 km
30 km
20 km
10 km
5 km
Other to Own interference ratio iul
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
Distance on the ground [km]
60
70
80
Figure 6.9: Illustrating the effect of HAP base station cell radius on
interference levels. A system of 3 HAPs is utilized here and a voice service
(12 kbps) from one HAP in combination with the data service (384 kbps) on
the other HAPs. The distance on the ground dm is varied from 0 to 70 km.
CHAPTER 7
COOPERATIVE SPACE-TIME PROCESSING
FOR POWER EFFICIENT WIRELESS
SENSOR NETWORKS
W
ireless Sensor Networks (WSN) have been attracting great attention
recently. They are relatively low cost to be deployed and to be used in
many promising applications, such as biomedical sensor monitoring (e.g., cardiac patient monitoring), habitat monitoring (e.g., animal tracking), weather
monitoring (temperature, humidity, etc.), low-performance seismic sensing,
environment preservation and natural disaster detection and monitoring (e.g.,
flooding and fire) [114–118].
The WSN applications analyzed in this chapter have a topology where
a large number of wireless sensor nodes are spread out over a large or
small geographic area (e.g., disaster regions, indoor factory, large sports
event areas, etc.). In this topology, an inefficient use of bandwidth and
transmitter power resources is resulted if each wireless sensor is transmitting
its measurement data to the base station (processing central). In this case,
each sensor node would have to be assigned its own frequency channel and,
if the base station is located a long distance from the sensor nodes, it would
also demand a higher than average sensor node transmitter power. By using
a coordinating cluster head, for each cluster of wireless sensor nodes, we can
instead use the combined transmitter power of the node cluster through the
use of beamforming to increase the transmitter-receiver separation and/or to
improve the signal-to-noise ratio (SNR) of the communication link. Another
Chapter 7. Cooperative Space-Time Processing for
170
Power Efficient Wireless Sensor Networks
advantage of using this cooperative transmission is that we can exert power
control to minimize the power consumption of each individual sensor node,
and thus maximizing network lifetime. In addition, in a cooperative network
the measurement data could be sent by using Time Division Multiplexing
(TDM) instead of Frequency Division Multiplexing (FDM) which improves
the overall bandwidth efficiency of the system. In this chapter, we propose
to use a cooperative beamforming approach in wireless sensor networks to
increase the transmission range, minimize power consumption and maximize
network lifetime. This will be of particular interest for outdoor applications,
especially when monitoring remote areas using aerial vehicles such as a High
Altitude Platform (HAP) or Unmanned Aerial Vehicle (UAV) as a platform
for the data collecting base station. We will investigate how the required
transmitter power of each sensor node is affected by the number of cooperating
transmission nodes in the network. In addition, we will also study if mitigation
of fixed interference can be achieved in this type of random antenna array
by exploiting ”null” directions in the beamforming pattern. Finally, we
present a comparison in the use of beamforming with the different forms
of diversity systems such as Multiple-Input Single-Output (MISO), SingleInput Multiple-Output (SIMO) and Multiple-Input Multiple-Output (MIMO)
for the same purpose of achieving a longer transmission distance (or range)
while maintaining a low energy consumption. Beamforming can of course be
interpreted as a form of MISO system although it differs from the normal
view of how a diversity system operates. This chapter is organized as follows:
Section 7.1 presents an overview and analysis of cooperative beamforming
using a large aperture random array. In section 7.2 is given a brief description
of MISO, SIMO and MIMO diversity schemes and analysis using the Rice
distributed fading channel model employed in the simulation. Section 7.3
present the numerical results of the simulated beamformer and MISO, SIMO
and MIMO diversity systems. Finally, section 7.4 list the concluding remarks.
7.1
Cooperative Beamforming
In this chapter we use the delay-and-sum beamforming technique which is the
oldest and simplest algorithm for Space-Time processing. This beamforming
is done through coherent excitation/reception of amplitude and phase of
the signal transmitted/received from each individual antenna element in a
collection or cluster of similar antenna elements also known as an antenna
array [119]. Antenna arrays can have different configurations (e.g. linear,
7.1. COOPERATIVE BEAMFORMING
171
planar, circular, triangular, rectangular or spherical etc.). Extensive research
has been done on uniform array beamforming using one (linear) or two
(planar) dimensional equi-distant element arrays [119–121]. In addition, there
is also work done on beamforming using circular, triangular and rectangular
arrays [1, 119].
