S. Praseetha, about MIMO systems, space time block codes, spatial modulation.

1. International Journal of Science and Engineering Technology (IJSET) Vol. 1, No.1, 2013
Comparitive Analysis of Bit Error Rates of Multiple
Input Multiple Output Transmission Schemes
(MIMO)
S.Praseetha1
1
Department of Electronics and Communication Engineering,
1
SNS College of Technology,
Coimbatore, Tamil Nadu
prase04@gmail.com
Abstract: Multiple Input Multiple Output (MIMO) transmission schemes such as spatial multiplexing, Space Time Block
Codes (STBC) and Space Time Block Coded Spatial Modulation (STBC-SM) methods are compared. The Spatial Multiplexing
system such as Vertical –Bell Lab Layered Space-Time (V-BLAST) system is proposed. It is a transceiver architecture offering
spatial multiplexing over multiple antenna wireless communication systems. In STBC multiple copies of data streams are
transmitted, to improve the reliability of data transfer. STBC-SM combines both Spatial modulation (SM) and STBC. In STBC-
SM the transmitted information are expanded in space, time and spatial domain and hence provides better performance
advantage than STBC and V-BLAST. The Bit Error Rate (BER) of these transmission schemes is analyzed for four transmit and
four receive antennas. From simulation results it is shown that STBC-SM method provides less BER than V-BLAST and STBC.
Keywords: about MIMO systems, space time block codes, spatial modulation.
1. Introduction
Under suitable channel fading conditions, having both multiple transmit and multiple receive antennas provides an
additional spatial dimension for communication and yields a degree-of-freedom gain. This additional degree of freedom can
be exploited by spatially multiplexing several data streams onto the MIMO channel, and lead to an increase in the capacity.
Multiple access system with multiple antennas at the base station allows several users to simultaneously communicate with
the base station. The multiple antennas allow spatial separation of the signals from the different users MIMO techniques
become the primary tool to increase capacity significantly in the high SNR regime. Several transmission strategies exist for
MIMO and here three techniques have been proposed, V-BLAST, STBC and STBC-SM. V-BLAST architecture multiplexes
independent data streams on to the transmit antenna array. The linear minimum mean-square-error (MMSE) receiver
structures are considered. The performance of these receivers can be enhanced by successively canceling the streams as they
are decoded. This is known as successive interference cancellation (SIC). It is shown that the MMSE-SIC receiver achieves
the capacity of the fast fading MIMO channel [4]. The V-BLAST architecture is very suboptimal for the slow you fading
MIMO channel, it does not code across the transmit antennas and thus the diversity gain is limited by that obtained with the
receive antenna array. All antennas transmit their own data streams at the same time and hence results in a high level of
inter-channel interference at the receiver and increase complexity of receiver [3]. Thus the error performance of the system
is degraded. On the other hand STBC offers low decoding complexity and simpler implementation. But for higher order
STBCs the complexity of decoding grows with constellation size [1]. It is also very expensive for future wireless
communication systems. Space time codes do not provide array gain due to lack of channel knowledge in the transmitter. In
STBC-SM method information is conveyed with an STBC matrix that is transmitted from combinations of the transmit
antennas of the corresponding MIMO system. STBC-SM combines both STBC and SM [2], to take advantage of benefits of
both the transmission schemes. It is found that STBC-SM provides better advantage than STBC and V-BLAST technique.
2. V-BLAST Technique
V-BLAST takes a single data stream and de-multiplexes it into M sub-streams where M is the number of transmitter
antennas. Each sub-stream is encoded into symbols and fed to a separate transmitter. The modulation method employed in
these systems are Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying(QPSK), 16-Quadrature Amplitude
Modulation (16-QAM) or 64-QAM. QAM combines phase modulation with amplitude modulation, making it an efficient
method for transmitting data over a limited bandwidth channel. BLAST's receivers operate co-channel, each receiving the
signals emanating from all M of the transmitting antennas. Here the method is proposed for four transmit and four receive
antennas. Since the entire sub streams are transmitted in the same frequency band, spectrum is used very efficiently. At the
receiver, an array of antennas is again used to pick up the multiple transmitted sub streams. The MMSE receiver suppresses
both the interference and noise components. This implies that the mean square error between the transmitted symbols and
the estimate of the receiver is minimized. To take advantage of the additional throughput offered, MIMO wireless systems
utilizes a matrix mathematical approach. As shown in Fig.1 data streams a1,a2,…. aM are transmitted from antennas 1, 2,….
