Novel time-frequency differential space-time modulation for multi-antenna OFDM systems1

Journal of Systems Engineering and Electronics , Vol .17, No. 1 , 2006, p p . 54

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Novel time-frequency differential space-time modulation for multi-antenna OFDM systems* Tian Jifeng , Jiang Haining, Song Wentao , Luo H a n w n & Xu Youyun Dept. of Electronic Engineering, Shanghai Jiaotong Univ. , Shanghai 200030, P. R. China (Received December 8, 2004) Abstract: Differential space-time (LET) modulation has been propased recently for multipleantenna systems over Rayleigh fading channels, where neither the transmitter nor the receiver knows the fading coefficients. Among existing schemes, differential modulation is always performed in the time domain and suffm performancedegradations in frequency-selective fading channels. In order to combat the fast time and frequency-selective fading, a novel time-frequency differential space-time (TF-DST) modulation scheme, which adopts differential modulation in both time and frequency domains, is propxed for multi-antenna orthogonal frequency division multiplexing (OFDM) system. A correspnding s u b optimal yet low-complexity non-coherent detection approach is also propc6ed. Simulation results demonstrate that the proposed system is robust for time and frequency-selective Rayleigh fading channels. Key w d : differential space-time modulation, MIMO, OFDM, time-varying channel.

1. INTRODUrnON Recently, there has been considerable interest in the wireless communication system with multiple transmit and receive antennas[1,2]. So far, most research on space-time modulation has assumed that accurate channel estimations are available at the receivers. Differential space-time ( DST ) modulation schemes were proposed to achieve diversity gains without channel state information ( CSI)[31. DST modulation schemes allow for slowly changing channels that have to remain invariant within two consecutive symbols. So it is less effective in rapidly fading environments. In order to allow for fast time varying fading channels, double differential space-time (DDST) block d i n g was proposed in Ref. [ 41, in which channel delay resulting from multi-path fading is assumed to be smaller than the symbol duration. However, this cannot be guaranteed in wireless channels. Orthogonal frequency division multiplexing ( OFDM )r51 , the spectrum efficient multi-carrier modulation technique, transforms a frequency-selective wide-band channel into a large number of non-selective narrow-band slices. To combat frequency-selective fading, an approach is proposed that OFDM is

concatenated with DDST, in which DDST is applied between adjacent OFDM frames in frequency domaid6]. In this paper, a novel time-frequency differential spacetime ( TF-DST) modulation scheme is developed and applied to OFDM systems. This system adopts the differential modulation in both time and frequency domains, and it is robust for time-and frequency-selectiveRayleigh fading channels. Moreover, our TF-DST scheme has a better performance than DDST-OFDM system in a fast fading channel, and it has less detection delay in receiver.

2. SYSTEM MODEL Figure 1 depicts the block diagram of our proposed TF-ET-OFDM system with N, subcarriers, Nt transmit antennas, and N,. receive antennas. At the transmitter, each information symbol is mapped into a space-time code word, which spans N, adjacent OFDM symbols and one subcarrier. We define the N, OFDM symbol intervals as one OFDM time blwk and denote TF-DST code matrix as c ( k , i ), in which k is the index of subcarriers and i is the index of OFDM time blocks. c ( k ,i ) is an N, x N t matrix, as shown below

* This project was supported by the National Natural Science Foundation of China (60272079) and National “863” High Technology Development Project of China (2003AAl23310).

Novel time-frequency differential space-time modulationfor multi-antenna OFDM systems

Consider the time-varying channel response between the m th transmitter antenna and the n th re-

55

ceiver antenna. The time-domain channel impulse response can be modeled as a tapped delay lineL7].

w

Fig. 1 Block diagram of TF-DST-OFDM system L

hmn(r;t) = C a m n ( p ; t ) a ( r -N%f)

(2)

p=1

where 6 ( ) is the Dirac delta function, L denotes the number of nonzero taps and a,, ( p ; t ) is the complex amplitude of the pth nonzero tap, whose delay is np/( N,A f), where np is an integer and Af is the tone spacing of the OFDM system. We assume that the time-varying effect is small and the Doppler frequency shift is invariable during the period of maximum channel delay. Then, a,, ( p ; t ) can be expressed as am,(p;t> = L , ( p > e x p (j2xfnt) (3) where f,is the Doppler frequency shift caused by relative motion between the transmit antennas and receive antennas. After discrete Fourier transform (DFT) , the frequency-domain channel response can be derived from the time-domain response as L