The antenna array formed by the individual sensor node antennas is
assumed to be a planar array, of randomly positioned sensor node antennas,
which is parallel with the plane containing all sensor nodes so that the sensor
nodes are only extended in x and y direction and not in z direction. This
is a valid assumption in most cases since the elongation of the networks in z
direction in most cases is very small compared to the distance between the
network cluster and the base station we want to communicate with [124]. The
design of this type of cooperative array is similar to the design of large aperture
arrays where we have an inter-element spacing that is random and larger than
half the wavelength. There are no known simplifying techniques for synthesis
of randomly spaced arrays, like Schelkunoffs polynomial method [1, 119] or
the Fourier Transform method [1, 119]. In the random array all properties e.g
array pattern, beam width, sidelobe level and gain are stochastic variables.
In figure 7.1 we show a scenario with N = 50 sensor nodes deployed inside
a circular boundary in the x-y plane with the radius R. The distribution of
these sensor nodes is uniform and independent. The nth sensor then has the
polar coordinates (rn , φn ) .
The signal yn (t) at the array sensor node n can then be expressed as
yn (t) = s(t − α0 · x0 ),
(7.1)
where s(t) is the signal to be transmitted/received and the nth sensor at
location xn transmits/receives the electromagnetic signal yn (t). The slowness
vector α0 is the required delay for each sensor to steer the array in a specific
direction toward the signal source or target, and is defined as
α0 =
d0
c
(7.2)
where d0 is the direction of the wave propagation and c is the speed of light.
The total output of the delay-and-sum algorithm can be expressed by
z(t) =
N
−1
n=0
α − α0 )·x0 ),
wn s(t + (α
(7.3)
Chapter 7. Cooperative Space-Time Processing for
172
Power Efficient Wireless Sensor Networks
R
Figure 7.1: 50 sensor nodes positioned according to an independent uniform
distribution within a cluster area of radius R.
7.2. SPATIAL DIVERSITY TECHNIQUES
173
where wn is the amplitude weights of the array tapering and α is the slowness
vector for the direction of observation. If we assume that all the sensor
nodes are approximately located in the same plane (i.e. the x-y plane) and
the source/target is located at the spherical coordinates d0 = (d0 , φ0 , θ0 )
in the far-field, and we are transmitting a narrow band signal then we can
approximate (7.3) as (see appendix D)
G(φ, θ) =
N −1
rn
1
wn ejω(t− c (cos(φn )u+sin(φn )v) ,
N n=0
(7.4)
where u = sin(θ) cos(φ)−sin(θ0 ) cos(φ0 ) and v = sin(θ) sin(φ)−sin(θ0 ) sin(φ0 )
for the direction of the incoming/outgoing wave (φ0 , θ0 ) and the direction of
observation (φ, θ). The function G(φ, θ) is then one ensemble of the array
amplitude gain function for one set of stochastic sensor locations. To find
the ensemble mean of the array amplitude gain functions we assume an
independent uniform distribution of the sensor locations within the radius
R,
(7.5)
E{G(φ, θ)} =
G(φ, θ)pR,φ (rn , φn ),
where pR,φ (rn , φn ) is the probability density function (PDF) of the sensor
locations.
In figure 7.2 we show the absolute squared average array gain function
|E{G(φ, θ)}|2 of 250 realizations of the array amplitude gain function G(φ, θ),
and in figure 7.3 we show the standard deviation for the distribution of the
amplitude sidelobe levels. From figure 7.2 we can also estimate a mean
sidelobe level that will converge toward ≈ −17 dB which is consistent with the
theoretical value, N −1 . The average signal to noise ratio of the array is defined
as SN Rarray = SN Rnode · G(φ, θ) which means that the array average SNR is
SN Rarray = N · SN Rnode when we are aiming the array toward the incoming
assumed plane wave. The SN Rarray is a Gaussian distributed parameter with
a mean of 17 dB, and a 95% confidence that the SNR of the array will be
higher than 7 dB.