M. Then there are a variety of paths that can be used with each path having different channel properties. To enable the
receiver to be able to differentiate between the different data streams it is necessary to use. These can be represented by the
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2. International Journal of Science and Engineering Technology (IJSET) Vol. 1, No.1, 2013
properties h12, travelling from transmit antenna one to receive antenna 2 and so forth. In this way for a three transmit, three
receive antenna system a matrix can be set up:
r1 = h11 a1 + h21 a2 + h31 a3 (1)
r2 = h12 a1 + h22 a2 + h32 a3 (2)
r3 = h13 a1 + h23 a2 + h33 a3 (3)
Where r1 = signal received at antenna 1, r2 is the signal received at antenna 2 and so forth. In matrix format this can be
represented as:
[R] = [H] x [A] (4)
To recover the transmitted data-stream at the receiver it is necessary to perform a considerable amount of signal processing.
First the MIMO system decoder must estimate the individual channel transfer characteristic hij to determine the channel
transfer matrix. Once all of this has been estimated, then the matrix [H] has been produced and the transmitted data streams
can be reconstructed by multiplying the received vector with the inverse of the transfer matrix.
[A] = [H]-1
x [R] (5)
This process can be likened to the solving of a set of N linear simultaneous equations to reveal the values of N variables.
Figure 1. Block diagram of V-BLAST system
3. STBC Technique
STBC is a technique used in wireless communications to transmit multiple copies of a data stream across a number of
antennas and to exploit the various received versions of the data to improve the reliability of data-transfer. The fact that the
transmitted signal must traverse a potentially difficult environment with scattering, reflection, refraction and so on and may
then be further corrupted by thermal noise in the receiver means that some of the received copies of the data will be 'better'
than others. This redundancy results in a higher chance of being able to use one or more of the received copies to correctly
decode the received signal. The data stream to be transmitted is encoded in blocks, which are distributed among spaced
antennas and across time as shown in the Fig.2. For each input symbol, the space-time encoder chooses the constellation
points to transmit from each antenna so that coding and diversity gains are maximized. STBCs are defined by mapping
operation of a block of symbols into space and time domain, creating orthogonal sequences that will be transmitted from
different transmit antennas. The receiver is composed of channel estimation, combining procedure in both space and time
domain and maximum likelihood detection rule. The STBC decoder is simple and achieves the diversity advantage. The
following cases of STBC are considered-Alamouti STBC, 1/2 code rate for four transmit antenna and ¾ code rate for four
transmit antenna. Code rate of an STBC measures how many symbols per time slot. The Alamouti code is the first STBC
that provides full diversity at full data rate for two transmit antennas. The information bits are first modulated using the
PSK modulation scheme. The encoder takes the block of two modulated symbols s1 and s2 in each encoding operation and
hands it to the transmit antennas according to the code matrix,
S = s1 s2
-s2
*
s1
* (6)
The first row represents the first transmission period and the second row the second transmission period. During the first
transmission, the symbols s1 and s2 are transmitted simultaneously from antenna one and antenna two respectively. In the
second transmission period, the symbol –s2
*
is transmitted from antenna one and the symbol s1
*
from transmit antenna two.
The two rows and columns of S are orthogonal to each other and the code matrix is orthogonal:
SSH =
s1 s2 s1 s2
-s2
*
s1
*
-s2
*
s1
*
= ( |s1|2
+ |s2|2
) I2 (7)
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3. International Journal of Science and Engineering Technology (IJSET) Vol. 1, No.1, 2013
where I2 is a (2 × 2) identity matrix. This property enables the receiver to detect s1 and s2 by a simple linear signal
processing operation. The received signals at the time t and
t + T can then be expressed as,
r1 = s1h1 + s2h2 + n1 (8)
r2 = −s2
*
h1 + s1
*
h2 + n2 (9)
where r1 and r2 are the received signals at time t and t + T, n1 and n2 are complex random variables representing receiver
noise and interference. This can be written in matrix form as:
r = Sh + n (10)
where h = [h1, h2]T is the complex channel vector and n is the noise vector at the receiver. For STBC with four transmit
antenna and for code rate ½ the transmission matrix is given as,
G3= s1 s2 s3
-s2 s1 –s4
-s3 s4 s1
-s4 –s3 s2 (11)
Then the process of modulation and detection is similar to Alamouti scheme except that more number of symbols will
be included.
Figure 2. Block diagram of STBC transmitter
4. STBC-SM
In the STBC-SM scheme, both STBC symbols and the indices of the transmit antennas from which these symbols are
transmitted, carry information. We choose Alamouti STBC and STBC for four transmit and four receive antennas. It is
similar to STBC except that the antenna domain is also taken into account. The modulation performed may be BPSK,QPSK,
8-PSK or 16 QAM. For four information bits to be transmitted in two consecutive symbol interval, the first two bits are
used to determine the antenna pair position and last two bits determine the BPSK symbol pair as shown in the Fig.3. Here M
refers constellation size and c implies the total number of antenna combinations.
