Adaptive Resource Allocation in MIMO-OFDM Communication System

IJSRD - International Journal for Scientific Research & Development| Vol. 1, Issue 7, 2013 | ISSN (online): 2321-0613
All rights reserved by www.ijsrd.com 1456
Abstract— Multiple Input and Multiple Output (MIMO) and
Orthogonal Frequency Division Multiplexing (OFDM)
system have the potential to achieve very high capacity
depending on the propagation environment. The objective of
this paper is the adaptive resource allocation in MIMO-
OFDM system using the waterfilling algorithm. Water
filling solution is implemented for allocating the power in
order to increase the channel capacity. The total system
capacity is maximised subject to the constraints on total
power, signal to noise ratio, and proportional fairness.
Channel is assumed as a flat fading channel and the
comparison is made for different 2×2, 2×3, 3×2 and 4×4
MIMO-OFDM systems using waterfilling algorithm with
allocated power. Also in order to prove that the MIMO-
OFDM with waterfilling algorithm provides the best
performance a comparison with various SISO –OFDM is
done
Keywords: OFDM, MIMO, Water filling algorithm channel
capacity, signal to noise ratio (SNR), power allocation
I. INTRODUCTION
Wireless communications, is by any measure, the fastest
growing segment of the communications industry. Cellular
systems have experienced exponential growth over the last
decade. Taking advantage of existing technologies and
discovery of new technologies that supports high data rates
are being carried out all over the world to meet the customer
demands. The next generation wireless network will be
required to support a wide range of high data rate
application ranging from video transfer to file download.
Two technologies which have gained much interest for
development in these future networks are the use of
Multiple-Input Multiple-Output (MIMO)systems which
utilize multiple antennas at the transmitter and receiver, and
Orthogonal Frequency-Division Multiplexing (OFDM).
High rate transmission is limited in part by frequency
selective fading and multipath propagation which give rise
to problems such as inter symbol interference (ISI).
The use of MIMO in wireless channels has been shown to
give a large increase in capacity [1]. It is especially useful in
mobile networks due to its ability to use multipath
propagation (a rich scattering environment) to its advantage.
By transmitting using spatial multiplexing the number of
users that can be serviced using a single base transceiver
station (BTS) can also be increased. OFDM is a modulation
technique that splits a given frequency-selective broadband
channel into a large number of flat-fading sub channels and
has received attention due its ease of equalization and
resistance to ISI. It is used in protocols for wireless network
systems such as IEEE802.16a.
In general, a lot of paths are arrived at the receiver in
wireless communications. In the time-domain signal
processing, the complexity for the multi-path equalization is
exponentially increased as the number of paths increases.
Therefore, if the complexity is limited, the performance is
degraded by the residual inter-symbol interference (ISI). On
the other hand, the multi-path fading is changed as a flat
fading on each subcarrier of OFDMA because OFDMA
consists of narrow-band subcarriers, and a cyclic condition
is satisfied by a guard interval insertion. Then, a severe
multipath fading can be equalized linearly in the frequency
domain in OFDMA and no ISI appears. By this property,
OFDMA is often used for transmission in the severe
multipath fading channel compared with FDMA (frequency
division multiple access) or TDMA (time division multiple
access) which have relatively wide bandwidth. In addition,
each subcarrier can flexibly be allocated to users according
to their instantaneous channels. This flexible subcarrier
allocation enables a larger channel capacity of the system,
and it is suitable to combine OFDMA with MIMO (multiple
input multiple output) which also aim at a capacity
enhancement. But also introduces new problems relating to
how these frequency and space sub channels are efficiently
divided among users. The allocation of space and frequency,
along with time, power and bits, is known as resource
allocation and is a vital part of designing networks [2],
[3].The focus of this paper is to increase the capacity of the
MIMO-OFDM communication system. To increase the
capacity a water filling algorithm is introduced in the
system. And to prove that MIMO with water filling is best, a
comparison with various SISO and MIMO systems are
done.
This paper is organized as follows: Section II includes
related works. Section III describes the concept of SVD and
Section IV describes the concept of waterfilling theorem.
Section V presents the experimental results and discussion.
