Low-Complexity Turbo Equalization for Alamouti ...

Low-Complexity Turbo Equalization for Alamouti Space-Time Block Coded EDGE Systems K. C. B. Wavegedara and Vijay K. Bhargava Department of Electrical and Computer Engineering, University of British Columbia, 2356 Main Mall Vancouver BC V6T 1Z4, Canada Email: {kapilaw,vijayb}@ece.ubc.ca Abstract— Enhanced Data Rates for Global Evolution (EDGE) based systems are expected to facilitate the same services as third generation WCDMA systems. This goal is achieved through physical layer enhancements to increase the data rate and spectral efficiency. Thus, it has become important to incorporate the recent advances in the physical layer. Recently, space-time block coding (STBC) has evolved as an effective transmit diversity technique. Convolutional channel coding is employed in EDGE systems. The combination of channel coding and STBC can be used to achieve high throughput over hostile wireless channels. On the other hand, turbo equalization can be employed in channel coded broadband wireless systems to further enhance the radio link performance. EDGE-based systems employ 8PSK highlevel modulation. Hence, maximum a posteriori (MAP)-based soft equalization is not suitable due to high complexity. Therefore, in this paper, we propose a low-complexity MMSE-based turbo equalization scheme for Alamouti space-time (ST) block coded multiple-input multiple-output (MIMO) systems. In the proposed iterative receiver, widely linear (WL) processing is used to exploit the rotational variance of the ST block coded transmit signal. Equalization and ST block decoding are jointly carried out at each iteration using the a priori information delivered by the convolutional channel decoder from the previous iteration. The simulation results demonstrate that high performance improvement can be obtained using the proposed iterative scheme in comparison to the non-iterative equalization. Due to the lowcomplexity, the proposed scheme is highly attractive for future EDGE-based systems with Alamouti STBC.

I. I NTRODUCTION Enhanced Data Rates for Global Evolution (EDGE) air interface has been standardized under the Third Generation Partnership Project (3GPP) as an evolution for the existing time division multiple access (TDMA)-based second generation wireless systems, namely, Global System for Mobile Communications (GSM) and Industrial Standard (IS)-136 system. The EDGE standard uses 8PSK high-level modulation and an improved link quality control scheme to achieve high data rates and high spectral efficiency. Two modes have been developed under EDGE: Enhancement General Packet Radio Service (EGPRS) and Enhanced Circuit Switched Data (ECSD). Among the two modes, EGPRS has become more popular as it is packet-switched based [1]. To achieve the goal of supporting broadband wireless services such as live video, we believe that recent advances in the physical layer, such as transmit diversity and turbo (iterative) equalization should be incorporated in EDGE-EGPRS systems. In recent years, space-time block coding (STBC) has received tremendous attraction as an effective transmit diversity technique. The concept of STBC was introduced for

two transmit antennas by Alamouti in [2]. Space-time (ST) block codes were originally designed for frequency-flat fading channels. Later, block-transmission based STBC schemes were proposed for frequency-selective fading channels, e.g., [3], [4]. These schemes assume that subchannels are invariant over two consecutive symbol blocks in order to satisfy the orthogonality condition. Although these schemes are able to yield the maximum possible diversity gain, the extension to the fast fading channels is yet to be addressed. Moreover, considerable error floor behavior is observed in the BER performance for fast time-varying channels [5]. On the other hand, direct application of symbol-based Alamouti ST block code for transmission over multipath fading channels was considered in e.g., [6]. In this approach, ST decoding is performed separately after conventional multiple-input multiple-output (MIMO)-equalization. However, in these schemes, multiple receive antennas are essential to achieve good performance. Recently, in [5], Gerstacker et al. proposed novel equalization techniques for symbol-based Alamouti ST block code. In [5], widely linear (WL) processing is used to exploit the rotational variance of ST block coded transmit signal. Interestingly, these WL processing based equalization schemes can be used to achieve a high performance without receiver diversity. Furthermore, in [5], it has been shown that the symbol-based Alamouti scheme is more attractive than block-transmission based schemes under moderate-to-fast fading conditions. However, the schemes proposed in [5] are restricted to non-iterative (i.e., hard-decision based) equalization. On the other hand, channel coding is usually employed in wireless systems to mitigate the effect of random noise. Hence, an additional performance improvement can be achieved through iterative soft (turbo) equalization compared to non-iterative hard-decision based approaches. Initially, turbo equalization was considered using full-state trellis based soft equalizers (e.g., soft-output Viterbi equalizer and maximum a posteriori (MAP) equalizer). Unfortunately, trellis based soft equalizers may be highly computationally-expensive for long channels and/or for large signal constellations. Hence, trellis based schemes are not suitable for EDGE systems which use 8PSK modulation. Low-complexity minimum mean square error (MMSE)-based turbo equalization schemes were proposed for single-input single-output (SISO) channels in e.g., [7]. Recently, in [8], an MMSE-based fractional turbo equalization scheme was proposed for MIMO systems. However, in that scheme ST coding was not considered. In [9], turbo equalization was considered for burst-based ST block coded transmis-

