Improved transmit diversity block coded OFDM systems for highly dispersive channels

Improved Transmit Diversity Block Coded OFDM

Systems for Highly Dispersive Channels

Bing-Hung Chiang I , Ding-Bing Linz, Hsueh-Jyh Li I , Jia-Li Wang2

I Graduate Institute

of

Communication Engineering, National Taiwan University, Taiwan, R.O.C., +886-2-2363525 1 Ext. 538, hjli@ew.ee.ntu.edu.tw

Institute

of

Computer, Communication and Control, National Taipei University

of

Technology, Taiwan, R.O.C.,

2

+886-2-2771-2171 Ext. 2274, dblin@ntut.edu.tw

Absnofr-In 2000, King proposed two g, -based transmit diversity block coded OFDM (TDBC-OFDM) systems, i.e., space-time block coded OFDM (STBC-OFDM) and space- frequency block coded OFDM (SFBC-OFDM). However, he employed the least square (LS) detector, which was designed under the assumption that the channel is static over the duration of a space-timelfrequency codeword. Thereupon, S T B C - O F D W

SFBC-OFDM suffers from highly timdfrequency selectivity of

the channel. Recently, Antony recommended three novel detectors for space-time block coding (STBC) to combat the rapid channel variation. In our work, these detectors are applied to improve the original g, -based TDBC-OFDM systems. Also, the performances of the improved g, -based TDBC-OFDM

systems are evaluated by computer simulation. Simulation resultr have revealed that significant performance improvement can be achieved even when the systems are operated in highly dispersive channels.

I. INTRODUCTION

Space-time block coding (STBC) or transmit diversity block coding (TDBC), an effective transmit diversity technique, was first proposed by Alamouti [l] for flat fading channels. Based

on the assumption that the channel is static over the duration of a space-time codeword, it can obtain the same performance as maximum ratio combining (MRC) for receive diversity by

least square (LS) detection [2]. Orthogonal frequency division

multiplexing (OFDM) is an excellent technique that is capable of reducing the frequency-selective fading into frequency- nonselective or flat fading [3]. Thus TDBC can be used for

OFDM systems to improve the performance.

According to Alamouti code, g,

,

King proposed two combinations of TDBC and OFDM, i.e., space-time block

coded OFDM (STBC-OFDM) [4] and space-frequency block coded OFDM (SFBC-OFDM) [ 5 ] . However, he employed the LS detector, which was designed under the assumption that the

channel is static over the duration of a space-timdfrequency codeword. Thereupon, STBC-OFDWSFBC-OFDM suffers from highly time/frequency-selectivity of the channel.

Recently, Antony recommended three novel detectors for space-time block coding (STBC) to combat the rapid channel variation. They are zero-forcing (ZF), decision-feedback (DF) and maximum-likelihood (ML) detectors [6].

In

this paper, instead of the original

LS

detector, these novel detectors are applied to improve the performances of

g, -based TDBC-OFDM systems. In addition, the performances of the improved g, -based TDBC-OFDM system are evaluated by computer simulation. Simulation results have revealed that significant performance improvement can be achieved even when the systems are operated in highly dispersive channels.

11. TRANSMIT DIVERSITY BLOCK CODED OFDM Notice that subsequent description about TDBC-OFDM is based on three assumptions: first, sufficient cyclic prefix (CP) is added to avoid inter-block interference (IBI); second, the channel is constant over one OFDM block duration; third, the channel estimation is perfect. As mentioned before, there are two types of g2 -based TDBC-OFDM, namely, STBC-OFDM and SFBC-OFDM. The comparison of these dual systems is shown in Fig. 1.

A. STBC-OFDM

For STBC-OFDM, two consecutive OFDM blocks,

X,,,,

and

X,.,,

, are transmitted from two transmit antennas in two

OFDM block durations. Hence, the equivalent STBC transmission matrix for g , is [4]

where

X*".?

=

L*p,o

Ln,,

'".*.*,.",.,P

f o r p = 1.2 . xln*p.* is the transmitted symbol for the kth subcarria in the (2ntp)th block, and N , is the number of subcarriers per OFDM block.

