Adaptive transmit diversity selection (atds) based on stbc and sfbc fir 2 x1 mimo ofdm systems

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 03 Special Issue: 07 | May-2014, Available @ http://www.ijret.org 56
ADAPTIVE TRANSMIT DIVERSITY SELECTION (ATDS) BASED ON
STBC AND SFBC FIR 2X1 MIMO OFDM SYSTEMS
K. Vinod Babu1
, G. Ramachandra Reddy2
, Bala Krishna Nallagatla3
, Bibin Baby John4
, Suraj Gawande5
Abstract
In this paper, a new adaptive transmit diversity selection (ATDS) scheme is proposed for future wireless communication system to
provide high spectral efficiency (SE) and good quality of service (QOS) .The ATDS scheme selects the space time block code (STBC)
orthogonal frequency division multiplexing (OFDM) scheme for flat fading channel and it selects space frequency block code (SFBC)
OFDM scheme for frequency selective fading channel. The proposed scheme provides low average bit error rate (BER) and high
average SE by using the benefits of STBC-OFDM for flat fading channel and SFBC-OFDM for frequency selective fading channel.
The obtained simulation results validate this statement.
Keywords- ATDS, Channel Index (CI), STBC-OFDM, SFBC-OFDM
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I. INTRODUCTION
The growing need for high rate spectrally efficient transmission
has always forced researchers to come up with better
transmission schemes. The flat fading and frequency selective
fading caused by multipath effect is one major concern issue for
future wireless communication systems. While flat fading
causes signal deterioration and can be easily compensated, the
Inter Symbol Interference (ISI) caused by frequency selective
fading requires the need of complex equalizers at receiver side
[1,2]. Multicarrier systems like OFDM can completely mitigate
the effect of ISI using Cyclic Prefix (CP). This simple one tap
equalization has made OFDM the favorite scheme for many 4G
standards. It is used for various applications such as Digital
Video Broadcasting (DVB), Digital Audio Broadcasting (DAB)
and Asymmetric Digital Subscriber Line (ADSL) services. It
can also be used for LTE, Wi-MAX based 4G systems [3].
Multi Input Multi Output (MIMO) systems were originally
developed for flat fading channels. It offers spatial multiplexing
as well as diversity gains which provides higher data rate and
improved reliability respectively. In order to use the same
concept in frequency selective channels, OFDM was used along
with MIMO to convert the frequency selective channel to a
number of flat fading channels. Transmit diversity and receive
diversity are the two different diversities implemented in
MIMO-OFDM systems [4, 5]. Transmit diversity is attractive
for downlink purposes as more number of transmitting antennas
can be used in the Base Station (BS). Transmit Diversity needs
accurate channel information at the transmitter side it is not
practically possible. STBC and Space Time Trellis Codes
(STTC) are other transmit diversity schemes which work
without the channel information at the transmitter side. In
STTC, with the increase in number of states the complexity
increases exponentially [3].
But both STTC and STBC are ideal only for flat fading
channels. The major drawback of applying STBC for frequency
selective fading channel is that fading destroys the
orthogonality of STBC matrix. So it is preferred only for indoor
environment and low data rate applications. MIMO equalizers
are used with STBC systems for frequency selective fading
channels. This again increases the complexity of the system.
Hence a frequency diversity scheme, SFBC is employed for
MIMO-OFDM to overcome frequency selective fading [3, 6].
In this paper, an adaptive transmit diversity selection scheme
(ATDS) that uses the best of space diversity (MIMO), time
diversity (STBC), frequency diversity (SFBC) and OFDM is
proposed. Alamouti codes are used with STBC and SFBC to
increase diversity gain [2, 5]. The ATDS estimate the channel
condition at the receiver and determines whether it is flat fading
or frequency selective fading. The channel fading index (CI=0
for flat fading and CI=1 for frequency selective fading) is fed
back to the transmitter. This helps in reducing the amount of
feedback data and thus providing with better spectral efficiency.
The transmitter then uses time diversity scheme for flat fading
and frequency diversity scheme for frequency fading channels.
The rest of the paper is organized as followed. A brief
explanation of STBC is given in section II. SFBC OFDM is
discussed in section III. The proposed ATDS is explained in
section IV. Section V contains simulation results and Section
VI concludes the paper.
2. STBC OFDM
Space Time Block Code (STBC) is an efficient way to provide
time diversity. The use of STBC along with MIMO OFDM
offer simultaneous time and space diversity. The use of
Alamouti code ensures orthogonality of the STBC matrix. A
communication system with 2 transmitter antenna and 1