7.2
Spatial Diversity Techniques
Another recently popular technique to improve the signal to noise ratio of the
long range transmission is to use some form of spatial diversity technique like
Multiple-Input Single-Output (MISO), Single-Input Multiple-Output (SIMO)
Chapter 7. Cooperative Space-Time Processing for
174
Power Efficient Wireless Sensor Networks
Figure 7.2: A plot showing a small part around the main lobe of the
absolute squared average array pattern of 250 realizations of the random
sensor locations.
Normalized Array Gain G
0.8
0.6
+ Standard deviation
Mean Gain
0.4
0.2
0
ï0.2
ï0.4
170
ï Standard deviation
175
180
185
Array aiming direction q0 [deg]
190
Figure 7.3: A cross-section of the main lobe of all 250 realizations of the array
amplitude gain pattern.
7.2. SPATIAL DIVERSITY TECHNIQUES
175
or Multiple-Input Multiple-Output (MIMO) antenna system. In the following
analysis of these diversity techniques we are assuming a perfect knowledge of
the propagation channel.
7.2.1
Cooperative MISO and SIMO
Consider a frequency flat fading propagation model with Ntx antenna elements
at the transmitter and one antenna element at the receiver. To take full
advantage of the antenna transmit diversity we send multiple weighed copies
of the signal sample through all the transmitting antenna elements. The
received baseband signal sample can then be expressed as
+
r[m] =
L−1
Es
hl wl s[m] + n[m],
Ntx
(7.6)
l=0
where r[m] ∈ C is the received sample, s[m] ∈ C is the transmitted sample
and n[m] is a noise sample with n[m] ∼ CN (0, σn2 ). The coefficient wl is the
channel weight for channel l and Es is the transmitted average symbol energy.
This can be expressed in vector notation as
+
Es
hws + n,
(7.7)
r=
Ntx
where h ∈ CNtx ×1 is the frequency flat fading channel vector with a Rice
distribution. The normalized Rician channel vector h can then be defined
as [125]
√
√
(7.8)
h c1 l + c2 Rtx hn ,
where l is the line of sight (LOS) component represented as a mean value
that satisfies the condition |l|2 = Ntx , and Rtx is the transmit correlation
vector. Rtx is assumed to be positive definite full rank matrix. hn ∼
CN Ntx (0Ntx , 1Ntx ) is a complex valued Gaussian vector representing the non
line of sight (NLOS) component. The coefficients c1 = K/(K + 1) and
c2 = 1/(K + 1) are normalizing factors, where K is the Rice factor which
represents the power ratio between the LOS and NLOS components. The
weight vector w that maximizes the received SNR is given by
w=
hH
,
Ntx
h
(7.9)
Chapter 7. Cooperative Space-Time Processing for
176
Power Efficient Wireless Sensor Networks
which is the transmit maximum ratio combining (MRC) method and is also
known as matched beamforming.
The SNR of the received signal can then be expressed as
γrx =
Es · |h|2
.
N0
(7.10)
The second type of spatial diversity is receive diversity in which we
are utilizing a single input multiple output (SIMO) frequency flat fading
propagation channel model with Nrx receiving antenna elements and a single
transmitting antenna element. To fully exploit the receive diversity we will
receive multiple copies of the transmitted signal through all the Nrx receiving
antenna elements. The received baseband signal sample can then be expressed
as
+
L
L
Es
(wl hl )s[m] +
wl nl [m],
(7.11)
r[m] =
Nrx
l=1
l=1
where rl [m] ∈ C is the received sample from receiving antenna element l ,
s[m] ∈ C is the transmitted sample and nl [m] is a noise sample at receiving
antenna element l with nl [m] ∼ CN (0, σn2 ). the coefficient wl is the channel
weight at receiving antenna element l and Es is the transmitted average
symbol energy. This can be expressed in vector notation as
(7.12)
r = Es wH hs + wH n,
where h ∈ CNtx ×1 is the frequency flat fading channel vector with a Rice
distribution. The normalized channel vector h can then be defined as [125]
h
√
c1 l +
√
c2 Rrx hn ,
(7.13)
where l is the line of sight (LOS) component represented as a mean value
that satisfies the condition |l|2 = Nrx , and Rrx is the receive correlation
vector. Rrx is assumed to be a positive definite full rank matrix. hn ∼
CN Nrx (0Nrx , 1Nrx ) is a complex valued Gaussian vector representing the non
line of sight (NLOS) component. The weight vector w that maximize the
received SNR at each antenna element is given by
w=
Nrx
hH
.