Section VI gives the snapshot description. The paper is
concluded in section VII
II. RELATED WORK
Two classes of optimization techniques have been proposed
in SISO/MIMO-OFDMA literature: margin adaptive (MA)
[4] and rate adaptive (RA) [5]. The margin adaptive
objective is to achieve the minimum overall transmit power
at the Base Station (BS). The rate adaptive objective is to
maximize each user error-free capacity with a total transmits
power constraint. In [5], the margin adaptive resource
apportionment was tackled. In [6], the rate adaptive problem
was probed, wherein the destination was to maximize the
total data rate over all users subject to power and BER
constraints. Then, this was extended in [7] to achieve almost
idea proportional rate distribution. For such a system, in [8]
a lower complexity has been formulated and in [7] a priority
based sequential scheduling criteria to enhance system
Adaptive Resource Allocation in MIMO-OFDM Communication
System
Saleema N. A.1
1
PG Scholar, Dept. Of Electronics and communication Engineering
1
KMEA Engineering College, Ernakulum, Kerala, India

Adaptive Resource Allocation in MIMO-OFDM Communication System
(IJSRD/Vol. 1/Issue 7/2013/0019)
capacity with largely reduced fairness has been introduced.
The tradeoff between capacity and fairness has been
discussed in [4]. But, these algorithms hardly ever consider
rate fairness among users or do not have a flexible
controllability on rate fairness. In [19], the system capacity
is maximized by subcarrier reorganization with a total
power constraint. However in [9], BER constraint is not
taken into account, which is a main parameter in deciding
the efficiency of the resource apportionment scheme. It will
be desirable in many applications to have a tradeoff strategy
between capacity and fairness for lending wireless
resources.
III. SINGULAR VALUE DECOMPOSITION
The SVD technique decouples the channel matrix in spatial
domain in a way similar to the DFT decoupling the channel
in the frequency domain. The channel matrix H is the T x R
channel matrix. If H has independent rows and columns,
SVD yields:
H = U∑Vh
Where U and V are unitary matrices and Vh is the hermitian
of V. U has dimension of R x R and V has dimension of T x
T. Σ is a T x R matrix. If T = R, then Σ become a diagonal
matrix. If T > R, it is made of R x R diagonal matrix
followed by T – R zero columns. If T < R, it is made of T x
T diagonal matrix followed by R – T zero rows. This
operation is called the singular value decomposition of H
In case, where T ≠ R, The number of spatial channels
become restricted to the minimum of T and R. If the number
of transmit antennas is greater than the receive antennas (T
> R), U will be an R x R matrix, V will be a T x T matrix
and Σ will be made of a square matrix of order R followed
by T-R zero columns[10]
IV. CONCEPT OF WATERFILLING ALGORITHM
Waterfilling is a metaphor for the solution of several
optimization problems related to channel capacity. The
simplest physical example is perhaps the case of spectral
allocation for maximal total capacity under a total power
constraint [12].
Many engineering problems that can be formulated as
constrained optimization problems result in solutions given
by waterfilling structure the classical example of which is
the capacity achieving solutions for the MIMO channel. The
problem of jointly designing the transmitter and the receiver
for communication through MIMO channel also results in a
Waterfilling solution. The well – known classical
waterfilling solution solves the problem of maximizing the
mutual information between the input and the output of a
channel composed of several sub channels ( such as a
frequency – selective sub channels arising from the use of
multiple antennas at both sides of the link ) with a global
power constraint at the transmitter. This capacity –
achieving solution has the visual interpretation of pouring
water over a surface given by the inverse of the sub channel
gains hence the name waterfilling or waterpouring [12].
A. Water filling capacity of MIMO channel
When the channel knowledge is absent at the transmitter, the
individual sub channels are not accessible. So the equal
power allocation in all the sub channels is logical under this
scenario. When the transmitter has perfect knowledge of the
channel, the waterfilling method theorem so the division of
total power in such a way that a greater portion goes to the
sub channels with higher gain and less or ever none to the
channels with small gains.
The sub channels with lower gain i.e. those with higher
noise for which no power is allocated at all refer to those
sub channels which are not used for transmitting any signal
during the transmission. One objective of this algorithm is to
allocate power across the channel so as to maximize the
total capacity. This power allocation is subject to the
constraint that the sum of the power poured into all sub
channels is equal to PT, the total power available to the
transmitter. The relative channel strengths and the amount of
power to allocate to each channel is determined by
knowledge of the channel matrix, H.
We use the Eigen decomposition of H to obtain as,
H(r-by-t) = UDV+
Where, UU+
= Ir = VV+
= It
D = diagonal matrix λ1, λ2, λ3…λn with λi as the positive
square root of ith eigen value and i =1 to n non zero ƛ
values.
The first step is to determine the parameter μ. The parameter
μ, is a mathematical parameter, used to determine the power
assigned to each of the sub channels of the composite
MIMO channel. After determining the μ, the square of the
inverse of Eigen values are compared with μ.
