Layered space-frequency coding and receiver ... - Semantic Scholar

Layered Space-Frequency Coding and Receiver Design for MIMO MC-CDMA Mikko Vehkaper¨a, Djordje Tujkovic, Zexian Li and Markku Juntti Centre for Wireless Communications (CWC) Tutkijantie 2E, P.O. Box 4500, FIN-90014 University of Oulu, Finland Email: [email protected]

Abstract— For the single-user communications pragmatic yet powerful methods known as layered space-time (LST) architectures provide means to increase the user data rate of a multiple-input multiple-output (MIMO) antenna system dramatically. To achieve better error rate performance, the LST transmission can be further accompanied with forward error correction coding. Future wireless communication systems will, however, require high data rates also in multiuser environments. For broadband multiuser wireless communications, multicarrier code-division multiple-access (MC-CDMA) has emerged as an attractive technique due to its low equalization complexity and robust performance in multipath fading channels. Utilizing strong channel coding and LST architectures with MC-CDMA, high spectral efficiency and good error rate performance can be obtained in diverse environments. In this paper, single and multiantenna turbo coded downlink MC-CDMA is combined with the concept of LST architectures. Due to the inevitable complexity restrictions, a suboptimal receiver interface for the underlying system is designed and its performance is evaluated in fading channels. The results demonstrate that significant improvement in both error rate performance and the system throughput can be achieved also with multiuser communications by using these MIMO techniques.

I. I NTRODUCTION In order to satisfy the remarkably high data rate requirements, future mobile communication systems are envisioned to use bandwidths of up to hundreds of MHz’s. That broad signaling bandwidth gives a rise to an extremely high channel path resolution [1]. Thus, in order to avoid severe degradation in error rate performance due to channel-induced intersymbol interference (ISI), computationally complex equalizer would be required with conventional single-carrier techniques. In multicarrier (MC) systems, on the other hand, ISI can be efficiently avoided by using proper length cyclic prefix (CP) and simple baseband signal processing, given that accurate subcarrier synchronization is guaranteed. Especially, the combination of orthogonal frequency division multiplexing (OFDM) and code-division multiple-access (CDMA), known as MC-CDMA [2], has gained significant attention as a promising air interface for the future broadband wireless communications. Assuming a rich scattering environment and low fading correlation between different transmit-receive (TX-RX) antenna pairs, the potential capacity of the MIMO channels is shown to This research was supported by the National Technology Agency of Finland, Nokia, the Finnish Defence Forces, Elektrobit and Instrumentointi.

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be enormous [3], [4]. Pragmatic methods to efficiently exploit the MIMO channel capacity are provided by different layered space-time (LST) architectures [5], in which spatial multiplexing at the transmitter and spatial filtering at the receiver are commonly used. Since the spatial filtering reduces complexity by transforming a multi-dimensional detection problem into a single-dimensional one, the cost is severely degraded error rate performance compared to the optimal maximum-likelihood (ML) detection unless higher orders of receive diversity can be achieved by some means of signal processing at the receiver. In this paper, the receiver design for downlink (base station to mobile) MC-CDMA system utilizing space-time coding (STC) or coded LST architectures is addressed. Symbollevel minimum mean squared error (MMSE) based receiver is derived and the proper modeling of the output of the proposed multiuser detector with residual multiple access interference (MAI) plus noise is studied. Parallel interference cancellation (PIC) of co-antenna interference (CAI) for additional receive diversity after the linear front-end is discussed. To ensure powerful error correcting capability and efficient operation with soft PIC algorithm, the selected channel coding schemes include single-antenna turbo codes (TCs) [6] and multi-antenna space-time turbo coded modulation (STTuCM) [7]. Performance of the proposed receiver is evaluated in frequency-flat and frequency-selective fading channels by using computer simulations. The rest of this paper is organized as follows. Section II gives a description of the system model, and the receiver design issues are covered in Section III. Performance evaluation of the proposed receiver is carried out in Section IV and conclusions are drawn in Section V. II. S YSTEM M ODEL A single cell downlink MC-CDMA system with Nc subcarriers and K users, all having the same spreading factor G is considered. Antenna configuration of N transmit antennas at the base station and M receive antennas at the mobile terminal is assumed. As shown in [8] for OFDM, if the CP is longer than the expected channel delay spread and separable channel clusters are located at the sampling instants of the transmitted signal, the system has an equivalent frequency-domain presentation. The frequency-domain MIMO MC-CDMA model described in this section is achieved by closely following the guidelines presented in [8].