h
(7.14)
7.2. SPATIAL DIVERSITY TECHNIQUES
177
The SNR of the received signal after we have performed a maximum ratio
combining (MRC) can then be expressed as
γrx =
7.2.2
Es · |h|2
.
N0
(7.15)
Cooperative MIMO
By combining the MISO and SIMO diversity techniques we create a system
of (Ntx and Nrx ) transmitting and receiving antenna elements respectively.
If we consider a frequency flat fading (Ntx × Nrx ) MIMO propagation model
the received signal can be written in vector notation as
+
Es H
w Hwtx s + wrx n.
(7.16)
r=
Ntx rx
In the MIMO case the Rice distributed channel matrix H can be derived
as
H
1
1
√
√
2
2
c1 L + c2 Rrx
Hn Rtx
,
(7.17)
where L represents the LOS component and is the arbitrary rank mean value
matrix with the condition that Tr(LLH ) = Nrx · Ntx , Rrx and Rtx are the
correlation matrices on the transmitter and receiver side respectively. Hn ∼
CN Nrx ,Ntx (0Nrx ×Ntx , INrx ⊗ INrx ).
To maximize the combined SNR at the receiver antenna elements we maximize
1 H
12
Hwtx 1
Es 1wrx
·
.
(7.18)
γrx =
N0 Ntx wrx 2
γrx is then maximized when wrx and wtx /Ntx are equal to the singular input
and output vectors of the channel matrix H corresponding to the maximum
singular value of the channel matrix H. Equation 7.16 can then be written as
(7.19)
r[m] = Es σmax s[m] + n[m].
where σmax is the maximum singular value of the channel matrix H and since
2
is the same as the maximum eigenvalue λmax of HHH we can now
σmax
express the received SNR of the MIMO diversity technique as
γrx =
Es
· λmax .
N0
(7.20)
Chapter 7. Cooperative Space-Time Processing for
178
7.3
Power Efficient Wireless Sensor Networks
Simulation Results
If we consider a base station mounted on an aerial platform such as a
HAP or a UAV to collect data from remote sensor networks then the
amount of obstructions in the transmission path would depend on the type
of environment at the sensor locations, although it can still generally be
assumed that the number of obstructions will increase with a decreasing
antenna elevation angle. Therefore the propagation effect of the change in
elevation can be translated into a change of the Rice distribution K-factor.
In the presented
simulations, the Rician K-factor was varied over an
interval of K ∈ 1 · 10−8 , 1 · 10+8 , where the low value represents a channel
with no LOS component and very little correlation between the different
signal paths and therefore resembles a Rayleigh fading channel. When the
Rician K-factor is gradually increased the correlation between the signal
paths will increase and the Direction of Departure/Direction of Arrival of
the signals will narrow into a smaller and smaller angular sector, until the
K-factor asymptotically goes toward infinity and all signal paths will be
correlated and pointing in the same direction. In figure 7.4 we see the
comparison between the ordinary random array beamformer performance and
the MISO/SIMO diversity systems performance. Inspecting figure 7.4, we
can see that the MISO/SIMO diversity system seems to maintain a constant
low node transmitter power Ptx even in a NLOS scenario by spreading the
energy over multiple paths instead of transmitting it all in one direction.
Furthermore, we can see from figure 7.4 that if the distance between the
transmitting nodes and the basestation is increased from 1 km to 10 km, the
nodes need a 100 fold increase of the total transmitted power to maintain the
same capacity. This is independent of whether we are using the nodes as a
beamforming array or a diversity system, which is consistent with the inverse
square law of the free space loss. If we now increase the number of receiving
antenna nodes to be equal to the number of transmitting antenna nodes we get
a 50 × 50 MIMO system which will increase the array and diversity gains even
further. This effect can clearly be seen in figure 7.5 where the performance
of the MIMO system outperforms the other systems in both LOS and NLOS
scenarios.