Fig. 1.

System Model-Part I: Transmitter Section

sion in EDGE systems. Nevertheless, in [9], low-complexity MMSE-based turbo equalization was not considered. In this paper, we develop an MMSE-based turbo combined equalization and ST block decoding scheme for Alamouti ST block coded EDGE-based systems with NT = 2 transmit antennas and NR ≥ 1 receive antennas. In the proposed iterative receiver, WL processing is used to improve the performance as it has been employed for non-iterative equalization in [5]. Our proposed iterative receiver performs combined equalization and ST block decoding at each iteration using the a priori information delivered by the channel decoder in the previous iteration. The primary contribution in this paper is the development of an iterative equalization scheme for Alamouti ST block coded MIMO-EDGE systems as an extension to the non-iterative WL-based linear equalization scheme proposed in [5]. Note that in [10], we proposed a similar MMSE-based receiver with WL processing for Alamouti ST block coded systems. However, in [10], BPSK modulation was considered. We will show through simulations that high performance improvements can be obtained using the proposed iterative receiver in comparison with non-iterative equalization. Notation: Bold lower case letters represent vectors while bold upper letters denote matrices; (.)T , (.)∗ , and (.)H denote the operations transpose, complex conjugate (componentwise), and Hermitian transpose, respectively; IM and 0M ×N denote the M × M identity matrix and an all-zero matrix of size M ×N ; diag(s) represents a diagonal matrix, where vector s on the diagonal. E{.} and Cov{.} stand for the expected value and covariance operator, respectively. d.e represents the ceiling function. II. S YSTEM M ODEL We consider Alamouti ST block coded transmission over a MIMO multipath fading channel. The transmitter is equipped with NT = 2 antennas, while the receiver can have either a single antenna or multiple antennas (NR ≥ 1). The transmitter and receiver sections of the discrete-time baseband system model are shown in Fig.1 and Fig.2, respectively. A. Transmitter b −1 A block of Nb information bits {b(k)}N k=0 , b(k) ∈ , {0, 1} is fed into a binary convolutional encoder of constraint length ν and code rate Rc . Note that each information frame is appended with ν − 1 long trellis terminating sequence before channel encoding. The resulting channel coded frame Nc− 1 of length Nc = Nb /Rc , {c(m)}m=0 is then interleaved by a random block interleaver. The random interleaver rearranges the ordering of the input sequence and outputs c(m0 ) m0 = 0, 1, . . . , Nc − 1, where m0 = Π(m) and Π(.) denotes the interleaver function. The interleaved code bits are