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receiver antenna is considered and hence STBC 2X1 block is
considered [5].
The two OFDM symbols x1(n) and x2(n) are transmitted in two
different time periods and through two different antennas,
thereby providing both time and space diversity. For efficient
implementation of STBC with 2x1 systems, the channel should
be Quasi Static (QS) for two OFDM symbol periods [4]. The
signal received at the receiver during the first and second
symbol durations can be written as
Ts 1,1 1,2 Ts
1 2y (n) h x (n) h x (n) w (n)   (1)
2Ts 1,1 * 1,2 * 2Ts
2 1y (n) h x (n) h x (n) w (n)    (2)
Where n=0, 1, 2,…., L-1.
Stacking (1) and conjugate of (2) in matrix form, we get
Ts 1,1 1,2 Ts
1
2Ts * 1,2* 1,1* 2Ts *
2
x (n)y (n) h h w (n)
x (n)y (n) h h w (n)
      
       
       
(3)
Let the weight matrix S be given as
1,1 1,2
1,2* 1,1*
2 22 1,1 1,2
h h1
S
h h h
where h h h
 
  
 
 
(4)
The detection of the transmitted OFDM symbols at the receiver
can be done by the following procedure. Now multiplying (3)
with SH
on both sides,




1
2
11
22
h 0y (n) x (n) w (n)
0 h x (n)y (n) w (n)
     
              
(5)
Where


1,1 1,2
Ts 2Ts
1
1,2 1,1
Ts 2Ts
2
h * h
y (n) y (n) y (n)
h h
h * h
y (n) y (n) y (n)
h h
 
 

1
1,1 1,2
Ts 2Ts *h * h
w (n) w (n) w (n)
h h
 

2
1,2 1,1
Ts 2Ts *h * h
w (n) w (n) w (n)
h h
  (6)
From (5)
 
 
111
222
y (n) h x (n) w (n)
y (n) h x (n) w (n)
 
 
(7)
The transmitted two OFDM symbols can be detected from (7)
with a simple Zero Forcing (ZF) equalization as


1
1
2
2
y (n)
x (n)
h
y (n)
x (n)
h


(8)
In STBC with 2 Transmitting antennas and 1 receiving antenna,
two OFDM symbols are transmitted in two OFDM symbol
periods. It is a Rate 1 system [5]. The STBC system is suitable
only for operation in flat fading channels. For frequency
selective channels, we go for SFBC system.
3. SFBC OFDM
Space Frequency Block Codes (SFBC) can be considered as the
counterpart of STBC which when used with MIMO system
provide frequency diversity together with space diversity. As in
the case with STBC, we use Alamouti codes for the purpose of
orthogonality and consider the same communication system
with 2 transmitter antenna and 1 receiver antenna that make use
of 2X1 SFBC matrix which is given as[4,5]
Fig 1: STBC 2X1 system using Alamouti Codes

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I I
* *
I I
X [2m] X [2m 1]
D
X [2m 1] X [2m]
 
    
(9)
Where
L
m 0,1... 1
2
 
In (9), XI denote the M-QAM modulated symbols for the lth
OFDM symbol and is given as
T
I I I I IX [X [0],X [1],X [2].....X [L 1]]  (10)
The symbols coded in the first and second column of the matrix
(9) are transmitted through first and second transmitting
antennas respectively. The outputs obtained from each column
is given for separate IFFT blocks and two different OFDM
symbols are generated for the same set of L modulated symbols
which is given by,
   
   
j2 mnL 1
1,1 1,1 L
I I
m 0
j2 mnL 1
1,2 1,2 L
I I
m 0
1
x n X m e
L
1
x n X m e
L
where n 0,1.......L 1