If the square of the inverse of ith Eigen value is greater than
μ, i.e if 1/λ-2 ≥ μ, then that ith eigen channel is too weak to
be used for the communication process. The last two sub
channels in the above illustrated example of a (7 – by – 7)
MIMO channel are such eigen channels which are not used
for transmitting any signal at that point of time. Such
channels are said to be switched off and they are put away
from the communication process which means that those
particular sub channels are not allocated with any
transmitting power.
Once the total available power, PT and the gains of the
parallel sub channels are known, the optimum power
allocated to the ith sub channel is,
If this quantity Pi is positive then the power is allocated to
the ith sub channel otherwise, the sub channel is left unused.
The waterfilling parameter „μ‟ is determined iteratively by
the total power pt , such that μ satisfies the following
equation,
I= 1,2,…..m; where m is the number of sub channels that
have survived after checking the above conditions and are to
be used for transmission of the signal. Now the capacity of
MIMO channel with waterfilling can be expressed as
Above equation enables the visualization of the MIMO
channel as a number of parallel SISO pipes with gain equal.
Therefore to the respective Eigen values and its enables as

to understand that the waterfilling capacity for MIMO
channels is the sum of the capacities of the SISO equivalent
parallel sub channels, obtained from performing SVD on
MIMO channel matrix. If the channel is known at the
transmitter, the capacity can be enhanced by using the good
channels i.e. those with the highest gain by applying an
unequal power distribution.
B. Step to power allocation with waterfilling algorithm
Summary of steps involved in the waterfilling power
allocation to the MIMO subchannels [12]
1. The first step is to determine the waterfilling parameter
or threshold, μ which is also shown as water level. The
μ is just a mathematical parameter used to determine the
power allocated to each of the eigen channels.
2. After determining μ, the inverse of eigen values of the
matrix H is compared with the threshold.
3. Now if 1/λ2 ≥ μ then, the gain of the ith eigen channel
is too small and this eigen channel will not be
considered for communication, the last two eigen
channel.
4. Assuming the case of a square dimension of MIMO
channel, i.e. r=t and also λ1≥λ2 > λ3……≥λn. And also
consider that m eigen values have survived after the
above described procedure.
5. Once the total available power, PT and the gains of the
parallel sub channels are known, the optimum power
allocated to the ith sub channel is
And the power allocated to each of these eigen channels, Pi
is determined by the waterfilling rule such that the above
equations are satisfied. When it is positive then the ith sub
channel otherwise, the sub channel is left unused. The
waterfilling parameter „μ‟ is determined next part. Under
ideal conditions, the information theoretic capacities of a
MIMO system grows linearly with the minimum of transmit
and receive antennas. However, various measurements show
that realistic MIMO channels show a significantly lower
capacity. This reduction of capacity is due to the spatial
correlation of the MIMO channel coefficients. But here with
waterfilling algorithm the capacity increases with
correlation as proved before as MIMO capacity analysis
with respect to linear increment in number of transmitting
and receiving antennas for fixed values of SNR with water
filling power allocation algorithm assumed[11][12].
V. EXPERIMENTAL RESULTS AND DISCUSSIONS
A. Simulation Parameters
Parameters Value
U 16
S 256
B 1MHz
Ptot 1W
Doppler shift 30Hz
Max delay spread 5µs
No -80dbW/Hz
Channel model Frequency selective Rayleigh channel
FSF 6,12,24
T=R 1=1,2=2,2=3,3=2,4=4
Table 1: Simulation Parameters
B. Simulation Snapshots
Fig. 1: Power allocation in the existing system
Fig. 2: Power allocation in MIMI-OFDM system with
proposed water filling algorithm
Fig 3: Comparison of the capacity of the existing system and
the proposed system

Fig. 4: Channel Capacity versus signal to noise ratio for
MIMO-OFDM system
Fig. 5: Comparison of PDF of different MIMO-OFDM
system
Fig. 6: Mean capacity versus SNR for different MIMO and
SISO systems
VI. SNAPSHOT DESCRIPTION
Figure 1 and Figure 2 shows the power allocation in the
MIMO OFDM system. From the figure it is clear that the
proposed MIMO-OFDM system with water filling algorithm
(Fig 2) requires lesser amount of power compared to the
existing system as shown in Figure 1.Figure 3 comparison
of the capacity for the existing system and the proposed
system. From the figure it is clear that there is an
improvement in capacity of MIMO-OFDM channel when
the water filling solution is implemented to achieve capacity
maximization is used to allocate different power to the sub
channels.
Figure 4 illustrate the channel capacity versus SNR for
different MIMO-OFDM systems. The graph shows that the
capacity of the MIMO-OFDM channel increases as the
number of antennas used at both the transmitter and the
receiver increases.