grouped into sets of Q bits, cn = {cn (1), cn (2), . . . , cn (Q)}, n = 0, 1, . . . , Ns − 1, where Ns = Nc /Q and Q is the modulation order (Q = 3 for 8PSK). Each set of Q modulating bits, cn is Gray mapped into 8PSK symbols s(n) ∈ {α0 , α1 , . . . , αM −1 }, where αν = ej2πν/M , ∀ν, ν = 0, 1, . . . , M − 1 and M = 2Q is the size of the signal constellation (M = 8 for 8PSK). P Note that the signal constellation M −1 has zero mean Es , 1/M ν=0 αν = 0 and unit variance PM −1 2 Vs , 1/M ν=0 |αν | = 1. We assume that symbols s(n), n = 0, 1, . . . , Ns − 1, are statistically independent. After constellation mapping, two consecutive symbols s(2n) and s(2n + 1) are fed into the ST block encoder. The ST block encoder outputs sequences s1 (i) and s2 (i) according to the following rule [2], ½ s(2n); i = 2n s1 (i) = (1) −s∗ (2n + 1); i = 2n + 1 ½ s(2n + 1); i = 2n (2) s2 (i) = s∗ (2n); i = 2n + 1 Then, ST encoded sequences, s1 (i) and s2 (i) are transmitted through the first and second transmit antenna, respectively. B. MIMO Channel For numerical results, we consider multipath propagation models for typical urban areas (TUA) and typical hilly terrains (THT) as specified in [11]. The continuous time received signal at each receive antenna is corrupted by a complex, zero mean, additive white Gaussian noise (AWGN) precess ηnr (t) with variance ση2 /2 per dimension. We employ a linearized Gaussian minimum shift keying (GMSK) pulse shaping filter [12] and a square-root raised cosine (SRC) filter as the transmitter and receiver filters, respectively. Let us define hnt ,nr , [hnt ,nr (0), . . . , hnt ,nr (L)]T , nt = 1, 2, nr = 1, 2, . . . , NR , NR ≥ 1, as the discrete-time overall subchannel impulse response (between the nt th transmit antenna and the nr th receive antenna) of transmit filter, the multipath channel, and the receiver filter. The discrete-time received signal in the nth symbol interval at the nr th receive antenna obtained by sampling the output of the receive filter at the symbol-rate can be expressed as rnr (n) =

L X

[h1,nr (l)s1 (n − l) + h2,nr (l)s2 (n − l)] +ηnr (n).

l=0

(3) Note that without loss of generality, we assume that the channel order, L is same for all subchannels between multiple transmit and receive antennas. We also assume that the multipath subchannels are time-invariant over a transmitted symbol burst and the fading between symbol bursts is independent. C. Receiver We use WL processing at the receiver to exploit the rotational variance of the ST block coded transmit signal as described for non-iterative suboptimal equalization approaches (i.e., for linear and decision feedback equalization) in [5]. In a WL receiver, the received signal and its complex conjugate are processed together. Hence, let us first define a vector comprising two consecutive samples of the received signal at

Fig. 2.

System Model-Part II: Receiver Section

the nr th antenna and the complex conjugates of the polyphase components as follows [5],

˜f = N1 +N2 . Note that vector ˜rn of length 4(N ˜f +1) where N is the input to the iterative equalizer in the nth time interval.

˜rnr (n) , [rnr (2n) rnr (2n + 1) rn∗ r (2n) rn∗ r (2n + 1)]T , (4)

III. MMSE- BASED TURBO RECEIVER

for nr = 1, 2, . . . , NR . We can express ˜rnr (n) as ˜rnr (n) =

˜ L X

˜ n (l)˜s(n − l) + η ˜ nr (n), H r

(5)

l=0

where ˜s(n) , [s(2n) s∗ (2n) s(2n + 1) s∗ (2n + 1)]T

(6)

˜ = dL/2e is the order of the equivalent channel model, L ˜ nr (n) = [ηnr (2n) ηnr (2n + 1) ηn∗ r (2n) ηn∗ r (2n + 1)]T . (7) η ˜ n (l) is defined at the bottom of the page in (8). and H r Note that for convenience we change the ordering of the ˜ n (l) is terms when defining ˜ s(n) compared with [5] and H r also modified accordingly. Then, we define a vector ˜rn , [˜rT1 (n) ˜rT2 (n) . . . ˜rTNR (n)]T by stacking signal vectors of NR receive antennas. ˜rn can be given as ˜ L X

(9)

=

˜ T (l) H ˜ T (l) . . . H ˜ T (l)]T [H 1 2 NR

(10)

=

˜ T2 (n) [˜ η T1 (n) η

(11)

l=0

where ˜ H(l) ˜ (n) η

P (s(n)=αν ) =

Q−1 Y

P (cn (q)=bν (q)),

(17)

q=0

˜ s(n − l) + η ˜ (n), H(l)˜

˜rn =

In this section, we describe the proposed MMSE-based iterative receiver for Alamouti ST block coded transmission. Differently from the existing MMSE-based turbo equalization schemes in e.g., [8], [13], [14], the proposed MIMO-MMSE based turbo equalizer performs equalization and ST block decoding jointly at each iteration with WL processing. At the beginning of each iteration (except in the first iteration), the mapper computes mean s¯(n) and variance υ 2 (n) of transmitted symbols s(n), n = 0, 1, . . . , Ns −1, and feed them into the soft equalizer. These statistics are obtained from the a0 priori P [c(m )=+1] log likelihood ratios (LLRs) LpE (c(m0 )) , ln P [c(m0 )=−1] , 0 m = 0, 1, . . . , Nc − 1, delivered by the channel decoder from the previous iteration. The symbol a priori probability can be computed as

...