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Let us assume that for user k = 1, 2, . . . , K, the encoding/modulation block outputs P symbols for each transmit antenna n = 1, 2, . . . , N , and is followed by a pseudorandom symbol-level interleaver. The resulting sequence of coded modulated symbols from alphabet M is mapped to space-frequency symbol matrix X k ∈ MN ×P so that the structure of the STC is preserved. The coded symbols are then multiplied with user specific signature sequences to form a space-frequency transmit matrix Z k ∈ CN G×P , i.e.,

X k = [x k,1 x k,2 · · · x k,P ] = [x T1,k x T2,k · · · x TN,k ]T Z k = [Z k,1 Z k,2 · · · Z k,P ], Z k,p = x k,p ⊗ s k ∈ CN G , (1) T G where s k = [s1k , s2k , . . . , sG is the signature sequence k] ∈ S of user k, S denotes the chip alphabet and ⊗ is the Kronecker product. In a downlink, orthogonal spreading codes are commonly used, and, thus, in order to preserve the number of user specific orthogonal signatures, we assign the same set of spreading codes for each transmit antenna. Due to spreading, Nf = GP/Nc OFDM symbols are used to transmit one coded frame for all users and the channel is assumed to be constant during this period. Assuming the whole coded frame, i.e., Nf consecutive OFDM symbols, is received, we can express the frequencydomain received signal in terms of code symbol intervals

r p = C p x p + ηp ,

p = 1, 2, . . . , P,

(2)

where, after omitting p for simplicity, received signal vector, transmit symbol vector and noise vector are defined as 1 G T r = [r11 , . . . , r1G , . . . , rM , . . . , rM ] ∈ CM G x = [x1,1 , . . . , x1,N , . . . , xK,1 , . . . , xK,N ]T ∈ MN K 1 G T η = [η11 , . . . , η1G , . . . , ηM , . . . , ηM ] ∈ CM G ,

(3)

respectively. The elements of η are independent and complex Gaussian with equal power real and imaginary parts, i.e., η ∼ CN (0, N0 I M G ).1 The average energy of a constellation point is Es = E{xk,n x∗k,n }, ∀k = 1, 2, . . . , K, n = 1, 2, . . . , N and the total radiated energy from the base station is held constant regardless of the number of transmit antennas. As a result, the signal-to-noise ratio (SNR) per receive antenna is defined as γ = N Es /N0 . Finally, the combined channel-spreading matrix C can be presented as

C = [c 1,1 · · · c 1,N · · · c K,1 · · · c K,N ] ∈ CM G×N K c k,n = [c T1,n,k , c T2,n,k , . . . , c TM,n,k ]T ∈ CM G (4) c(p+1) 1 c(p+2) 2 c(p+G) G T c m,n,k = [Hm,n sk , Hm,n sk , . . . , Hm,n sk ] ∈ CG c(p+g)

where Hm,n ∼ CN (0, 1), g = 1, 2, . . . , G is the frequencydomain channel coefficient between TX antenna n and RX antenna m at subcarrier c(p + g) ≡ (p − 1)G + g (mod Nc ), following from the assumption of a quasi-static channel. The frequency-domain channel coefficients are uncorrelated between all TX-RX pairs and derived from the time-domain tapped delay line presentation of the channel via Fourier transform as discussed in [8]. 1 If η ∼ CN (0, N I ), η is a complex Gaussian random vector with zero 0 mean and covariance matrix N0 I .