 

 (11)
In  i,j
Ix n , the superscript i, j represents receiving and
transmitting antenna indexes respectively. The signal received
at the receiving antenna is given as
   1 1,1 1,1 1,2 1,2 1
I I I Iy [n] x n h [n] x n h [n] w [n]     (12)
where 1
Iw [n] is Additive White Gaussian Noise (AWGN).
1,1
h [n]and
1,2
h [n]are the fading channels corresponding to
first and second transmitting antennas respectively. After L
point FFT in the receiver,
   1 1,1 1,1 1,2 1,2 1
I I I IY [m] X m H [m] X m H [m] W [m]   (13)
Where m=0,1,…,L-1
The decoding of SFBC coded symbols in first two subcarriers is
explained below. The same procedure is carried out to detect
the symbols available in the rest of the subcarriers.
   
   
1 1,1 1,1 1,2 1,2 1
I I I I
1 1,1 1,1 1,2 1,2 1
I I I I
Y [0] X 0 H [0] X 0 H [0] W [0]
Y [1] X 1 H [1] X 1 H [1] W [1]
  
   (14)
As in the case with STBC, the quasi static condition must be
satisfied for SFBC also. Hence the channels for two
neighboring subcarriers are assumed to be constant [4].
1,1 1,1
1,2 1,2
H [0] H [1]
H [0] H [1]


(15)
Substituting (15) in (14)
   1 1,1 1,2 1
I I I IY [0] X 0 H [0] X 1 H [0] W [0]   (16)
   
* *1 1,1 1,2 1
I I I IY [1] X 1 H [0] X 0 H [0] W [1]    (17)
Stacking (16) and conjugate form of (17) in matrix form as
 
 
1 11,1 1,2
II I
1 11,2 1,1
II I
X 0Y [0] W [0]H [0] H [0]
X 1Y [1] W [1]H [0] H [0]  
     
      
     
(18)
Let the weight matrix S be given as
1,1 1,2
1,2 1,1
2 22 1,1 1,2
H [0] H [0]
H(0) H(0)
S
H [0] H [0]
H(0) H(0)
where H(0) H [0] H [0]
 
 
 
 
 
 
  
 
(19)
Multiplying both sides of (18) with SH
,
 
 
II I
II I
Y [0] H[0] X [0] W [0]
Y [1] H[0] X [1] W [1]
 
 
(20)
Where


1,1 * 1,2
1 1
I I I
1,2 1,1
1 1
I I I
H [0] H [0]
Y [0] Y [0] Y [1]
H(0) H(0)
H [0] H [0]
Y [1] Y [0] Y [1]
H(0) H(0)



 
 


1,1 * 1,2
1 1
I I I
1,2 1,1
1 1
I I I
H [0] H [0]
W [0] W [0] W [1]
H(0) H(0)
H [0] H [0]
W [1] W [0] W [1]
H(0) H(0)



 
 
(21)
A simple zero forcing equalizer can be used to detect the
transmitted coded OFDM symbols from (20)


I
Y[0]
X [0]
H[0]