H,,(K ;t =

C a m , ( p ;t )exp( - j 2 x k n p / ~ c=)

p=1

L

[Ci,,(p p=1

>exp ( - j 2 x k n p / ~ , ] exp (j2xfnt) =

-

H m n ( k)

fi,,

. exp(j2xfnt )

(4)

It is assumed that ( k ) remains invariant during at least two consecutive OFDM symbols and the Doppler frequency fn is common to all transmit an( k ) is tennas. For simplicity for description, gmn called fading component and exp ( j2xfnt ) is called Doppler component in the rest of the paper.

At the nth receive antenna, DFT is applied to the signals received from Nt transmit antennas, and the received signal at the kth subcarrier and during the i th OFDM time block, denoted as X , ( k ,i ) , is obtained as X , ( k , i ) = 4"fn"N.n,C(k,i)H,(k) + Z , ( k , i ) Ta7ha-e

A:

= diag

(1,PL ,...,P L " . - ~ ' ) , ~ ( k ) :

(5) =

,iiz,( ~ ) , . . . , F I N r ( k ) > ~ , z , ( k ,isi ) the noise

(~l,(k)

and defined as Z, (k ,i ) : = ( z , (k ,iN,) ;*-, z, (k ,iN,+ N, - 1))T , which is circularly symmetric aHnplex Gaus-

sian distributed with variance No.

3. TI?-DST MODULATION AND DETECI'ION -ME The method proposed in Ref. [ 61 , in which OFDM is concatenated with double differential space-time d i n g (DDST) , is an effective way to oppress timeselective and frequency-selective fading. In DDSTOFDM system, DDST is introduced in consecutive OFDM symbols and the fading component of frequency-domain channel response H,, ( k ) is assumed to be constant during three consecutive OFDM symbols, i. e. it needs three OFDM symbols to detect one information symbol. In this paper, a novel time-frequency differential space-time modulation scheme is proposed for multi-antenna OFDM system. The new modulation scheme adopts differential modulation in

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Tian Jifeng , Jiang Haining, Song Wentao , Luo Hanwen & X u Youyun

56

both time and frequency domains and needs only two OFDM symbols to detect the information symbols.

3.1

TF-DST Modulation Scheme

TF-DST code matrix, denoted as C( k ,i ) , is chosen as one whose columns are orthogonal, i. e. C H ( k , i ) C ( k , i ) = NJ.,

tion approach is proposed in this paper. Firstly, the unknown fading components H, ( k - 1 ) and H,, ( k ) are removed with the characteristic of differential modulation between two adjacent OFDM time blocks in the same subcarrier, which is described as X,(k - 1 , i ) - Z,(k - 1 , i ) = e i 2 w w ( k - 1 , i )

(6) Inordertomaximkthetransmissonrate, N,=N,=N

[ X , ( k - 1 , i - 1) - Z,(k - 1,i - l ) ] x , ( k , i ) - Z , , ( k , i ) = &2zfKN&(k,i) (10) [ X n ( K , i - 1) - ~ n ( ~ ,- iI ) ]

is assumed. Differential modulation is introduced into both time-domain and frequency-domain and our TFDST code matrices are designed to satisfy

And then, the Doppler component is got rid of by performing the outer product diag { [ X , ( k - 1 , i ) - Z,(k - l , i ) ]

C(k,i) = G(k,i)C(k,i - 1) i 2 2 , k = 1,2,-..,Nc (7) where the generation matrix G( k ,i ) obeys G(k,i) = F(k,i)G(k - 1,i) k = 2 , 3 , - . - , N c , i3 1 G ( k , l ) = I@, k = 1,2;-.,NC (8) where k is the index of subcarriers and i is the index of OFDM time blocks. The matrix F ( k , i ) is