179
7.3. SIMULATION RESULTS
4
10
Required node transmitter power Ptx [W]
Array ï Node Ptx at 10 km receiver distance
Array ï Node Ptx at 1 km receiver distance
2
10
MISO ï Node Ptx at 10 km receiver distance
MISO ï Node Ptx at 1 km receiver distance
0
10
ï2
10
ï4
10
ï6
10
ï8
10
ï80
ï60
ï40
ï20
0
20
40
Riceïfactor 10 u log10 ( K ) [dB]
60
80
Figure 7.4: Comparison between of the Array Beamformer and MISO/SIMO
system for different K-factor values at two different distances from the base
station of 10 km and 1 km, respectively.
8
10
Required node transmitter power Ptx [W]
SISO ï Node Ptx
Array ï Node Ptx
6
10
MISO/SIMO ï Node Ptx
MIMO ï Node Ptx
4
10
2
10
0
10
ï2
10
ï4
10
ï80
ï60
ï40
ï20
0
20
40
Riceïfactor 10 u log10 ( K ) [dB]
60
80
Figure 7.5: Performance of the Array Beamformer, MISO/SIMO and MIMO
systems for different K-factor values and compared with a single antenna SISO
system.
Chapter 7. Cooperative Space-Time Processing for
180
7.4
Power Efficient Wireless Sensor Networks
Conclusions
In this chapter we have investigated how the required transmitter power
of each sensor node is affected by the number of cooperating transmission
nodes in a traditional random beamformer array. Due to the randomness
of the sensor node positions there is no simple algorithm for mitigation of
interference from a fixed direction. This is because the sidelobe levels and
the sidelobe positions are random. A comparison in the use of beamforming
with diversity systems such as MISO/SIMO and MIMO for the same purpose
of achieving a longer transmission distance or maintaining a low energy
consumption. It is clear from these investigations that the MISO/SIMO
and MIMO diversity systems are superior in performance to both the SISO
link and the traditional form of array beamforming, especially when the LOS
component is small or non-existent. The best performance though, is given
by the MIMO system where we have multiple antenna nodes on both the
transmitting and receiving end of the link. Even one extra antenna at the
receiving basestation will increase the performance of the system two-fold in
a LOS scenario and give an improved performance in NLOS as well.
CHAPTER 8
CONCLUSIONS
T
his thesis has presented an extended scope of space-time processing
by proposing novel applications in a variety of wireless communication
systems. These have included increasing the spectral efficiency of satellite
and high altitude platform (HAP) communication systems, enhancing link
quality for Bluetooth links in indoor office environments, reduction of
possibly harmful electromagnetic radiation from mobile phones, enhancing the
coverage and capacity of integrated multiple-HAP 3G systems, and improving
the energy efficiency of cooperative wireless sensor networks (WSN).
• In chapter 2 we proposed a novel multiple antenna channel model and
associated simulator which takes into account the spatial, temporal and
polarization (STP) properties affecting signal transmission in wireless
communications. In addition, we presented the theoretical background
and analysis, features and properties, and implementation of the
proposed STP channel simulator. Further, we tested the simulator for
various propagation conditions. The results of the simulator have shown
good agreement with the theoretical ones. We have also investigated
the impact of depolarization on the probability distributions of the
simulated signals and their adverse effect on performance. The proposed
STP simulator was employed in chapter 3 to investigate the performance
of satellite and high altitude platform communication links.
• In chapter 3 we investigated the potential gain of using a MIMOOFDM antenna system in combination with platform diversity in
182
Chapter 8. Conclusions
order to increase the capacity of satellite and high altitude platform
communication systems. Simulation results have shown that the
platform diversity system provides superior performance as compared
to the single platform system and that by careful design of the 3D
MIMO antenna array we can create independent space-polarization
sub-channels for increasing the capacity through multiplexing. In
addition, a novel multi channel fading simulator which takes into account
the temporal, spatial and polarization properties experienced by these
systems was developed and tested in different propagation scenarios.