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

I
Y[1]
X [1]
H[0]
 (22)
4. ADAPTIVE TRANSMIT DIVERSITY
SELECTION
The Adaptive transmit Diversity Selection (ATDS) adaptively
selects a diversity scheme based on the current channel
condition. The receiver estimates the channel and determines
whether it is flat fading or frequency fading. Based on this
information, the diversity scheme determination is done at the
receiver and the channel index (CI=0 for flat fading and CI=1
for frequency fading) is fed back to the transmitter side.
The ATDS block at the transmitter assigns the diversity scheme
using the received channel index (CI). For CI=0, the ATDS
assigns Path 0 that provide time and space diversity using
Alamouti STBC coding. The OFDM signals at the output of the
IFFT block undergoes STBC encoding (see section II) and is
transmitted through two transmitting antennas to obtain spatial
diversity. On the other hand, for CI=1, Path 1 is assigned which
give frequency diversity. The M-QAM modulated symbols are
SFBC encoded (section III) and then produce two separate
OFDM symbols that are transmitted through two transmitted
antennas just like Path 1 in order to achieve spatial diversity.
At the receiver side decoding is done in the same way based on
CI. The Diversity Determination block chooses the path in the
receiver side. Path 0 provides STBC decoding
Table 1: The Proposed ATDS Algorithm
Whereas Path 1 provides SFBC decoding. Unlike the
conventional diversity techniques which could follow both time
or frequency diversity, the ATDS adaptively selects the
diversity scheme and hence uses the full benefits time,
frequency and spatial diversity techniques and thus improves
the overall system performance.
Fig 2: ATDS block diagram
5. SIMULATION RESULTS
To test the performance of proposed ATDS scheme we take the
following parameters. The number of Subcarriers in one OFDM
symbol is 64 and Bandwidth (B) is assumed to be 5 MHz,
number of transmitting antennas (NT) are 2 and number of
receiving antenna (NR) is 1, the code rate (RC)is one and the
target BER is 10-4
. The performance of the proposed scheme is
evaluated for 100 channels and the average BER and SE results
are compared with the conventional system. The fading process
is assumed to be stationary and the channel is assumed to be
static during one OFDM block length.
The instantaneous BER of mth
subcarrier in Ith
OFDM symbol
with M-QAM is given as
2 21,1 1,2S
I b(m)
1.6
BER (m) 0.2exp ( H [m] H [m] )
2(2 1)
   
  
 
(23)
where , S S 0E N  and ES is the symbol energy at the
transmitter and N0/2 is the variance of Additive White
Gaussian Noise (AWGN), b(m) is the number of bits loaded on
the mth
subcarrier and 1,1 1,2
H [m],H [m] are the mth
sub channel
amplitudes of transmitter antennas to the receiver antenna[4].

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L 1
m 0
1
BER BER(m)
L


  (24)
Where L represents the total number of subcarriers in one
OFDM symbol[3, 4].
The Average SE of the Ith
OFDM symbol is given as
L 1
I I
m 0u g
1
SE b(m)(1 BER (m))
B(T T )


 

 (25)
Where uT is the useful symbol duration and gT is the guard
interval [4,5].
Fig 3 Average BER comparison of proposed scheme and
conventional STBC-OFDM over frequency selective fading
channel.
Fig 4 Average Spectral Efficiency comparison of Proposed
Scheme and Conventional STBC-OFDM over frequency
selective fading channel.
In the frequency selective fading channel multiple versions of
the faded transmitted signal delayed in time are received and it
induces inter symbol interference (ISI). A four tap channel is
considered for the analysis.
In Figure 3, the average BER values of the proposed scheme
and conventional STBC-OFDM system over frequency
selective fading channel are calculated with equation (24) by
varying the SNR values from 0 to 40dB. For the proposed
scheme (SFBC-OFDM) the average BER value at 0dB SNR is
3
10
but this BER value is achieved at 7dB SNR in case of
conventional STBC-OFDM, i.e., the proposed scheme gains
7dB over frequency selective fading channel.
Figure 4 shows the spectral efficiency comparison of proposed
scheme and conventional scheme over frequency selective
fading channel. The SE values are calculated by equation (25).
For the proposed scheme (SFBC-OFDM) the average SE value
at 12dB SNR is 4bits/Hz but in case of conventional STBC-
OFDM the value is 2bits/Hz. So the SFBC-OFDM over
frequency selective fading channel provides high SE compared
to the STBC-OFDM.
In flat fading channel the spectral characteristics of the
transmitted signal are maintained at the receiver but the strength
of the received signal varies with time due to fluctuations in the
gain of the channel caused by multipath and for analysis of this
a single tap channel is considered.
In Figure 5 the average BER values of the proposed scheme and
conventional SFBC-OFDM system over flat fading channel are
calculated with equation (24) by varying the SNR. For the
proposed scheme the average BER value at 0dB SNR is
3
0.07 10
 but this same BER value is achieved at 14dB SNR
in case of SFBC-OFDM, which implies that the proposed
scheme gains 14dB over flat fading channel.
Figure 6 shows the spectral efficiency comparison of proposed
scheme and conventional scheme over flat fading channel.
0 5 10 15 20 25 30 35 40
10
-4
10
-3
10
-2
10
-1
SNR(dB)
AverageBER
Proposed System (SFBC-OFDM)
Conventional System (STBC-OFDM)
0 5 10 15 20 25 30 35 40
0
2
4
6
8
10
12
14
SNR(dB)
AverageSpectralEfficieny(b/s/Hz)
Proposed System (SFBC-OFDM)
Conventional System (STBC-OFDM)