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III. R ECEIVER D ESIGN FOR LST MC-CDMA As we have no orthogonality restrictions for the transmitted signals, the simultaneous transmissions mixed in the channel cannot be straightforwardly separated at the receiver. Therefore, chip combining methods proposed for single-antenna MC-CDMA systems are not directly applicable to the considered MIMO system. Without the loss of generality, let us assume in the following a single symbol instant p and omit the explicit notation of p for notational simplicity. A. Symbol-Level Joint Space-Frequency MMSE Detector We begin the receiver design for the underlying MIMO system by deriving a space-frequency MMSE (SF-MMSE) multiuser detector. The mean squared error (MSE) minimization is taken now jointly over all subcarriers and antennas 
(5) D2 = min E  x − W H r 2F , W

 where = tr A A H denotes a squared Frobenius norm of matrix A . Matrix filter W = [W 1 W 2 · · · W K ] ∈ CM G×N K can simultaneously estimate the transmissions from all antennas for all users k = 1, 2, . . . , K, and is obtained by using the well known Wiener solution [9]
H −1
H  (6) W = R −1 E rx , rr R rx = E rr A 2F



which reduces to the familiar form −1  W = C R xx C H + R ηη C R xx ,

(7)

when the receiver has perfect channel state information (CSI) and noise is uncorrelated with the transmitted signals and fading processes. R xx denotes the transmit signal covariance matrix and R ηη the noise covariance matrix. Because the SF-MMSE detector has no knowledge of the channel code structure, we assume that the symbols are uncorrelated in space and frequency, that is R xx = Es I N , even though in the case of STC the symbols do correlate in space. The noise between the receive antennas and subcarriers is also considered to be uncorrelated, and, thus, R ηη = N0 I M G . Using (7), raw symbol decisions for user k on an uncoded system are then given by 2 
 (8) x k = arg min x − W Hk r F . x ∈M

In case of a turbo coded system utilizing maximum a posteriori (MAP) decoding, however, for an efficient operation the decoder has to be informed with a proper equivalent channel and a noise power. We address this problem in the next subsection. B. MAP Decoding and Gaussian Approximation of SF-MMSE Output In [10], it was proved that under various asymptotic conditions, the MAI-plus-noise at the output of the linear MMSE multiuser detector can be approximated as being Gaussian distributed. In the non-asymptotic two-user case, the relative entropy (or Kullback-Leibler distance) between the real distribution of MAI-plus-noise and Gaussian distribution was also

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shown to be small in all cases of interest. Since the two-user case is unfavorable for the approximation, it is reasonable to assume that Gaussian approximation is valid also for all nonasymptotic cases of interest with K > 2. We write now the equivalent system model for the decoder as xˆ k = W Hk r = Ωk x k + ϕk , (9) where xˆ k ∈ CN is an estimate of x k . The residual MAI-plusnoise term ϕk ∈ CN is considered to be Gaussian with PDF CN (0, R ϕϕ ). Let us assume next R xx = I N and that the total number of transmit antennas is divided into J groups, called layers, each containing J0 = N/J antennas. The number of antennas per group depends on the channel coding method so that for the single-antenna channel coding J0 = 1, whereas for the multi-antenna channel coding J0 > 1. Extending the work of [11] for a multi-antenna coded MCCDMA system, we define a residual channel matrix   Q1 Ωk,1   H N ×N .. , (10) Ξk =   = WkCk ∈ C . Ωk,J

Q2

where C k = [c k,1 c k,2 · · · c k,N ] ∈ CM G×N , the block diagonals of Ξk are Ωk,j ∈ CJ0 ×J0 and Q 1 , Q 2 contain the rest of the elements of Ξk . Using (10) we define the equivalent channel and residual MAI-plus-noise covariance matrices for the decoder at considered symbol interval p as   0 Ωk,1   N ×N .. Ωk =  ∈C .