In other words, at block instant (2rrtO),

X,,,,

and

X,,,,

are transmitted kom antenna 1 and 2, respectively. Then, at block instant (2n+l),

-Xim+,

and X;n+o are transmitted from antenna 1 and 2 , respectively. Therefore, the system function for STBC-OFDM system can be expressed as

ymc

=%A"

+ wmc

where

hj,2n+p,, is the channel frequency response from the ith transmit antenna to the receive antenna for the Rth subcarrier in the (2rrtp)th block.

H,.2"*p =diag[h,,>",p,o h,,,"*?,, " ' h,.*"*p,",.,l f o r i = l 2 '

For subcarrier

k,

the detectors consider a pair of symbols, namely, the nth space-lime codeword as follows.

y.=h.x.+w,

[".+ti]

- - p ; z n + o . i hz,zn+o,k X20+0t (3)

Yzn+i.i h2,2,+,,k -h[,.+~,k][x,"+,,,]+[

2::;:]

'

it__

e

SpsUolly Encoding DIncUon S ~Cd".$ ~ ~ ~ ~ ~ ~ , ~ ~ ~

Fig. 1 STBC-OFDM VS SFBC-OFDM.

I ) Least Square Detector: The original LS detector first performs matched filtering on the received symbols, i.e.,

Z. = hHy, =

n,x.

+ q., (4)

where 2. = [Gn+o.it Z 2 n + 1 . k r ,

'In = h f w n and

P

= h~,z~+o~hz,zn+o,~ -h;in+i.kh2.zn+i,k

.

It is clear that

P

is the spatial inter-symbol infe$erence (ISI) resulting from rapid channel variation. Nevertheless, the LS

detector ignores this spatial IS1 and obtains the bad estimates

and

i,,,,,,

by performing hard-decision on z , ~ ~ ~ . ~ and independently.

2) Zero-Forcing Detector: The novel ZF detector forces the

spatial IS1 to zero without the consideration ofnoise [6],'i.e., where z. = [z,n+,,k i, "+,. r a n d

i.

= hi'w.

.

in

= hi'y, = x.

+ i n ,

( 5 )

Apparently, the noise component,

in,

is correlated, but the ZF detector disregards the correlation and acquires the suboptimum estimates i,.,,,, and i,.+,,k by performing hard-decision on i,,+o,, and i2"+,,* separately.

3) Decision-Feedback Defector: The novel DF detector benefits from the whitened-matched filtering output [ 6 ] , i.e.,

G , =

where x , z r * o =[x..o x,.z " x m , Z k + O . . x . . N s . z P .

for k = O , I , . . , (N,/Z-I).

x#.Zk+l = 6 ; m . I x n . 3 ~ ' x n , 2 k + 1 ' . x n . N , - I P 3

Therefore, at the first half of each OFDM block duration,

X,,k,, and X,,,,,I are transmitted from antenna I and 2, 0

lht,zn+o.khbn+i.k + h2.zn+a.kh;.zn+i.k

1

& . z n + l , k ) 2 + Ihz.zn+o.r12

$ % 2 . + 1 , k 1 ~ + Ihz.zn+o.illz

-

hl.zn+o.th;.zn+o.k - h~.2n+l.kh;.zn+i,i J l h l , 2 n + , , k 1 2 + l h 2 , 2 n + 0 , k 1 2

respectively. Then, at the second half of each OFDM block duration, -Xi,,,+, and X;,,k+o are transmitted from antenna 1 and 2, respectively. Consequently, the system function for SFBC-OFDM system is expressed as

YSFBC = H S F B C ~ S F B C + WSFK

[ " 2 * + 0 ] - [ " y ~ + o

-

H 2 , n . z ~

x,,,,+o

Wn,2k+0

y n . 2 k + l _H,,n,zk+, - H ; . n , 2 k + l ] [ x n , Z k + ! ] + [ w c k + l ] ' (13) where H i . n . 2 k + ~ = diag[hi,.o hi.".2 ..h,,,2,+o

' 4 n , ~ , - ~ l ,

H,.,,,,+I = diag[h; ...I hj,",3 ..h,,,,2k+l - h r . n . ~ r - l l ,

for i = 1 2 and k = O , l , . . , ( N s / 2 - l ) .