__________________________________________________________________________________________
Fig 5 Average BER comparison of proposed scheme and
conventional SFBC-OFDM over flat fading channel
Fig 6 Average Spectral Efficiency comparison of Proposed
Scheme and Conventional SFBC-OFDM over flat fading
channel.
The SE values are calculated by equation (25). For the proposed
scheme (STBC-OFDM) the average SE value at 12dB SNR is
2bits/Hz but in case of conventional SFBC-OFDM the value is
1bits/Hz. So the STBC-OFDM over flat fading channel
provides high SE compared to the SFBC-OFDM. From the
results, it can be seen that the proposed ATDS scheme greatly
improves the performance of a system by selecting the
transmission scheme based on the present channel condition.
6. CONCLUSIONS
An adaptive transmit diversity selection (ATDS) scheme is
proposed in this paper. The proposed scheme greatly improves
the performance of a system in terms of Spectral Efficiency(SE)
and quality by using the benefits of STBC-OFDM for flat
fading channel and SFBC-OFDM for frequency selective
fading channel as compared to a conventional system where
either STBC-OFDM or SFBC-OFDM are used for both flat
fading and frequency selective fading channels. Simulation
results shows that in flat fading channel the proposed scheme
(using STBC-OFDM) gains 14dB SNR compared to SFBC-
OFDM system for getting
3
0.07 10
 BER and SE is 2bits/Hz
rather than 1bits/Hz for conventional system at 12dB SNR. In
frequency selective fading channel the proposed scheme gains
7dB SNR compared to STBC-OFDM for getting
3
10
BER and
SE is 4bits/Hz rather than 2bits/Hz for STBC-OFDM at 12dB
SNR.
REFERENCES
[1] Theodore S Rappaport, 2002, Wireless Communications
Principles and Practice, Pearson Education Inc, India.
[2] Ramjee Prasad, 2004, OFDM for Wireless
Communication Systems, Artech House, Inc. Boston,
London.
[3] Yong Soo Cho, Jaekwon Kim, Won Young Yang and
Chung G. Kang, MIMO-OFDM Wireless
Communications with Matlab, John Wiley & Sons Pvt.
Ltd, Asia, 2010.
[4] Mohammad Torabi, “Antenna selection for MIMO-
OFDM systems,” Signal Processing, vol. 88, 2008, pp.
2431-2441.
[5] S.M. Alamouti, “A simple transmit diversity technique
for wireless communications,” IEEE Journal on Selected
Areas in Communication, vol. 16, no. 8, 1998, pp. 1451-
14558.
[6] Mohammad Torabi, “Adaptive modulation for space-
frequency block coded OFDM systems,” International
Journal of Electronics and Communications, vol. 62, no.
7, 2008, pp. 521-533.
0 5 10 15 20 25 30 35 40
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
SNR(dB)
AverageBER
Conventional System (SFBC-OFDM)
Proposed System (STBC-OFDM)
0 5 10 15 20 25 30 35 40
0
2
4
6
8
10
12
SNR(dB)
AverageSpectralEfficieny(b/s/Hz)
Conventional System (SFBC-OFDM)
Proposed System (STBC-OFDM)

Adaptive transmit diversity selection (atds) based on stbc and sfbc fir 2 x1 mimo ofdm systems

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Adaptive transmit diversity selection (atds) based on stbc and sfbc fir 2 x1 mimo ofdm systems