Int. J. Communications, Network and System Sciences, 2010, 3, 507-510
doi:10.4236/ijcns.2010.36068 Published Online June 2010 (http://www.SciRP.org/journal/ijcns/).
Efficiency Improvement of Space Time Block Codes
Zahoor Ahmed Baloch1, Mohammad Usman Baloch2, Noor Hussain3
1
Université de Limoges-Ecole Nationale Supérieure d'Ingénieurs de Limoges (ENSIL), Rue Atlantis-Parc ESTER-BP
Limoges cedex, France
2
Balochistan University of Engineering & technology, Khuzadar, Pakistan
3
Universiti Teknologi Petronas, Bandar Seri Iskandar, Malaysia
E-mail: zahoor.ahmed@ensil.unilim.fr, musman@buetk.edu.pk, nhussain@petronas.com.my
Received March 24, 2010; revised April 29, 2010; accepted May 30, 2010
Abstract
Unlike most of the existing methods in Space Time coding (STC) system which focus on design of STC
gaining full rate and/or maximum diversity, we propose an approach to improve spectral efficiency of the
code. The proposed scheme carries more information symbols in each transmission block as compared to its
counterpart code, and yet retains the property of simple decoding. Simulation results show that transmit diversity is retained with improvement of code efficiency. We mainly focus on Four transmit antenna scheme
but it can be generalized for any number of transmit antennas.
Keywords: Space Time Block Code, Spectral Efficiency
1. Introduction
Since 1998 when Alamouti in [1] presented the idea of
Space Time Coding, significant progress has been made
in code design for achieving better diversity and code
rate over multiple wireless communication channels.
Space Time Coding (STC) system is one of the compromising scheme to meet the fast growing challenges for
reliable and high data rate communication over multiple
input multiple out (MIMO) channels. In [2,3] V.Tarokh
et el discusses in detail the design of different classes of
ST codes for achieving maximum diversity and full rate.
However to counter the problem of unfeasibility/impracticability of having multiple receiver antennas at end users has put the researchers on work for alternates. In [2]
it was shown that code rate cannot be greater than one.
In fact even the maximum diversity and full rate codes
do not exploit high efficiency. For example, if we look at
(1), which is a Space Time Block Code (STBC) transmission matrix for four transmit antennas.
x1
x
2
x3
x4
x2
x3
x1
x4
x4
x3
x1
x2
x4
x3
x2
x1
(1)
where only the four symbols of first row of the matrix
(i.e. x1 , x2 , x3 , x4 ) have been taken from a particular constellation (QPSK) while the other symbols are redundant
Copyright © 2010 SciRes.
and totally depend on four useful symbols. In other words
out of sixteen symbols, only four symbols are carrying
useful information.
In [4], Foschini proposed BLAST coding technique,
which offers higher spectral efficiency by exploiting the
spatial multiplexing to transmit independent data streams
over Multiple-Input Multiple-output channels. Such type
of scheme outperforms to its counterpart STBC having
multiple antennas at both transmitter and receiver, but
contrary in [5] it was shown that the decoding of such a
scheme does not work well if the numbers of receiver
antennas are less than that of number of transmit antennas.
In [6] a scheme for increasing the spectral efficiency
of Alamouti code has been presented. But such a scheme
does not contribute significant improvement in code efficiency for more than two transmit antennas.
In this paper we propose a technique to improve the
spectral efficiency of STBC for four transmit antennas
retaining maximum diversity, full rate and simple maximum likelihood (ML) decoding characteristics of original code. Although the main focus of this paper is to design efficient code for four transmit antennas scenario,
but same idea can be extended in a straightforward manner for STBC having more than four antennas.
The rest of the paper is organized as follow: Section 2
presents the system model. In Section 3, different techniques for increasing the code efficiency are discussed.
Simulation results are given in Section 4 and finally conclusion in Section 5.
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Z. A. BALOCH ET AL.
508
2. System Model
4
rt i cti nt
(5)
i 1
We consider a wireless communication system having
four transmit antennas and one receiver antenna. We
assume that transmission at the base band employs a real
constellation A with 2b elements. The input binary
stream is first split into two sub-stream by a serial to parallel converter. Each binary sub stream then passes
through a QPSK constellation denoted by A to map
binary bits into symbols, i.e. setting xi si for
i 1, 2,3, 4 , We arrive at a matrix C = O( s1 , s2 , s3 , s4 )
with entries s1 , s2 , s3 , s4 . At each time slot
t 1, 2,3, 4 signals Ct ,i are transmitted simultaneously
from four transmit antennas. Clearly the rate of transmission is b bit/s/Hz.
The fading coefficients from first to last transmit antennas to receiver antenna at time t are denoted by h1 (t ) ,
h2 (t ) , h3 (t ) and h4 (t ) respectively. Assuming that
the fading coefficients are constant across four consecutive symbols transmission periods, and are expressed as
h1 (t ) h1 (t T ) h1 h1 e jQ1
h2 (t ) h2 (t T ) h2 h2 e jQ2
(2)
h3 (t ) h3 (t T ) h3 h3 e jQ3
h4 (t ) h4 (t T ) h4 h4 e jQ4
where hi
and i , for i 1, 2,3, 4 are the amplitude
gain and phase shift for the path from transmit antenna i
to the receive antenna, and T is the symbol duration.