• Chapter 4 investigated the wave propagation effects of a short-range
wireless device, such as the Bluetooth technology. Specifically, we
assessed the fading phenomenon for Bluetooth link in an indoor office
environment by simulation of different propagation scenarios and used
measurement results to confirm our findings. The investigations were
carried out using FEM to model the electromagnetic wave propagation
for NLOS and LOS propagation scenarios. The measurement trails
and simulations were shown to be in good agreement. This was also
confirmed by comparison with the theoretical statistical probability
distribution of the signal in both scenarios. A power-distance exponential propagation law was found to be sufficient to describe the
propagation for corridors (where a wave guide phenomena was observed)
and through office walls. In addition, we investigated a diversity system
utilizing different combining techniques in spatial diversity and spatial
multiplexing schemes, and assessed their performance over a fading
radio channel in a NLOS propagation environment. Our results show
a substantial gain is achieved by using a MIMO spatial multiplexing
system.
• In chapter 5 we presented a FEM model which simulate a physical
MIMO antenna system which is controlled by various adaptive signal
processing algorithms in order to suppress the electromagnetic field
at a certain volume in space. We have also presented the solution
for constraining the total output power of the system to a predefined
level. Further, we have investigated the effects of the size and number
of MIMO antenna elements on the performance of the system and
also tested the algorithms at different carrier frequencies. The SAR
attenuation levels achieved from these simulations suggest the possibility
of using an active antenna system for the reduction of electromagnetic
field density. However, our result also show some limitations associated
183
with implementing these antenna arrays in mobile phones, for which
further research is needed to find practical solutions.
• In chapter 6, we investigated the possibility of multiple HAP coverage
of a common cell area in WCDMA systems with and without space-time
diversity techniques and in particular we have studied the uplink. From
the simulations we have shown that as the service data rate decreases,
the number of possible HAP base stations that can be deployed to cover
the same geographical area increases. It has further been shown that
this increment in number of HAP base stations can be enhanced by using
space-time diversity techniques. It was also concluded that there is a
possibility of deploying 3-5 (SISO), or 5-8 (1x2 SIMO, 2x2 MIMO and
4x4 MIMO) HAPs covering the same cell area in response to increase
traffic demands, depending on the type of service used. Simulation
results have also shown the limit on the number of HAPs that could be
deployed using space-time diversity techniques.
• Finally, in chapter 7 we have investigated how the required transmitter
power of each sensor node in a WSN could be improved upon by
using cooperating transmission nodes either as a traditional random
beamformer array or as a diversity system. A comparison between the
diversity systems (MISO, SIMO and MIMO) with the beamformer for
the purpose of achieving a longer transmission distance or maintaining a
low energy consumption was performed. Simulation results have shown
that the diversity systems are superior in performance to both the SISO
link and the traditional form of array beamforming.
This thesis has clearly shown the varied applications of space-time processing
in wireless communication systems, and the broad range of ways they play in
improving the performance and economics of these systems. This is the reason
why space-time processing is seen as one of the main critical components in
future wireless communication systems. Consequently, further research into
these applications and other applications is still necessary in order to optimize
energy efficiency, capacity, coverage and quality of these systems.
184
Chapter 8. Conclusions
APPENDIX A
SPHERICAL VECTOR HARMONICS
APPENDIX
A.1
187
Spherical Vector Harmonics
The spherical vector harmonics are defined for l > 0 as:
⎧
⎪
lm (θ, φ)
lm (θ, φ) = 1
⎪
LY
(TE-multipole)
⎪X
⎨
l(l + 1)
1
⎪
⎪X
ˆ
lm (θ, φ) (TM-multipole)
⎪
LY
⎩ lm (θ, φ) = r ×
l(l + 1)
(A.1)
= −jr×∇ is an angular momentum operator borrowed from quantum
where L
physics. Ylm is the scalar spherical harmonics and is a function of the angular
spherical coordinates θ and φ.
1
Plm (cos θ)ejmφ
Ylm (θ, φ) = √
2π
(A.2)
where Plm is the associated Legendre function of the first kind, degree l, order
1
m and normalized to unity −1 (Plm (x))2 dx = 1.