˜ TNR (n)]T . η

Let us now introduce a sliding-window model for MMSE based iterative equalization in the nth time interval as follows, ˜ sn + η ˜rn = H˜ ˜ n,

(12)

with ˜rn , [˜rT (n + N2 ) . . . ˜rT (n) . . . ˜rT (n − N1 )]T (13) ˜ T(14) ˜sn , [˜sT (n + N2 ) . . . ˜sT (n) . . . ˜sT (n − N1 − L)] ˜ n , [˜ ˜ T (n) . . . η ˜ T (n − N1 )]T (15) η η T (n + N2 ) . . . η ˜f + 1) × 4(N ˜f + L ˜ + 1) channel and 4NR (N  ˜ ˜ L) ˜ H(0) ... H( 0 ... ˜ ˜  0 H(0) . . . H(L) 0 ˜ =  H  . . . .. ..  .. ˜ 0 ... ... 0 H(0)

matrix ... ... ...

 0 0   , ..  . ˜ ˜ H(L) (16)

where bν (q) ∈ {0, 1} based on symbol αν , ν = 0, 1, . . . , M − 1 and the a priori probabilities of code bits P (cn (q)=1) = p (cn (q)) Lp E (cn (q)) ) and P (c (q)=0) eLE /(1 + e = 1/(1 + n p eLE (cn (q)) ). Now we can obtain the mean of the symbol s(n) as M −1 X s¯(n) , E{s(n)} = αν P (s(n)=αν ) (18) ν=0

and the variance as υ 2 (n) , E{|s(n)|2 } − |¯ s(n)|2 , (19) PM −1 where E{|s(n)|2 }, ν=0 P (s(n) = αν )|αν |2 . The linear MMSE estimates, ˆsn,j = [ˆ s(2n+j) sˆ∗ (2n+j)]T of ˜sn,j = [s(2n + j) s∗ (2n + j)]T can be given as [13], H ˆsn,j = E{˜sn,j } + Wn,j [˜rn − E{˜rn }],

for j = 0, 1. (20)

˜f + 1) × 2 is designed so that The filter, Wn,j of size 4NR (N ˆsn,j andi ˜sn,j the Bayesian mean square error (MSE) between h 2 is minimized as Wn,j = arg minWn,j E |ˆsn,j − ˜sn,j | and is given by Wn,j = Cov{˜rn ˜rn }−1 Cov{˜rn˜sn,j }.

(21)

Based on the turbo principle, when code symbol s(2n + j) is estimated, the a priori information of the same code symbol provided by the channel decoder is not used, i.e., we set s¯(2n + j) = 0 and υ 2 (2n + j) = σs2 as in the first iteration. ˜ sn,j , This yields in (20) E{˜sn,j } = [0 0]T and E{˜rn } = H¯ T T T ˜ T where ¯sn,j , [¯s (n + N2 ) . . . ¯sj (n) . . . ¯s (n − N1 − L)] ∗ ∗ T with ¯s(˜ n) = [¯ s(2˜ n) s¯ (2˜ n) s¯(˜ n + 1) s¯ (˜ n + 1)] for n ˜ 6= ˜ n − N1 − L ˜ + 1, . . . , n + N2 and ¯s0 (n) = n, n ˜ = n − N1 − L, [0 0 s¯(2n + 1) s¯∗ (2n + 1)]T , ¯s1 (n) = [¯ s(2n) s¯∗ (2n) 0 0]T . Let us now consider the input vector to the iterative equalizer, ˜ s − ¯s] + η ˜rn − E{˜rn } = H[¯ ˜ . It is wroth mentioning that the term [˜rn − E{˜rn }] in (20) can be functionally viewed as soft inter-symbol interference (ISI) and co-antenna interference (CAI) cancelation. In the schemes of [13], [15], only soft ISI cancelation is performed as those schemes were proposed for single-transmit antenna systems. We can show that the covariance of ˜r, Cov{˜r˜r} required in computing the MMSE filter in (21) is given by ˜ ss,j (n)H ˜ H + σ2 I Cov{˜r˜r} = HR ˜f +1) , n 4NR (N