At the receive antenna, the received signals over four
consecutive symbol periods, denoted by r1 , r2 , r3 and
r4 for t 1,.., 4 respectively, can be expressed as
r1 h1 x1 h2 x2 h3 x3 h4 x4 n1
r2 h1 x2 h2 x1 h3 x4 h4 x3 n2
r3 h1 x3 h2 x4 h3 x1 h4 x2 n3
(3)
r4 h1 x4 h2 x3 h3 x2 h4 x1 n4
where n1 , n2 , n3 and n4 respectively from time 1 to
4 are independent complex variable with zero mean
power spectral density No/2 per dimension, representing
additive white Gaussian noise. We may re-write Equation (3) into matrix form as:
x1
x
r1 r2 r3 r4 h1 h2 h 3 h4 x2
3
x
4
n1 n2 n3 n4
or more precisely
Copyright © 2010 SciRes.
x2
x3
x1
x4
x4
x3
x1
x2
x4
x3
x2
x1
(4)
where i denotes channel coefficients. Assuming perfect channel state information is available at receiver, the
receiver computes the decision metric
4
4
t 1
t 1
rt a c
2
(6)
i
i t
The maximum likelihood decoding for si can be
achieved by decoupling the signals transmitted from different antennas, [4,6].
2
(7)
sˆi arg min ri s
s A
For i 1,.., 4 and decide in favour of si among all the
constellation symbols
3. Efficiency Improvement Code
Assume that all the symbols in (1) are drawn from a
QPSK constellation with gray constellation as shown in
Figure 1. Although the code given in (1) is full rate code
but its efficiency is too low. To find out the code efficiency over a QPSK constellation, we represent (1) by its
corresponding bit representation. There might be 256
different patterns, and each pattern comprises of 32 bits.
To lay down all 256 different patterns is a fatigable and
un-necessary work. To save space we lay down just one
such pattern below in (8), by assuming
j
s1 e j 0 , s2 e 2 , s3 e j and s4 e
00
10
00
01
01 11 10
00 01 11
10 00 10
00 10 00
j 3
2
(8)
Now if we look at (8), the useful or informative bits
are only 8 bits enumerated in first row of (8) while all
other 24 (in 2nd, 3rd and 4th rows of (8)) bits are redundant
and totally depends on 8 useful bits. We define the code
efficiency η as the ratio of the number of useful bits and
the total number of bits in each pattern of code matrix. In
this particular case, the code efficiency is η = 8/32 =
0.25.
All full rate Space Time Block Codes having 4 or
more than 4 transmit antennas do not gain code efficiency more than 0.25, even the case is worse for
non-full rate codes.
Here we discuss some technique to improve the spectral efficiency of the code for four transmit antennas.
One way is to split the original data bit stream into
group of 4 × 8 like that in (8), i.e. the redundant bits have
dual function, at the same time they represent as redundant bits and information bits. In this case we can have
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Z. A. BALOCH ET AL.
full efficient code η = 1. But as our original data is random, so the probability of getting such a code pattern is
28 / 232 0.66 % which is too small and practically near
to zero probability.
Another way to improve the code efficiency η is the
technique very similar to that used in [6] for two transmit
antenna Alamouti code. The original data stream is divided into group of nine bits. The first eight bits are arranged as useful bits in matrix form as in (8) and the
ninth bit is used to decide which constellation to choose
between the two constellation schemes shown in Figure
1 and Figure 2, for transmission of eight useful bits. For
example if ninth bit 1, we choose the constellation A,
shown in Figure 1, otherwise constellation B shown in
Figure 2. It turns out that the transmission matrix has the
same format as that in (8) but each transmission block
now contains nine information bits instead of eight bits.
The code efficiency increases to 9/32 = 0.28125.
As in this technique the code efficiency increases by a
single bit we call this technique, bit efficient Eb code.
Another way to increase the code efficiency is to first
divide the source binary data in to group of ten bits and
then convert them into two binary sub-stream by a serial
to parallel converter. For simplicity we show these five,
2-bits parallel bit stream by following symbols.
x1 x2
x3 x4 x5
(9)
Before passing the symbol through constellation we
tally the fifth symbol with other four symbols in (9) by
its corresponding bit representation and find out the
symbol which is same as fifth symbol. In case if there are
more than one matching symbols, then we take the first
one in that vector and in case if there is no any matching
symbol then we ignore the fifth symbol for that specific
transmission.
We use two type of constellation (as shown in Figure 1 and Figure 2). In transmitting the useful symbols
x1 x2 x3 x4 , the symbol which is same as x5 is transmitted from constellation A whereas the rest of the symbols are transmitted from constellation B.