R ϕϕ

0  ρ1  .. = . 0

Ωk,J  0  N ×N ∈R

(11)

where (12)

We assume next that at the receiver, the decoder uses a posteriori probability (APP) module [12] to calculate the conditional probabilities P [b p |r ] = Ap−1 [ξ S ()] Γp [r , b p ()]Bp [ξ E ()], :b p ()=b p

(13) with  defining an edge of a trellis section, ξ S () the starting state of the edge, ξ E () the ending state of the edge and b p () the input bits to encoder evoking trellis transition ξ S () → ξ E (). The state probabilities Ap and Bp are calculated recursively as shown in [12], and
 Γp [r , b p ()] = exp log {P [b p ()]} + log {p [r |b p ()]} (14) so that using (11), the conditional likelihood (or Euclidean metric) for user k and layer j = 1, 2, . . . , J becomes  
J0  Ωk,j x k,j − xˆ k,j 2 , (15) x k,j | b p,j ()] = log p [ˆ F tr(ρj )

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C. PIC with Iterative Detection and Decoding Using the linear SF-MMSE detector discussed previously with N = M antenna setup, the maximum spatial diversity order of the system is J02 . Thus, in a channel where the frequency diversity is limited, the error rate performance of the system can be poor, especially if J0 = 1. One solution to this is to apply iterative detection and decoding (IDD) with PIC of CAI at the receiver where, in an ideal case, a receive diversity of order M can be achieved. However, strong channel coding is required to provide reliable CAI cancellation and increased receive diversity. Also, if hard IC is used, error propagation may seriously limit the benefits of the IDD receiver. Let us decompose the system model of (2) as  k,j x˜ k,j + C  x˜ + η , r = C k,j x k,j + C

      desired

CAI

MAI

(16)

noise

where the first right hand side (RHS) term represents the desired received signal of user k from layer j, the second one denotes the channel-spreading matrix and data vector of the desired user k for layers j  = j and the impact of the rest of the users is included in the third RHS term. It is to be noted that a layer refers now to antenna groups j = 1, 2, . . . , J, each containing J0 antennas. When the receiver enters the IDD phase, the MMSE detector has to be updated so that for the desired user, the MSE minimization is written as [13]  2  (W k,j , Ψk,j ) = arg min E x k,j − W H r − Ψ , (17) (W ,Ψ)

ρJ ,

2 J0 ×J0 ρj = ||Ωk,j − Ωk,j ΩH . k,j ||F · I J0 ∈ R

where x k,j ∈ MJ0 follows from uniquely defined edge inputoutput relation and one-to-one modulation mapping.

where W k,j ∈ CM G×J0 and Ψk,j ∈ CJ0 represent the filter coefficients and self-CAI cancellation term for the user of interest, respectively. Following [13], by differentiating with respect to Ψ the solution is found to be 
 ˜ k,j , (18) Ψk,j = W H k,j C k,j E x  k,j corresponds to the channel-spreading matrix of the where C second RHS term in (16). Symbol estimates of the jth layer at the output of SF-MMSE detector can be calculated as    k,j E{˜ xˆ k,j = W Hk,j r − C x k,j } , (19) where the filter coefficients, taking into account MAI and the same assumptions as for deriving (7), are given by

W k,j = (D + V + M + N0 I )−1 C k,j ,

(20)

where

D = C k,j C Hk,j   H  k,j I N −J − diag(E{˜  V =C x k,j }E{˜ x k,j }H ) C k,j 0

(21)

H

C  . M =C The term V represents  the “covariance-matrix” of the symbol
expectations E x˜ k,j , so that when the interference estimates

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TABLE I U NIFORM 24- PATH CHANNEL Path group (8 separable paths in each) Path delays (in samples) Average amplitudes of paths

1. 3− √10 1/ 24

2. 35 √ − 42 1/ 24

3. 67 √ − 74 1/ 24

0

10

−1

FER

10

−2

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G=K=1, MMSE G=K=8, MMSE G=K=32, MMSE G=K=1, EGC G=K=8, EGC G=K=32, EGC

−3

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5 SNR [dB]

6

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8

Fig. 1. Performance of a turbo-coded SISO MC-CDMA system employing EGC and MMSEC receivers in a 24-path uniform channel.

are correct with high probability V → 0. The symbol expectations of the encoder outputs are E{x} = xw · P {x = xw } x
w ∈M

 κ κ    1 1 + ˜bi,w tanh (log P {ci }/2) , xw = 2
i=1 xw ∈M

(22) where ˜bi,w = 2bi,w − 1, bits {bi,w }κi=1 form the constellation point xw and log P {ci } are log-likelihoods of the coded bits corresponding to x, calculated by soft-input soft-output (SfISfO) Log-APP decoder as proposed in [12]. The output of the SF-MMSE during PIC iterations can be considered again as Gaussian as discussed in Section III-B since the interference cancellation is done in the spatial-domain.