(22)

˜f + L ˜+ where Rss,j (n) is a block diagonal matrix of size 4(N ˜ ˜ 1) × 4(Nf + L + 1), which is defined as ˜ T. Rss,j (n) , diag[Φ(n+N 2) . . . Φ(n, j) . . . Φ(n−N1 −L)] (23) Let us define the matrices Φ(˜ n) for n ˜ 6= n; n ˜ = n − N1 − ˜ . . . , n + N2 and Φ(n, j) for j = 0, 1, as follows L,   2 υ (2˜ n) υ 2 (2˜ n) 0 0  υ 2 (2˜  n) υ 2 (2˜ n) 0 0 , Φ(˜ n) ,   0 0 υ 2 (2˜ n + 1) υ 2 (2˜ n + 1)  0 0 υ 2 (2˜ n + 1) υ 2 (2˜ n + 1) and



σs2 σs2 0  σs2 σs2 0 Φ(n, 0) ,   0 0 υ 2 (2n + 1) 0 0 υ 2 (2n + 1)  2 υ (2n) υ 2 (2n) 0  υ 2 (2n) υ 2 (2n) 0 Φ(n, 1) ,   0 0 σs2 0 0 σs2

 0  0 , 2 υ (2n + 1)  υ 2 (2n + 1)  0 0  . σs2  σs2

Since in the first iteration, no a priori information is delivered to the soft equalizer, υ 2 (i) = σs2 , ∀i, n =0, 1, . . . , Nc −  1. 1 1 0 0  1 1 0 0   It follows that Φ(˜ n) = Φ(n, j) , σs2 .   0 0 1 1 , 0 0 1 1 ˜ for n ˜ = n − N1 − L, . . . , n + N2 and j = 0, 1. In the first iteration, Rss,j (n) is same for every code symbol to be estimated and thus, it is sufficient to perform matrix inversion

Cov{˜r˜r}−1 only once per frame in computing the MMSE filter coefficients. It can also be shown that Cov{˜rn˜sn,j } in (21) is given by h ¯ jH ˜ T (L) ˜ Cov{˜rn˜sn,j } = 02×4NR (N2 −L) Φ ˜ iT ¯ jH ˜ T (L ˜ T (˜0) 02×4N N ¯ jH ˜ − 1) . . . Φ Φ , (24) 1 R · ¸ · ¸ ¯ 2 = σ 2 . 0 0 1 1 . We ¯ 1 = σ 2 . 1 1 0 0 and Φ where Φ s s 11 0 0 00 11 can express the MMSE filter, Wn,j , for j = 0, 1 as h i−1 ˜ ss,j (n)H ˜ H + σ2 I Wn,j = HR . ˜ n 4NR (Nf +1) h iT ¯ ˜T ˜ ¯ ˜ T 0) 02×4N N (25) 02×4NR (N2 −L) . ˜ Φj H (L) . . . Φj H (˜ 1 R Finally, we can obtain the code symbol estimates as follows sˆ(2n)

=

sˆ(2n + 1)

=

H ˜ sn,0 ] and e1 Wn,0 [˜rn − H¯ ˜ sn,1 ], e1 WH [˜rn − H¯ n,1

(26) (27)

where e1 = [1 0]. We assume that the estimates of code symbols obtained from MMSE linear equalization can be approximated using a Gaussian distribution, i.e., sˆ(2n + j) ∼ ¡ ¢ N µ ˆ(2n + j)s(2n + j), σ ˆ 2 (2n + j) . Hence, sˆ(2n + j) may be represented as the output of the equivalent AWGN system model as sˆ(2n + j) = µ ˆ(2n + j)s(2n + j) + ηˆ2n+j ,