[ X f I ' ( k i) , - Zf;l(k,i ) ] 1 = G(k - 1,i) * diag { [ X , ( k - 1,i - 1) - Z,(k - 1 , i - 1 ) l [ X F ( k , i - 1) - Z f I ' ( k ,i - 1>11 GH(k - l , i ) F H ( k , i ) = diag { [ X , ( k - 1 , i - 1) - Z,(k - 1 , i - l ) ] (11) [ X f I ' ( k , i- 1) - Z f ; ' ( k , i- l ) l t P ( k , i )

mapped from the information symbol one-to-one. In the design of the transmit matrices, we consider diagonal unitary space-time coding, i. e. P ( k , i ) ~ ( ki ), = I ~ V ( F(K,~)E~)

X , ( k , i - 1) = X , 3 , X n ( k , i ) = x,4 (12) Z,, ,Z,, ,Z,, ,Zn4 are also defined similarly to ( 12) , and F is the denotation of F ( k ,i ) . Then, (11) can be rewritten as diag [ ( X n 2 - z n 2 ) (XF4 - ZF4>I = diag [ ( X , , - Zn1> 1 p (13) We collect all noise terms in Eq. (13) to the right-

i

> 1 , k = 1,2,-*,Nc

where SZ is the group of N-by-N unitary and diagonal matrices.

3.2 Sub-Optimal TF-DST Detection Scheme From the description of generation of TFDST code C ( k , i ) in Eqs. (7) and (8) and the expression of the received signal in the nth receiver antenna expressed in ( 5 ) , four corresponding receive matrices X , ( k - 1 , i - l ) , X , ( k - 1, i ) , X , ( k , i - l ) ,

X , ( k ,i ) that are adjacent in time and frequency domains can be written as X , ( k - 1 , i - 1) = & 2 z f n ( i - 1 ) N z A,c( k - 1 , i - 1) * H,(k - 1) + Z , ( k - 1 , i - 1) X , ( k - 1,i) = ,i2.fn&z G(k - 1 , i ) A,C(k - 1,i - l)H,(k - 1) + Z , ( k - 1 , i ) X,(k,i - 1) = , i 2 n f n ( i - 1 ) N z A,C(k, i - 1) H,(k)+ Z,(k,i- 1) X , ( k , i ) = e'2zfnNz G(k,i)A,C(k,i - 1) H,(k) + Z,(k,i) (9) Considering the complexity of ML detection, a

.

sub-optimal yet low-complexity non-coherent detec-

-

-

-

For simplicity, we define X , ( k - 1,; - 1) = X , , , X , ( k - 1 , i ) = Xn2

hand side and get diag (Xn2xF4) = diag ( x n l X f I I 3 ) P+ N,(14) where N, = diag [ Xn2ZfIi4+ Zn2XfIi4+ Zn1ZF32722 z F 4 -

x n 1zfI'3- z n 1XF3 I

(15)

For notational simplicity, (14) is rewritten as r , ( i ) = r , ( i - 1 ) P + N, (16) where r , ( i ) = diag (Xn2XF4) = diag (X,(k - l,i)XfIi(k,i)) r , ( i - 1) = diag (X,lXfI'3) = diag ( X , ( k - 1 , i - l)X!(k,i - 1 ) ) (17) Then, the signal of all the receive antennas can be written as R ( i ) = R(i - 1) [IN OFH] + N (18) where R ( i ) = diag [ rl ( i ) ,r2( i ) , = diag

,rNr( i ) ] ,N

(N1, N 2 , .--, N N ) . @ stands for Kronecker

Novel time-frequency differential space-time modulationfor multi-antenna OFDM systems product. In order to derive the sub-optimal detection rule, the second-order noise term in N is ignored and the noise N is approximated as a zero-mean complex Gaussian vector whose covariance matrix is denoted as

I

0

C,J

where

en

= E(N,JVF) = Nodiag (XnlXFl

+

(20) ~ 2 x+ 5xfII3xn3 + xj114xn4) Because N is complex Gaussian, so the probability density function of R ( i ) conditioned on R ( i - 1 ) and F can be written as f(R(i) I R(i - 1),F) =

1

57

see from the Fig. 2 that TF-DST-OFDM system has a better performance than DST-OFDM system and DDST-OFDM. Figure 3 shows the performance of the three systems in a very fast fading channel, in which Doppler frequency f d T is chosen as 0.1. At this time, DSTOFDM system has a very high BER even at high SNR, which means DST-OFDM system is not suitable for very fast fading channel. However, the performance of TF-DST-OFDM system nearly does not degrade compared with the performance in fast fading channel shown in Fig. 2 and our TF-DST-OFDM system keeps better performance compared to DDSTOFDM system.