As our source data stream is random, so it difficult to
calculate the matching probability between fifth and
other symbols. However for large data size we expect
10
509
10
00
11
01
Figure 2. QPSK Constellation ‘B’ with gray coding.
maximum probability. If first four symbol in (9), in its
corresponding bit representation, are different to each
other, then the probability that the fifth symbol will
match with one of the other four symbols is 100%, if any
three symbols are different then the probability that the
fifth symbol will match with one of the other four symbols is 75%, so probability is 50% if two symbols are
different and it is 25% if one symbol is different.
We assume that in each block of transmission we find
a matching symbol. In this case the code efficiency is
10/32 = 0.3125. As code efficiency is increased by a
symbol, we call this technique as symbol efficient Es
code
Let x5 x1 x2 x3 x4 x5 denote the fifth symbol and
x1 x2
x3 x4 x5 A, B
Then the transmission matrix (1) can be represented as
j s5
2
x
e
1
j s
x2 e 2 5
j s5
2
x
e
3
j s5
x4 e 2
x2 e
j s5
2
x1e
j s5
2
x3 e
x4 e
x4 e
j s5
2
x3 e
j
2
s5
x4 e
j s5
2
x1e
j s5
2
x2 e
j s5
x3 e 2
j s5
2
x2 e
j s5
x1e 2
j s5
2
j s5
2
j
2
s5
(10)
S5 is decided by the location of ri 1,.., 4 which is
closer to the decision boundary. Maximum likelihood
decoding of Si 1,.., 4 can be decoupled
j s5
sˆi arg min ri si e 2
s A
2
(11)
4. Simulation Results
11
00
01
Figure 1. QPSK Constellation ‘A’ with gray coding.
Copyright © 2010 SciRes.
At transmitter two types of QPSK constellation are used.
The minimum Euclidean distance between two QPSK
constellations is the same as that of 8PSK constellation.
Therefore in worse case the BER performance of the
symbol efficient STBC code will be slightly worse due to
additional error of symbol S5, as compare to 8PSK
modulation. On the contrary, if the recovery of S5 is perIJCNS
Z. A. BALOCH ET AL.
510
fect i.e. the number of errors related to S5 is zero, then
the selection of the QPSK constellation at the receiver is
always correct, and the minimum Euclidean distance
turns out to be the same as that of a QSPK constellation.
Thus in the best case, the BER performance of symbol
efficient STBC will be slightly better as compare to ordinary STBC code.
Our simulation results in Figure 3 prove our claim of
better spectral efficiency of symbol efficient Es STBC
code as compare to conventional STBC.
Table 1 shows some specific results of a neat comparison between STBC, Bit efficient STBC, symbol efficient STBC and 8PSK.
5. Conclusions
Table 1. Performances of QPSK modulation under different
scenarios.
6. References
Scheme
Efficiency
R
bit/s/Hz
4-QPSK
0.25
2
4-PSK Eb
0.282
2.25
4-PSK Es
0.32
0.5
8PSK
0.25
3
BER
[1]
S. M. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communication,” IEEE Journal on
Selected Areas in Communications, Vol. 16, No. 8, 1998,
pp. 1451-1458.
[2]
V. Tarokh, H. Jafarkhani and A. R Calderbank, “Space
Time Block Codes from Orthogonal Designs,” IEEE
Transactions on Information Theory, Vol. 45, No. 5,
1999, pp. 1456-1467.
[3]
V. Tarokh, H. Jafarkhani and A. R. Calderbank, “Space
Time Block Coding for Wireless Communication: Performance Result,” Journal on Selected Areas in Communications, Vol. 17, No. 3, 1999, pp. 451-462.
[4]
G. J. Foschini, “Layered Space-Time Architecture for
Wireless Communication in a Fading Environment When
Using Multi-Element Antennas,” Bell Labs Technical
Journal, Vol. 1, No. 2, 1996, pp. 41-59.
[5]
G. D. Golden, G. J Foschini, R. A. Valenzuela and P. W.
Wolniansky, “Detection Algorithm and Initial Laboratory
Results Using V-BLAST Space Time Communication
Architecture,” Electronics Letters, Vol. 35, No. 1, 1999,
pp. 14-16.
[6]
Q. Ling and T. T. Li, “Efficiency Improvement for
Alamouti Codes,” IEEE 40th annual conference on Information Sciences and systems, Princeton, 22-24 March
2006, pp. 569-572.
Low
High
Eb/No/dB
Figure 3. BER performance of STBC and spectral efficiency STBC with 4 -Transmit antennas.
Copyright © 2010 SciRes.
Unlike most of the recent work, which are concentrated
on design to achieve full rate and full diversity codes.
We tried to invite researchers’ concentration to explore
new techniques to augment the spectral efficiency of
STB Codes. We presented a technique which enables us
to send more symbols per transmission as compared to
ordinary STB Codes. This approach also achieves full
transmit diversity and allows maximum likelihood decoding for signals. The additional plus point of this technique is its flexibility to any number of transmit antennas.
IJCNS