Plm (cos θ) = sinm θ
dm
Pl (cos θ)
d(cos θ)m
(A.3)
where Pl is the Legendre polynom.
The vector spherical harmonics form a complete orthonormal set for
tangent vector fields on the spherical surface. This describes the tangential
behavior of the solution of Helmholtz equation obtained by separation of
variables in a spherical coordinate system.
⎧
lm (θ, φ)
(TE-modes)
⎨ η0 gl (kr)X
(A.4)
⎩ jη0 ∇ × fl (kr)X
lm (θ, φ) (TM-modes)
k
where k is the wave number, fl (kr) and gl (kr) are spherical Hankel functions
fl = jl ± jyl with jl being the spherical Bessel function and yl the spherical
Neuman function.
A vector field satisfying the homogenous vector Helmholtz equation in a
spherical shell can be written as a weighted sum of the TE and TM modes
(
'j
lm ) + aM (l, m)gl (kr)X
lm
= η0
aE (l, m)(∇ × fl (kr)X
(A.5)
E
k
l,m
188
A.1. SPHERICAL VECTOR HARMONICS
A similar derivation can be formed for the magnetic vector field.
The weights aE (l, m) for the electric multipole moments and aM (l, m)
for the magnetic multipole moments can be evaluated by making use of the
orthogonality property of the spherical harmonics [2, 3]
∗ ·E
dΩ
(A.6)
aE (l, m)jl (kr) = X
lm
where we get the electric multipole weight aE (l, m) by projecting the electric
far-field of the antenna on to the vector spherical harmonics. This results
lm is for a
in the weight aE (l, m) expressing how strong a certain mode X
particular antenna far-field pattern. The magnetic multipole weight aM (l, m)
is derived in a similar manner. For simplicity we are using an asymptotic
far-field approximation of these multipole weights [2, 3].
⎧
1
k
⎪
∗
dΩ
⎪
Ylm
(l,
m)f
(kr)
≈
·
(θ, φ) r · E
a
⎪ E
l
⎨
η0
l(l + 1)
(A.7)
k
⎪
∗
⎪
⎪
Ylm (θ, φ) r · H dΩ
⎩ aM (l, m)gl (kr) ≈ −
l(l + 1)
APPENDIX B
ANTENNA TYPES
APPENDIX
B.1
Antenna types
Figure B.1: Antenna type: Half wave model 1
Figure B.2: Antenna type: Half wave model 2
Figure B.3: Antenna type: Half wave model 3
191
192
B.1. ANTENNA TYPES
Figure B.4: Antenna type: Quarter wave model 2
Figure B.5: Antenna type: Quarter wave model 1
APPENDIX C
WCDMA POWER CONTROL
195
APPENDIX
C.1
WCDMA Power Control
Derivation of Equation (6.16):
Equation (6.14) can be reformulated by multiplying with the expression
of the total interference on both sides of the equation
⎡
⎤
γireq
K
⎢
pw ⎥
gk (θm )
⎢
⎥ = ptx
+
ptx
k ·
i .
⎣
gi (θm )
gi (θm ) ⎦
(C.1)
k=1
n =n
Multiplying each term inside the brackets with γireq will then yield
K
γireq ·
k=1
n =n
gk (θm ) tx
pw
· pk + γireq ·
.
gi (θm )
gi (θm )
(C.2)
Substituting each term with an indexed variable according to
gk (θm )
gi (θm )
pw
req
,
= γi ·
gi (θm )
[aik ]K×K = γireq ·
[bi ]K×1
for n = n
and, [aik ] = 0
for n = n
(C.3)
will simplify Equation (C.2) into
K
tx
ai,k · ptx
k + bi = p i ,
(C.4)
k=1
n =n
By identifying
K
k=1
n =n
ai,k · ptx
k as a matrix multiplication we can now write
Equation (C.4) in matrix form as
A · ptx + b = Iptx .