5. Comparison of V-BLAST, STBC AND STBC-SM
The results of all the three schemes are compared. It is found that STBC-SM provides better performance compared to V-
BLAST and STBC. The table I shown below indicates the BER values of different transmission schemes for SNR from 1 to
8 values. It is seen that STBC-SM has minimum error rates and becomes zero for higher values of SNR.
Table I Comparison of SNR and BER values
SNR Transmission Schemes
V-BLAST STBC STBC-SM
1 0.3571 0.3198 0.0015
2 0.3935 0.3214 0.0012
3 0.2706 0.2097 0.0001
4 0.0793 0.1667 0
5 0.0445 0.0961 0
6 0.0425 0.0649 0
7 0.0279 0.0211 0
8 0.0084 0.0266 0
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4. International Journal of Science and Engineering Technology (IJSET) Vol. 1, No.1, 2013
Figure 3. Block diagram of STBC-SM transmitter
6. Simulation Results
Simulation results of V-BLAST, STBC and STBC-SM are presented. Also these schemes are compared. The Bit Error Rates
of these systems are evaluated as a function of Signal To Noise Ratio.
0 5 10 15
0
0.05
0.1
0.15
0.2
0.25
SNR
BER
Figure 4. BER performance for V-BLAST system using
16 QAM.
0 5 10 15
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
SNR
BER
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5. International Journal of Science and Engineering Technology (IJSET) Vol. 1, No.1, 2013
Figure 5. BER performance of V-BLAST system for 64 QAM
The V-BLAST system uses MMSE detection with ordered successive interference cancellation (SIC) decoding. For STBC,
the Alamouti scheme and the ½ code rate scheme for four transmit and four receive antenna are evaluated.
1 2 3 4 5 6 7 8
10
-4
10
-3
10
-2
10
-1
10
0
S NR / (dB )
SymbolErrorProbability
Figure 6. BER performance of Alamouti STBC
1 2 3 4 5 6 7 8
0
1
2
3
4
5
6
x 10
-4
SNR
BER
Figure 7. BER performance of ½ code rate STBC
It is seen that ½ code rate provides better performance advantage than Alamouti STBC since number of antennas are
increased.
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6. International Journal of Science and Engineering Technology (IJSET) Vol. 1, No.1, 2013
1 2 3 4 5 6 7 8
0
1
2
3
4
5
6
x 10
-4
S NR
BER
Figure 8. BER performance of STBC-SM for 16-QAM
1 2 3 4 5 6 7 8
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
SNR
BER
V-BLAST
STBC
STBC-SM
Figure 9. Comparison of BER performance of V-BLAST, STBC AND STBC-SM
Comparing the three schemes it can be seen that the STBC-SM scheme is the best.For higher values of SNR the BER of
STBC-SM decreases and approches zero values.
7. Conclusion
In this paper a high rate transmission scheme called STBC-SM method is introduced which is compared with other
MIMO transmission schemes called V-BLAST and STBC. Through computer simulations it is shown that STBC-SM offers
significant improvements in BER performance compared to V-BLAST and STBC systems. Simulations are performed
assuming four transmit and four receive antennas for MIMO structure. STBC-SM scheme can be very useful for emerging
wireless communication systems such as WiMAX and LTE.
References
[1] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-ime block codes from orthogonal designs," IEEE Trans.
Inf. Theory, vol. no. 5, pp. 1456-1467, July 1999.
[2] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, “Spatial modulation:optimal detection and performance analysis,"
IEEE Commun. Lett., vol.12, no. 8, pp. 545-547, Aug. 2008.
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7. International Journal of Science and Engineering Technology (IJSET) Vol. 1, No.1, 2013
[3] P. Wolniansky, G. Foschini, G. Golden, and R.Valenzuela, “V-BLAST:an architecture for realizing very high
data rates over the rich-scattering wireless channel," in Proc. International Symp. Signals, Syst., Electron.
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Author Profile
Mrs. S. Praseetha is currently working as an assistant professor at SNS college of
technology, Coimbatore. She has secured her M.E. degree in Communication systems from
Karpagam college of engineering, Coimbatore. She has completed her B.E. in ECE from
VLB Janakiammal college of engineering, Coimbatore. She has a working experience of
three years and has presented papers related to MIMO at National conference held at Sri
Krishna college of engineering, Coimbatore.
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