(28)

where µ ˆ(2n + j) and ηˆ2n+j are the amplitude and zero mean complex white Gaussian noise with variance σ ˆ 2 (2n+j) of the equivalent AWGN system model, respectively. Note that a similar approximation is used e.g., for iterative soft interference cancelation in CDMA systems [16] and for turbo equalization [13], [15]. We believe that the same approximation holds for the problem at hand as will be verified through simulations. After some manipulations, we can show that H ˜ T (L) ˜ ˆj H µ ˆ(2n + j) = e1 Wn,j [02×4NR (N2 −L) φ ˜ ˜ T (L ˜ T (˜0) 02×4N N ]T , ˜ − 1) . . . φ ˆj H ˆj H φ 1 R ¡ ¢ σ ˆ 2 (2n + j) = σs2 µ ˆ(2n + j) − µ ˆ2 (2n + j) ,

(29) (30)

ˆ = [1 1 0 0]T and φ ˆ = [0 0 1 1]T . for j = 0, 1 where φ 1 2 The demapper computes the extrinsic information LeE (c(m0 )) for each code bit m0 = 0, 1, . . . , Nc − 1. It can be shown that (see e.g., [7], [14] for detailed derivation), LeE (cn (q)) P = ln P

∀s(n):cn (q)=1

P (ˆ s(n)/s(n))

∀s(n):cn (q)=0

P (ˆ s(n)/s(n))

Q Q

∀q 0 ,q 0 6=q

P (cn (q 0 ))

∀q 0 ,q 0 6=q

P (cn (q 0 ))

, (31)

where ∀s(n) : cn (q) = {1, 0} denotes the subset of symbols having the qth bit, cn (q) = {1, 0}. After deinterleaving, the



 h1,nr (2l) h2,nr (2l − 1) h2,nr (2l) −h1,nr (2l − 1)  h2,nr (2l) h2,nr (2l + 1) −h1,nr (2l)  r (2l + 1) ˜ n (l) ,  h1,n  H ∗ ∗ ∗ r  h2,n (2l − 1)  h1,nr (2l) −h1,nr (2l − 1) h∗2,nr (2l) r h∗2,nr (2l) h∗1,nr (2l + 1) −h∗1,nr (2l) h∗2,nr (2l + 1)

(8)

0

extrinsic information LeE (c(m0 )), m0 = 0, 1, . . . , Nc − 1 is passed to the channel decoder as the a priori information.

10

IV. N UMERICAL R ESULTS AND D ISCUSSION

10

Average BER

−2

10

−3

10

−4

10

STBC, It#1 STBC, It#2 STBC, It#5 STBC, PA SISO, It#1 SISO, It#2 SISO, It#5 SISO, PA

−5

10

4

5

6

7 Eb/N0 dB

8

9

10

Fig. 3. Average BER performance of the proposed turbo combined equalization and ST block decoding scheme: MCS-5, TUA channel model 0

10

−1

10

Average BER

We investigate the performance of the proposed turbo combined equalizer and ST block decoder for Alamouti ST block coded transmission. In simulations, we closely follow the radio link (downlink) specifications of EGPRS systems as given in [12], [17], [18]. We choose two modulation and coding schemes: MCS-5 and MCS-7. We use the block length of binary data bits, Nb = 448 and Nb = 2×448 in MCS-5 and MCS-7 schemes, respectively. A rate-1/3 nonsystematic convolutional code with generators (133, 171, 145)8 is employed. Puncturing is used to achieve the desired code rate (and the desired coded block length) Rec = 0.37 and Rec = 0.76, in MCS-5 and MCS-7, respectively. For simplicity, instead of the interleaving operation described in [18], a random block interleaver is used. Coded data block is combined with the block of coded header bits and flag bits and this results into a block of 1392 bits. Each combined block is mapped into 4 bursts (i.e., 4 × 348 bits). Bursts are Gray mapped into 8PSK symbols. Each burst is composed of 2×52 (2 × 51) data symbols, 2 × 6 (2 × 7) header symbols and flag symbols, 26 training symbols in the middle of the burst and three guard symbols at the both ends of MCS-5 (MCS7). For simplicity in simulations, we assume the same power delay profile for all subchannels. As mentioned before, we assume that every subchannel is time-invariant within each burst and vary independently from burst to burst (i.e., ideal frequency hopping). This assumption is well justified for lowto-moderate mobile speeds with the specifications of EDGEEGPRS systems. Furthermore, it is also assumed that the perfect channel information is available at the receiver. In all cases considered below, the total channel power gain is normalized to one. For channel decoding, we use the BCJRMAP algorithm with the modifications found in [16]. Note that the results presented in this paper are obtained without receiver diversity (i.e., NR = 1). In Fig.3 and Fig.4, we present the average bit error rate (BER) performance of the proposed turbo receiver with the MCS-5 coding scheme for TUA and THT channel models, respectively. Also included as the benchmark performance is the performance obtained using the perfect a priori (PA) information at the combined equalizer-ST block decoder. It should be noted that as ISI is completely removed, the performance obtained using the PA information corresponds to the matched filter bound (MFB). Furthermore, for comparison purpose, we also include the performance of SISO transmission obtained using MMSE-based turbo equalization. We observe that at high Eb /N0 values, ≈ 3 dB performance gain can be obtained using the proposed turbo receiver after five iterations compared to the 1st iteration for the TUA profile. It is also seen that symbol-wise STBC transmission clearly outperforms SISO transmission. Particularly, we can see that at BER = 10−3 there is about 2 dB difference in the performance between SISO and STBC transmissions after 5 iterations. Thus, these results reconfirm that in multipath fading channels a substantial performance improvement is guaranteed using