Fig. 1 presents the frame-error-rate (FER) performance of a turbo coded single-input single-output (SISO) MC-CDMA system in a frequency-selective channel [15]. As expected, the MMSE based receiver offers a robust error rate performance also in multiuser environment and we take this as a comparison case for the following MIMO results. The performance of an MC-CDMA system utilizing STTuCM encoding and decoding blocks is shown in Fig. 2, where frequency-selective fading and 2 × 2 antenna setup is assumed. For a comparison, the FER performance curve of a single-user system employing optimal decoder aided detection (denoted MRC-D) [15] is shown. The proposed SF-MMSE detector with the Gaussian approximation gives close to the same performance as the MRC-D in a single-user system and G = K = 8 is degraded by 1 dB at FER = 10−2 . If an equivalent system model after MMSE filtering is not calculated, i.e., we set Ωk,p = I N and R ϕϕ = N0 I N , an additional loss of over 1 dB in FER performance is experienced. Thus, in the following results, Ωk,p and R ϕϕ are always properly calculated as discussed in Section III-B. Figs. 3, 4 and 5 demonstrate the performance of coded LST MC-CDMA system utilizing STTuCM or turbo coding and the proposed MMSE based receiver. Since STTuCM provides transmit diversity within the layer, notable performance gains compared to the turbo coded cases are achieved when a linear SF-MMSE detector is used. With additional PIC iterations, receive diversity can be achieved, and, thus, the coding schemes come closer to each other. Significant improvement in error rate performance of all LST schemes is experienced also in multiuser cases. Compared to the SISO system of Fig. 1, the layered STTuCM with two soft PIC iterations gives roughly 3 dB and 2.5 dB gains in FER of single and multiuser cases, respectively. As a reference, the capacity of 4 bps/Hz with 10% and 1% outage in the considered 24-path uniform channel can be theoretically achieved at SNRs γ = 1.7 dB and γ = 2 dB, respectively. Thus, the single-user LST system equipped with STTuCM and proposed SF-MMSE receiver and PIC iterations operates roughly within 1.5 dB of the channel outage capacity.

IV. S IMULATION R ESULTS

V. C ONCLUSIONS

In this section, we provide simulation results to illustrate the performance of the LST architectures and the proposed receiver. A downlink single-cell MC-CDMA system with Nc = 512 subcarriers is assumed. Coded frame consists of P = Nc QPSK symbols per antenna and punctured turbo codes or STTuCM for J0 = 2 [7] is used, resulting in a spectral efficiency of N bps/Hz. Spreading codes are realvalued Walsh-Hadamard and the system is fully loaded, i.e., G = K in all cases. In frequency-selective cases the power delay profile conforms 24-path uniform channel [14] described in Table I, with maximum delay shorter than the cyclic prefix. In all cases the channel is assumed to be quasi-static, i.e., constant during one coded MC-CDMA frame and changing independently from frame-to-frame.

Downlink MIMO MC-CDMA system utilizing LST architectures was considered. A linear MMSE based receiver was proposed and extended to include soft co-antenna PIC iterations. The importance of a proper Gaussian approximation of the SF-MMSE MIMO detector output was addressed and optimal MAP decoding using this information was discussed. Performance gains achieved by performing additional soft CAI cancellation rounds were shown to be significant in both single and multiuser environments. The results showed that a LST MC-CDMA system with 4 × 4 antenna topology and SF-MMSE receiver can offer a quadrupled throughput with several dB’s better FER performance over conventional turbo coded SISO MC-CDMA. Using layered STTuCM blocks and iterative receiver, the proposed system performs within

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0

0

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FER

FER

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MRC−D, G=K=1 SF−MMSE w/Gaussian approx., G=K=1 SF−MMSE w/Gaussian approx., G=K=8 SF−MMSE w/o Gaussian approx., G=K=1 SF−MMSE w/o Gaussian approx., G=K=8

−3

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G=K=1, Linear SF−MMSE G=K=1, SF−MMSE 1 iteration G=K=1, SF−MMSE 2 iterations G=K=8 Linear SF−MMSE G=K=8, SF−MMSE 1 iteration G=K=8, SF−MMSE 2 iterations 3

3.5

4

SNR [dB]

4.5

5

5.5

6

SNR [dB]

Fig. 2. Performance of a MIMO MC-CDMA system employing STTuCM. Optimal MRC-in-decoder (MRC-D) and joint SF-MMSE receivers in a 24path uniform channel. Antenna configuration of N = M = 2.

