Journal o f Systems Engineering and Electronics, V o l . I ? , No. 2 , 2 0 0 6 , p p . 258-262

Efficient spread space-time block coding scheme in multiple antenna systems *

QLu Ling & Zheng Xiayu Dept. of EEIS, Univ. of Science and Technology of China, Hefei 230027, P. R. China

(Received May 10, 2005)

Abstract : Space-time coding is an important technique that can improve transmission performance at fading environ-

ments in mobile communication systems. In this paper, we propose a novel diversity scheme using spread space

time block coding (SSTBC) in multiple antenna systems. At the transmitter, the primitive data are serial to parallel converted to multiple data streams, and each stream is rotated in constellation. Then Walsh codes are used to

spread each symbol to all antenna space in a space-time block. The signals received from all receiver antennas are

combined with the maximum ratio combining (MRC) , equalized with linear equalizer to eliminate the inter-code in-

terference and finally demodulated to recover to transmit data by using the onesymbol maximum likelihood detec-

tor. The proposed scheme does not sacrifice the spectrum efficiency meanwhile maintains the transceiver with low

complexity. Owing to the transmission symbols of different transmit antennas passing through all the spatial sub-

channels between transceiver antenna pairs, the system obtains the partial additional space diversity gain of all spa-

tial paths. It is also shown that the diversity gain is better than the previous space-time block coding (STBC)

schemes with full transmission rate.

Key words: multiple antennas, spread space-time block coding (SSTBC) , diversity, full transmission rate.

1. INTRODUCTION

Recently, an intense interest has focused on wire- less systems that can provide good quality and high data rate. Space-time coding is an important tech- nique that can improve system performance at fa- ding environments by obtaining diversity gains and

coding gains in multiple antenna systems.

To make multiple antenna system practical,

methods that can obtain diversity gains with mod-

erate complexity and provide acceptable bit error rate ( BER ) performance are investigated in"'. Alamouti proposed a simple two-transmit-antenna space-time block coding (STBC)[", which can ob- tain space diversity gain similar to space-time trel-

lis coding (STTC) with the same transmit anten-

nas. The former involves only simple linear pro- cessing at the receivers to do the maximum likeli-

hood detection, while vector Viterbi decoders are required in STTC. Due to the practicality of simple construction and linear processing detector, STBC is generalized to any number of transmit antennas by V. TarokhC3'. But until now, STBC which can

achieve full diversity gain and keep full .transmis-

sion rate with simple linear processing at receiver

when the number of transmit antennas is more

than two is still not known to exist"'. The re-

search on multiple antenna system is inspired to

look for diversity techniques which have low com-

plexity, high performance while still keeping full

transmission data rate.

In Ref. [4], the author proposes a full trans-

mission rate STBC scheme. However, its perform-

ance improvement becomes less along with the in-

crease of the transmit antennas and introduces in-

terferencel5' . The technique proposed in this paper is an ef-

ficient transmit diversity scheme that uses Walsh

codes to spread each symbol to all antenna space in

a space-time block. It differs from orthogonal

transmit diversity ( OTD)C6' in that OTD achieves

multi-path gain in time domain at a symbol period

using transmit interleavers and more finger RAKE receivers while SSTBC obtains multiple antenna

space diversity in a space-time block. The pro-

* This project was supported by the National Science Foundation of China (60496314).

An e f f ic ien t spread spacetime block coding scheme in multiple antenna systems 259

posed SSTBC will not decrease symbol transmis- sion rate and will maintain simple receiver struc- ture. Simulation results show that the proposed method not only improves the performance of mul- tiple antenna system, but also has better diversity gain than the existing full transmission rate STBC schemer4’.

2. SPREAD SPACE-TIME BLOCK CODING

To differentiate the space data in each antenna, we use different Walsh code for each antenna. Walsh codes are generated by the following recursive Walsh-Hadamard matrix as follows.

H , - H , (1)

A two-transmit antenna and one-receive antenna (2 X 1) system using SSTBC is shown as Fig. l ( a> .

Channel Estimation

Equalization and Detection

(a) (2 X 1) antenna system using SSTBC

antenna 1 antenna 2 time t (SI cl,l+sz C Z , ~ ) 0

time t+T 0 (s1 ’ Cl,Z+SZ * CZ,Z)

T denotes the symbol duration

(b> The operation of SSTB encoding

Fig. 1 Antenna system and operation of SSTBC

Let the primitive data in a spacetime block be { s, ,m= 1 , 2 1.

XI = s1 C1,l +sz cz,1 XZ = s1 c1,2 +sz c2.2 (2)

where cm,k(m=1,2,k=1,2) is them‘ row, k‘ col- umn Walsh code in a Walsh-Hadamard matrix with

length of two. At the transmitter, the primitive data are first spread transformed to X1 and Xz ac- cording to Eq. (2).