−1

−2

10

−3

10

−4

10

STBC, It#1 STBC, It#2 STBC, It#5 STBC, PA SISO, It#1 SISO, It#2 SISO, It#5 SISO, PA

−5

10

4

5

6

7 E /N dB b

8

9

10

0

Fig. 4. Average BER performance of the proposed turbo combined equalization and ST block decoding scheme: MCS-5, THT channel model

the Alamouti ST block code with WL receiver processing compared with SISO transmission. Moreover, we can also see a performance improvement of about 0.5 dB for the THT profile compared with that for the TUA profile. This is due to the fact that there are more multipath components (i.e., longer delay spread) in the THT profile compared with TUA profile. Hence, these results indicate that our proposed iterative scheme is capable of exploiting the multipath diversity in addition to the antenna diversity. In Fig.5, we present the average BER performance of the proposed iterative scheme for the TUA channel model using the MCS-7 coding scheme. It is observed that the MCS-5 scheme significantly outperforms the MCS-7 scheme by ≈ 5 dB due to more puncturing in MCS-7. Nevertheless, the MCS7 scheme offers a data rate that is twice higher than the MCS5 scheme. Similarly to the MCS-5 scheme, in this case with MCS-7, it is possible to yield about 3 dB improvement using iterations. Note that due to space limitation, the performance obtained for schemes MCS-8 and MCS-9 is not shown here. It is seen that substantial performance improvements can still be

0

10

non-iterative equalization and decoding. Hence, our proposed iterative receiver scheme is highly attractive to be used in future EDGE systems supporting broadband wireless services to improve the radio-link performance. Furthermore, simulation results have also reconfirmed the effectiveness of WL processing to obtain substantial performance improvements using Alamouti ST block coded transmission over multipath fading channels. Further research includes investigation of the system performance under fast time-varying channel conditions and theoretical performance and convergence analysis of the proposed turbo receiver.

−1

Average BER

10

−2

10

−3

10

−4

10

STBC, It#1 STBC, It#2 STBC, It#5 STBC, PA

−5

10

9

10

11

12 E /N dB b

13

14

15

0

Fig. 5. Average BER performance of the proposed turbo combined equalization and ST block decoding scheme: MCS-7, TUA channel model 0

10

Average BLER

−1

10

−2

10

STBC, It#1 STBC, It#2 STBC, It#5 STBC, PA

−3

10

9

10

11

12 Eb/N0 dB

13

14

15

Fig. 6. Average BLER performance of the proposed turbo combined equalization and ST block decoding scheme: MCS-7, TUA channel model

obtained for MCS-8 and MCS-9. Hence, the proposed iterative scheme may be even more useful to achieve high performance at low signal-to-noise ratio values when a coding scheme with a high coding gain (such as MCS-8, MCS-9) is employed. In Fig.6, the average block error rate (BLER) performance is shown for the TUA channel model and the MCS-7 coding scheme. Interestingly, it is clearly seen that a significant improvement in the BLER performance is possible using our proposed iterative receiver compared with non-iterative onetime equalization and decoding. Hence, our proposed receiver can substantially reduce the number of retransmissions required in practice. This eventually leads to enhancements in the system throughput. V. C ONCLUSIONS In this paper, we have developed a novel MMSE-based turbo combined equalization and ST block decoding scheme for symbol-wise Alamouti ST block coded transmission over multipath MIMO channels in EDGE-EGPRS systems. Widely linear (WL) processing is used to improve the performance. Our proposed iterative receiver carries out soft equalization and ST block decoding functions jointly at each iteration using the a priori information delivered by the convolutional channel decoder from the previous iteration. Simulation results have shown that a high performance improvement can be obtained using the proposed iterative receiver compared to