Figure 5 represents the power spectral density (PDF) versus
SNR of different MIMO-OFDM systems. These two graphs
depict that the 4x4 MIMO systems provides better channel
capacity and PDF than any other combinations. This
indicates that a higher order MIMO system increases the
system performance. It is interesting to note that the system
performance remains almost the same when the number of
transmitter and receiver antennas is altered (2x3 MIMO and
3x2 MIMO systems).Figure 6 gives the comparison between
various MIMO and SISO systems. This graph shows that
MIMO System with water filling algorithm has the better
performances compared to the all other systems.
VII. CONCLUSION
In this paper, adaptive resource allocation in MIMO-OFDM
system is done by using a water filling algorithm. By using
the water filling solution it is clear that the power required is
less compared to the existing power allocation algorithm.
Also channel capacity of MIMO- OFDM systems is
estimated using water filling algorithm The use of multiple
antennas on both the transmitter and receiver side of a
communication network have shown to greatly improve the
efficiency of wireless system. The mean capacity allocation
in wireless cellular network based on the water filling power
allocation in order to enhance the capacity of MIMO-OFDM
system with different channel assumptions. It is observed
that maximum power is allocated to the channel having
greater gain. The graphs of capacity versus SNR, shows that
the capacity of the MIMO-OFDM channels increases as the
number of antennas used at the transmitter and receiver
increases.
REFERENCES
[1] G. J. Foschini and M. J. Gans, "On limits of wireless
communications in a fading environment when using
multiple antennas", Wireless Pers.Commun., vol. 6,
pp. 311-335, Mar. 1998.
[2] Y. J. Zhang and K. B. Lataief, "An efficient resource-
allocation scheme for spatial multi-user access in
MIMO/OFDM systems", IEEE Trans. Commun., vol.
53, no. 1, pp. 107-116, Jan. 2005.
[3] Z. Hu, G. Zhu, Y. Xia, and G. Liu, "Multiuser
subcarrier and bit allocation for MIMO-OFDM

systems with perfect and partial channel
information", Proc. IEEE Wireless Communications
and Networking Conference (WCNC'04), vol. 2, Mar.
21-25, 2004, pp. 1188-1193.
[4] J. M. Choi, J.S. Kwak, H. S. Kim, and J. H. Lee,
“Adaptive Subcarrier Bit, and Power Allocation
Algorithm for MIMO-OFDMA System”, in Proc.
VTC 2004-Spring, vol.3, pp.1801–1805.
[5] Bin Da, C. C. Ko, “A New Scheme with Controllable
Capacity and Fairness for OFDMA Downlink
Resource Allocation”. in Proc. IEEE VTC 2007-fall,
pp. 1817-1821.
[6] C. Fragouli, N. A;-Dhahir, and S. Diggavi, “Pre-
filtered space-time M-BCJR equalizer for frequency
selective channels”, IEEE Trans. Commun., pp. 742-
53, May 2002.
[7] Z. Shen, J. G. Andrews, and B. L. Evans, “Adaptive
Resource Allocation in Multiuser OFDM Systems
With Proportional Rate Constraints”, IEEE Trans.
wireless commun., vol. 4, pp. 2726- 2737, November
2005.
[8] I. C. Wong, Zukang Shen, B. L. Evans, and J. G.
Andrews, „A Low Complexity algorithm for
Proportional Resource Allocation in OFDMA
Systems‟, in Proc. Signal Processing Systems Conf.,
SIPS 2004, pp. 1-6.
[9] Bin Da and C.C. Ko, “Resource Allocation in
Downlink MIMO-OFDMA with Proportional
Fairness”, Journal of Communications, vol.4, no.1,
February 2009.
[10] Md. Noor-A-Rahim1, Md. Saiful Islam2, Md. Nashid
Anjum3, Md. Kamal Hosain4, and Abbas Z. Kouzani
“Performance Analysis of MIMO-OFDM System
Using Singular Value Decomposition and Water
Filling Algorithm” International Journal of Advanced
Computer Science and Applications, Vol. 2,No- 4,
2011
[11] V. Jagan Naveen, K. Murali Krishna and K. Raja
Rajeswari “Channel capacity estimation in MIMO-
OFDM system using water filling algorithm”
International Journal of Engineering Science and
Technology (IJEST), Vol. 4 No.06 June 2012
[12] Suchismita Bhattacharjee and A. Dinamani Singh,”
Channel Capacity of MIMO System over
NAKAGAMI- m Fading Channel”, International
Journal of Computing, Communications and
Networking, Volume 1, No.1, July – August 2012
[13] K. Sumathi and M. L. Valarmathi, “Fairness Aware
Resource Apportionment in Downlink MIMO-
OFDMA Systems”, European Journal of Scientific
Research, Vol.71 No.2 (2012),

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