Then XI and Xz are formed to spread space time block (SSTB) and sent to the two transmit antennas respectively at two different symbol peri- ods. The operation of SSTB encoding in space and time domains is illustrated as Fig. l(b).

Assuming channel fading responses at two consecutive symbol periods can be written as

hi (t> = hi hz(t+T> =hz ( 3 )

The received signals then can be expressed as

rl = r(t> = x1 hl +nl rz = r ( t+T) = .q hz +nz (4)

where { ni , i= 1 , 2 } are complex Gaussian variables representing noise and interference at the receiver.

To separate the two transmitted symbols, we can use a sub-optimum detector. Let the received signals be equalized by a linear equalizer, and then detect each symbol with scalar maximum likelihood detector. If the zero-forcing (ZF) linear equalizer is adopted here, then

F p == (HHH)-’HH (5)

where H= [hl 0 hz O] .Jz [’ 1 -1 ] is the equiv-

alent channel response matrix Supposing that the channel can be estimated

perfectly at the receiver, we can get the equalized signal as

2 = [::I= F [::I ( 6 )

The signal 2 is then decided by onesymbol maxi- mum likelihood detector to recover the transmitted data as {im,m=1,2} in each SSTB. S is the set of all possible symbols.

If an optimum detector is used, we can use vector maximum likelihood detector as follows.

where r = [::I is the vector of the received sig-

260

+ + + + - Equaliza--)

. Received tion . : in i m C i : STB detection - + *

Qiu Ling & Zheng Xiayu

7

Rebuilt P data 1 -

-

nals. C, is the original signal constellation set. Next, we extend the proposed (2 X 1) antenna

system using SSTBC to M - transmit antenna and N-receive antenna case.

In the proposed scheme, first Walsh codes are used to accomplish spread transform that spreads each symbol in a spread space-time block to all sub- channels. Then the transformed signals are trans- mitted by transmit antennas respectively in a spread space-time block. The receiver uses sub-op- timum detector (including linear equalizer and one- dimension maximum likelihood detector) or opti-

mum detector to separate different data streams from different transmit antennas and then to recov- er the transmitted data. Thus, the space diversity gain is obtained. The number of transmit antenna is required to satisfy M=ZL ( L can be any positive integer) to reduce the complexity. N can be any positive integer and maximum ratio combining is a- dopted at the receiver.

Ref. "81 indicates that a rotated transform will have more diversity gain compared with the general trans- form. The extended ( M X N ) system using rotation in constellation and SSTBC is shown as Fig. 2.

Transmitter

Fig. 2 ( M X N) antenna system using SSTBC

First, the primitive transmission data are serial to parallel converted to M data streams, and each stream is rotated in constellation, then the spread transformed signals are multipled as follows.

x = T D(a) s (8)

where x=[x1 *.. X M l T is the data signal after spread transform. From Eq. ( l ) , it has T =

H M . s = [ s ~ ~2 .*. s M I T is the primitive data. D ( a ) is a diagonal matrix with

where C= is the modulation co-

efficient. The spread transformed signals are sent to

STB forming unit. Supposing that each space time block has M symbol durations which are denoted by the period [ t , t f ( M - l ) T ] . Finally, we can get the transmitted signals as follows.

rx1 0 01

(9)

At the receiver, supposing the signals received at nm (l<n<N) receive antenna and M symbol peri- ods of a space-time block are as follows.

r" = [fl"*&]T (10)

All signals received form N receive antennas are multiplied with the estimated conjugate channel response and are added to do the maximum ratio combining (MRC).

rh:,l 0 O 1 0 h;,2

y" = D" (h , ) . r" = I : : I ' . I

(11)

N

Y = C Y " (12) n=1

Here y = [y1 * - - y N I T is the signal vector after MRC.

The signal after MRC operation is then equalized and demodulated to recover the transmitted data Here, we can also use linear equalizer to eliminate the inter-code interference and then do the one-symbol maximum likelihood detection similar to that in

An ef f i c i en t spread space-time block coding scheme in mul t ip le untennu systems 261

section 2. The linear equalizer can be ZF linear equal- izer of &. ( 5 ) or Minimum Mean Square Error (MMSE) linear equalizer as follows.

(13)

where, d is the noise variance. I is the unit matrix. Supposing the channels between the trans-

ceiver antenna pairs are independent and have the same noise variances, the equivalent channel ma- trix is

(14)

We can get the equalized signal as follows.

where, F is the linear equalizer. The signal 2 is then decided by onesymbol maximum likelihood detector to recover the transmitted data. We can also use vector maximum likelihood detector as follows

(16)

where, the definitions of C, , y , and H are as Eqs. (7) , (12) and (14).