R EFERENCES [1] A. Furuskar et al., “EDGE: enhanced data rates for GSM and TDMA/136 evolution,” IEEE Personal Commun. Mag., vol. 6, pp. 56– 66, June 1999. [2] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Select. Areas Commun., vol. 16, pp. 1451– 1458, Oct. 1998. [3] E. Lindskog and A. Paulraj, “A transmit diversity scheme for channels with intersymbol interference,” in Proc. IEEE Int. Conf. on Commun. (ICC’00), New Orleans, LA, USA, June 2000, pp. 307–311. [4] S. Zhou and G. B. Giannakis, “Space-time coding with maximum diversity gains over frequency-selective fading channels,” IEEE Signal Processing Lett., vol. 8, pp. 269–272, Oct. 2001. [5] W. Gerstacker et al., “Equalization concepts for Alamouti’s space-time block code,” IEEE Trans. Commun., vol. 52, pp. 1178–1190, July 2004. [6] N. Al-Dhahir, A. F. Naguib, and A. R. Calderbank, “Finite-length decision feedback equalization for space-time block coded signals over multipath-fading channels,” IEEE Trans. Veh. Technol., vol. 50, pp. 1176–1182, July 2001. [7] M. Tuchler, A. C. Singer, and R. Koetter, “Minimum mean squared error equalization using a priori information,” IEEE Trans. Commun., vol. 50, pp. 673–682, Mar. 2002. [8] X. Wautelet, A. Dejonghe, and L. Vandendorpe, “MMSE-based fractional turbo receiver for space-time BICM over frequency-selective MIMO fading channels,” IEEE Trans. Signal Processing, vol. 52, pp. 1804–1809, June 2004. [9] N. Nefedov and G. Mattellini, “Evaluation of potential transmit diversity schemes with iterative receivers in EDGE,” in Proc. IEEE Int. Symposium on Personal, Indoor and Mobile Radio Commun. (PIMRC’02), Sept. 2002, pp. 2087–2091. [10] K. C. B. Wavegedara and V. K. Bhargava, “Turbo equalization for alamouti space-time block coded transmission,” in Proc. IEEE Int. Conf. on Commun. (ICC’06), Istanbul, Turkey, June 2006. [11] Digital cellular telecommunications system (Phase 2+); Radio transmission and reception, ETSI Technical Specification 3GPP TS 05.05 version 8.20.0, Nov. 2005. [Online]. Available: http://www.etsi.org [12] Digital cellular telecommunications system (Phase 2+); Modulation, ETSI Technical Specification 3GPP TS 05.04 version 8.4.0, Nov. 2001. [Online]. Available: http://www.etsi.org [13] M. Tuchler, R. Koetter, and A. C. Singer, “Turbo equalization: principles and new results,” IEEE Trans. Commun., vol. 50, pp. 754–767, May 2002. [14] C. Laot, R. L. Bidan, and D. Leroux, “Low-complexity MMSE turbo equalization: A possible solution for EDGE,” IEEE Trans. Wireless Commun., vol. 3, pp. 965–974, May 2005. [15] D. Reynolds and X. Wang, “Low complexity Turbo-equalization for diversity channels,” Signal Processing, Orlando, FL:Elsevier, vol. 81, pp. 989–995, May 2001. [16] X. Wang and H. V. Poor, “Iterative (Turbo) soft interference cancellation and decoding for coded CDMA,” IEEE Trans. Commun., vol. 47, pp. 1046–1061, July 1999. [17] Digital cellular telecommunications system (Phase 2+); Physical Layer on the Radio Path (General Description), ETSI Technical Specification 3GPP TS 05.01 version 8.9.0, Nov. 2004. [Online]. Available: http://www.etsi.org [18] Digital cellular telecommunications system (Phase 2+); Channel coding, ETSI Technical Specification 3GPP TS 45.003 version 6.8.0, Oct. 2005. [Online]. Available: http://www.etsi.org