c

rNtNrdet(

)

EdNold13

- -:DST-OFDM; -o-:DDST-OFDM

Y R(i)l = argmaxcRe TriF

-A-

[diag (XnlXfl',)]*

*=I

:TF-DST-OFDM

Fig. 2 Performancecomparison in fast fading

[diag I-l

channel ( f d T z O . 0 5 )

diag ( Xn2Xs1141 1 (22) It is easy to recover the information symbols from f: , since the mapping between the information and matrix F is one-to-one.

4. SIMULATIONRESULTS In this section, we' provide computer simulation results to illustrate the performance of our proposed TF-DST-OFDM system over a time-and frequencyselective fading channel, namely two-tap equal-power fading channel with Doppler frequency fd , compared with DST-OFDM and DDST-OFDM systems. The optimal (4; 1, 1) group codes with R = 1 are employed for all the systems. Figure 2 illustrates the performances of the three systems in a fast fading channel, whose Doppler frequency fd is chosen to satisfy f d T = 0.05, where T denotes the period of one OFDM time block. We can

IO-J-) 0

2

4

6

8

10 12 14

16 18 20

EdNddB

-m -:DST-OFDM; -o-:DDST-OFDM -A-

:TF-DST-OFDM

Fig. 3 Performance comparison in very fast fading channd ( f d T = O . l )

A conclusion can be drawn from Fii. 2 and Fig. 3 that TF-DST-OFDM system is robust to time-selective frequency-selectivefading and it has a better performance than DDST-OFDM system.

58

Tian Jifeng , Jiang Haining , Song Wentao, Luo Hanwen 8z Xu Youyun

5. CONCLUSION In this paper, a novel time-frequency differential spacetime (TF-DST) modulated OFDM system is proposed. First, we give the model of the TF-DSTOFDM system over time-and frequency-selective channel. And then a novel TF-DST modulation scheme is proposed, in which differential space - time modulation is introduced into both time domain and frequency domain. At receiver, a suboptimal yet low-complexity non-coherent detection scheme is proposed. 'TF-DST-OFDM system is proved to be robust for the time-selective frequency-selective channel by simulations. Moreover our TF-DST scheme has a better performance than DDST-OFDM system in a fast fading channel, and it has less delay in detection, for the fact that it needs only two OFDM symbols to detect the information symbols, while DDSTOFDM system needs at least three OF'IIM symbols.

REFERENCES [ l ] Tmkh V, %hadxi N , Calderbank A R. Space-time codes for high data rate wireless communication: performance criterion and code construction. IEEE Trans. Infm. T b y , 1998, 44(2): 744-765.

[2] Tarokh V, Jafarkhani H, Calderbank A R. Spacetime block codes from orthogonal designs. IEEE Trans. Inf o m . T h r y , 1999, 45(5): 1456-1467. [3] Hughes B L. Differential space-time modulation. lEEE Trans. I n f m . Themy, 2000, 46(7) : 2567-2578. [4] Liu Zhiqiang, G i a n ~ kGi ~B, Hughes B L. h b l e differential space-time block d i n g for timeselective fading channels. IEEE Trans. Camm., 2001, 49(9): 15291539. [ 51 Bingham J A C. Multicarrier modulation for data transmission: an idea whose time has m e . IEEE Camm. M a g . , 1990, 2 8 ( 5 ) : 5-14. [61 Yao Yi, Howlader M. Multiple symbol double differential space-timeadedOFDM. VTC, 2002. 6-9. [7] Proakis J G. Digital communications, (3' Edition). New York : M G a w - H i l l , 1995.

Tian Jifeng was born in 1976. He received his B. S. and M. S. degrees in electronic engineering from Harbin Engineering University in 1999 and 2001, respectively. He is currently working toward the Ph. D. degree in Electronic Engineering at Shanghai Jiaotong University. His research interests include MIMO technique, OFDM technique and B3G mobile communication systems. E-mail: jftian @ vip. Sina. com