According to the property of Hadamard ma- trix, a fast Hadamard transform ( F H T ) can be implemented here which uses length-two Walsh codes as a basic unit to make multiple spread

transform of the transmitted dataL7’. This will re- duce the operation times of addition and multipli- cation. The multiple spread transform is comple- ted by L times spread transform with length-two Walsh code. The L times recursion processing is as follows.

Initialization: S1 ( k ) = s k

Recursion: S+,(k) = c S j ( k + t l ( i , k ) ) X 2

,=1

C z 2 ( z , k ) , z 3 ( i , k ) t 1 < j < L , l < K < N End: x k = S M + l ( k ) where,

xk denotes the data transmitted by the km transmit antenna at symbol period t + ( k - l )

3. SIMULATION RESULTS AND ANALYSIS

In this section, we provide some simulation results that demonstrate the potential of our proposed method. The simulation results are listed in Figs. 3 and 4. In the simulation, we assume that perfect channel estimation and the amplitudes of fading from each transmit antenna to each receive antenna are mutually uncorrelated and quasi-static Rayleigh distributed. Furthermore, BPSK digital modulation is adopted and the average SNRS at each receive antenna are the same.

262 Qiu Ling & Zheng Xiayu

In Fig. 3 , we can see that the proposed SSTBCS has similar diversity gain as Alamouti’ s STBC with two transmit antennas. Since Alamouti’ s STBC gets the full spatial diversity, we can conclude that two transmit-antenna SST- BCs also achieve full diversity gain. This is be- cause the equally distributed signals after spread transform with rotated constellation maximize the diversity.

In Fig. 4 , we compare the performances of the proposed SSTBC and ABBA STCC4] with different antennas. We can see that the proposed SSTBC has a better performance than ABBA STC. It can be concluded that the ABBA space-time codes are severely worsen due to the non-orthogonality a- mong block codes with more than two transmit an- tennas. But the proposed SSTBC can achieve more diversity gain while using more transmit antennas and maintaining full transmission rate.

4. CONCLUSION

An efficient diversity scheme using spread space- time block coding in multiple antenna system is presented. It is shown that the proposed SSTBC can improve system performance while still main- taining the full data transmission rate. With the increase of transmit antennas, many extended ST- BC codes like ABBA STC can only obtain deterio- rated diversity. But the proposed SSTBC can a- chieve a better performance. It is shown that SST- BC can also get the same full diversity when the niumber of the transmit antennas equals two as Alamouti’ s STBC. Furthermore, the simple con- struction of SSTBC and the low complexity of line- ar processing at the receivers make it possible to be a potential future practical technique.

REFERENCES

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[2] Alamouti S M. A simple transmit diversity technique for wireless communications. IEEE Journal on Select-

ed Areas in Communications, 1998, 16 ( 8 ) : 1451 -1458.

[3] Tarokh V, Jafarkhani H, Calderbank A R. Space-time block coding for wireless communications : performance results. IEEE Journal of Selected Areas in Communi- cations, 1999, 17(3) : 451-460.

[4] Tirkkonen 0, Ebariu A, Hottinen A. Minimal non-or- thogonality rate 1 space-time block code for 3-t tx-an- tennas. Proc. ISSSTA’2000, 2000: 429-432.

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[ 6 1 Motorola. Orthogonal transmit diversity for CDMA for- ward link. Contribution to TIA , TR45. 5. 4 /97. 12.08. 05, December 8- 11, 1997.

[7] Zheng Xiayu, Qiu Ling, Zhu Jinkang. Performance and implementation of a novel space-time block coded 0 m M system. Proc. ICICS-PCM 2003, 2003: 2l34. 7. 1-4. ’

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Qiu Ling was born in 1963. She received the B. S. degree from South East University and the M. S. , the Ph. D. degrees from University of Science and Technology of China (USTC) in 1990, 1997 and 1999 respectively. She is now an associate profes- sor in Department of Electronic Engineering and Information Science, USTC. She has published two books and more than forty papers. Her cur- rent research interests include mobile communica- tions, spread spectrum and CDMA communica- tion, adaptive signal processing in mobile commu- nications, space-time signal processing and infor- mation theory. E-mail: lqiu@ustc. edu. cn

Zheng Xiayu was born in 1978. He received B. S. and M. S. degrees from University of Science and Technology of China (USTC) in ZOO1 and 2004 re- spectively. He is currently working toward the Ph. D. degree at the University of Florida, USA, His current research interests are in the spacetime coding in multiple antenna systems, information theory and sensor networks.