(C.5)
Rearranging Equation (C.5) we now solve for the necessary transmitter
power ptx to fulfil the required SINR for a particular quality of service.
ptx = (I − A)
−1
b
(C.6)
196
C.1. WCDMA POWER CONTROL
APPENDIX D
BEAMFORMING
APPENDIX
D.1
199
Beamforming
Derivation of Equation (7.3):
The slowness vector α in (7.2) is defined as
α=
d
.
c
(D.1)
The d vector represents the direction of observation and can be expressed in
cartesian coordinates as
d = d · {− sin(θ) cos(ϕ), − sin(θ) sin(ϕ), cos(θ)} .
(D.2)
Assuming that the sensor nodes are only distributed in the x − y plane. In
addition, if we assume a farfield plane wave solution, then the individual
propagation induced time delay ∆tn is calculated from the slowness vector α
and the position vector xn of each node n as
rn
(− sin (θ) cos (ϕ) cos (ϕn ) − sin (θ) sin (ϕ) sin (ϕn ) − 0)
c
(D.3)
rn
(D.4)
∆tn = − (sin(θ) cos(ϕ − ϕn ))
c
The actual direction of propagation d0 is used to calculate the slowness vector
α0 of the centre point of the array
∆tn = α · xn =
∆t0 =
rn
(sin(θ) cos(ϕ0 − ϕn ))
c
(D.5)
Substituting (D.4) and (D.5) into (7.3) results in
z(t) =
N
−1
n=0
wn s(t −
rn
((sin(θ) cos(ϕ − ϕn )) − (sin(θ) cos(ϕ0 − ϕn )))). (D.6)
c
Denoting u = sin(θ) cos(φ) − sin(θ0 ) cos(φ0 ), v = sin(θ) sin(φ) − sin(θ0 ) sin(φ0 )
and assuming a sinusoidal signal s(t), (D.6) can be expressed as a time
harmonic solution,
G(φ, θ) =
N −1
rn
1
wn ejω(t− c (cos(φn )u+sin(φn )v) .
N n=0
(D.7)
200
D.1. BEAMFORMING
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Wireless mobile communication networks are
rapidly growing at an incredible rate around the
world and a number of improved and emerging
technologies are seen to be critical to the improved economics and performance of these networks. The technical revolution and continuing
growth of mobile radio communication systems
has been made possible by extraordinary advances
in the related fields of digital computing, highspeed circuit technology, the Internet and, of
course, digital signal processing. Improved third
generation (3G) and future generation wireless
communication systems must support a substantially wider and enhanced range of services with
respect to those supported by second generation
and basic 3G systems. The never-ending quest for
such personal and multimedia services, however,
demands technologies operating at higher data rates and broader bandwidths. This combined with
the unpredictability and randomness of the mobile propagation channel has created many new
technically challenging problems for which innovative, adaptive and advanced signal processing
techniques may offer new and better solutions.
Space-time processing techniques have emerged
as one of the most promising areas of research
and development in wireless communications
for the efficient utilization of the physical mobile
radio propagation channel. Space-time processing signifies the signal processing performed on
a system consisting of several antenna elements,
whose signals are processed adaptively in order
to exploit both the spatial (space) and temporal
(time) dimensions of the radio channel. This can
significantly improve the capacity, coverage, quality
and energy efficiency of wireless systems.
This thesis expands the scope of space-time processing by proposing novel applications in wireless communication systems. These include the
reduction of possibly harmful electromagnetic radiation from mobile phones, enhancing the quality
of Bluetooth links in indoor office environments,
increasing the spectral efficiency of satellite and
the novel high altitude platforms (HAPs) communication systems, enhancing the coverage and
capacity of integrated multiple-HAP 3G systems,
and improving the energy efficiency of cooperative wireless sensor networks. The performance
of these systems is assessed by theoretical analysis, by computer simulations under a range of propagation environments including realistic channel
models, advanced commercial electromagnetic
modeling software, and a proposed novel multichannel simulator suitable for various space-time
applications.
space-time processing
applications for wireless communications
ABSTRACT
Tommy Hult
View publication stats
ISSN 1653-2090
ISBN 978-91-7295-146-4
2008:12
2008:12
space-time processing applications
for wireless communications
Tommy Hult
Blekinge Institute of Technology
Doctoral Dissertation Series No. 2008:12
School of Engineering
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