For the nth block, the detectors consider a pair of symbols,

namely, the kth space-frequency codeword as follows. Y k =hixk + w k

P*+o]

- - [hl.,"+o h2.;2k+o ~ n , z i t + o (14)

Y~.Z*+I h,,.,,,,, -h,,,,,+l][x.,.~+,]'[~::::P] '

Subsequently, the operations of the detectors for SFBC- OFDM are similar to that for STBC-OFDM.

111. CHANNEL MODEL

In this paper, the systems are assumed to be operated in the

WSSUS Rayleigh fading channel with exponentially decaying

power delay profile described as follows [7]. The fading power of the mth path is

U: = ~ ? e - " " ~ for m=1,2,..M, (15)

where M i s the number of paths. Note that dcontrols the delay spread and Cis chosen to satisfy the constraint

Then solving for C yields

It is clear that a small d indicates a small delay spread, and vice versus

For simplicity, the T,-spaced channel model is used here for the simulation of wideband multipath fading channel [7], where T, is the reciprocal of the system bandwidth. Furthermore, each of the uncorrelated taps is of U-shape

power spectral density and is generated by the mobile fading channel simulator independently [8].

Iv.

PERFORMANdE RESULTS

For all simulations, the parameters are as follows. Firstly, the number of uncorrelated paths is 16 and hence the duration of CP is 16T, seconds; secondly, the number of subcaniers is 64 and hence the total OFDM block duration SOT, seconds; thirdly, the system bandwidth is 20MHz; finally, the modulation is BPSK.

Fig. 2 and Fig. 3 are the simulation results for STBC- OFDM and SFBC-OFDM, respectively. As seen from the figures, all detectors obtain similar performances in smoothly dispersive channels, whereas the three novel detectors outperform LS detector significantly in highly dispersive channels. In addition, the error probabilities for ML detectors remain nearly constant with increasing fmT, (normalized Doppler frequency) for STBC-OFDM or with increasing Td,JT, (normalized delay spread) for SFBC-OFDM; indeed, one can conclude that ML detector is robust to channel selectivity. Furthermore, it is obvious that, with the aid of ML detectors, the error probabilities of TDBC-OFDM systems are much lower than that of conventional OFDM systems.

As shown in Fig. 4

-

Fig. 7, the performances of TDBC- OFDM systems are compared

in

four extreme

scenarios,

namely, LTLF, HTLF, LTHF and HTHF, respectively. For instant, LTHF stands for low time-dispersion (i.e. frequency- selectivity) and high frequencydispersion (i.e. time- selectivity). Since STBC-OFDM and SFBC-OFDM are sensitive to frequency-dispersion and timedispersion, respectively, they obtain similar performance for both LTLF (Fig. 4) and HTHF (Fig.

7).

Additionally, STBC-OFDM performs better than SFBC-OFDM for HTLF (Fig.

9,

and vice versus (Fig. 6). Again, TDBC-OFDM system with ML detectors are always of the best performance as a result of considering the spatial IS1 and noise simultaneously.

V. CONCLUSIONS

In this paper, three novel detectors are applied to TDBC-OFDM systems. To combat the spatial IS1 resulting

from high channel dispersion, ZF detectorjust force the spatial

IS1 to zero, DF detector alleviates the spatial IS1 by

whitened-matched filtering and ML detector reduces the spatial IS1 and noise simultaneously. Thereupon, ML detector

is of the best performance but highest complexity, while DF and ZF detectors are of poorer performance but less complexity. However, with the aid of these novel detectors, TDBC-OFDM system are now compatible with the requirements for wideband wireless applications in highly dispersive channels.

REFERENCES

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2002. [4] [ 5 ] 161 [7] (81 1176

Exp~entia PDP lo* 1 ML 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SdldUner: S F B W F D M Ddld tinas : STBWFDM Unss wlfh a n t s : STBWFDM. S F B M F D U

U m wlmaut p M m : OFDM wlthaut a \ F d y fmTs(10E-3)

Fig. 2 P w k " improvements for STBC-OFDM.

i

pg

3.5 4

Td,rmsITs

Fig. 3 Performance improvements for SFBC-OFDM.

SNR (dB)

Fig. 4 Performance comparison for LTLR

Unes W h mints : STBCQFDM. SFBCOFDM

une wl& points : OFDM wllhout dhenify

5 10 15 20 25 30 35 40

SNR (d6)

Fig. 5 Perfomnce comparison for HTLF.

t

Exoanenll PDP

i

SNR W)