Fig. 4. Performance of a MIMO MC-CDMA system employing turbo coding and linear SF-MMSE front-end with soft PIC iterations at the receiver. A 24path uniform channel and antenna configuration of N = M = 4. 0

0

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−1

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FER

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TC, Linear SF−MMSE TC, SF−MMSE 1 iteration TC, SF−MMSE 2 iterations STTuCM, Linear SF−MMSE STTuCM, SF−MMSE 1 iteration STTuCM, SF−MMSE 2 iterations

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G=K=1, Linear SF−MMSE G=K=1, SF−MMSE 1 iteration G=K=1, SF−MMSE 2 iterations G=K=8 Linear SF−MMSE G=K=8, SF−MMSE 1 iteration G=K=8, SF−MMSE 2 iterations 3

3.5

4

4.5

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SNR [dB]

SNR [dB]

Fig. 3. Performance of a MIMO MC-CDMA system employing STTuCM or turbo coding. Linear SF-MMSE front-end with soft parallel CAI cancellation at the receiver. Antenna configuration of N = M = 4 and 1-path channel.

Fig. 5. Performance of a MIMO MC-CDMA system employing STTuCM and linear SF-MMSE front-end with soft parallel CAI cancellation at the receiver. A 24-path uniform channel and antenna configuration of N = M = 4.

1.5 dB from the outage capacity in a frequency-selective fading channel.

[7] D. Tujkovic, “Space-time turbo coded modulation for wireless communication systems,” Ph.D. dissertation, volume C184 of Acta Universitatis Ouluensis. University of Oulu Press, Oulu, Finland, 2003. [8] Z. Wang and G. B. Giannakis, “Wireless multicarrier communications: Where Fourier meets Shannon,” IEEE Signal Processing Mag., vol. 17, no. 3, pp. 29–48, May 2000. [9] S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory. New Jersey: Prentice Hall PTR, 1993. [10] V. Poor and S. Verd´u, “Probability of error in MMSE multiuser detection,” IEEE Trans. Inform. Theory, vol. 43, no. 3, pp. 858–871, 1997. [11] X. Wang and H. V. Poor, “Iterative (turbo) soft interference cancellation and decoding for coded CDMA,” IEEE Trans. Commun., vol. 47, no. 7, pp. 1046–1061, July 1999. [12] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, “A soft-input soft-output APP module for iterative decoding of concatenated codes,” IEEE Commun. Lett., vol. 1, no. 1, pp. 22–24, Jan. 1997. [13] M. Sellathurai and S. Haykin, “TURBO-BLAST for wireless communications: Theory and experiments,” IEEE Trans. Signal Processing, vol. 50, no. 10, pp. 2538–2546, Oct. 2002. [14] H. Atarashi and M. Sawahashi, “Variable spreading factor orthogonal frequency and code division multiplexing (VSF-OFCDM),” in MultiCarrier Spread-Spectrum & Related Topics. Fazel, K and Kaiser, S. (eds.), 2002, pp. 113–122. [15] Z. Li, M. Vehkaper¨a, D. Tujkovic, M. Juntti, M. Latva-aho, and S. Hara, “Performance evaluation of space-frequency coded MIMO MC-CDMA system,” in Proc. IST Summit, Aveiro, Portugal, June 15–18 2003.

ACKNOWLEDGEMENT The authors would like to thank Mr. Shigehiko Tsumura of the Osaka University for many useful discussions. R EFERENCES [1] J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed. John Wiley & Sons, 2001. [2] S. Hara and R. Prasad, “Overview of multicarrier CDMA,” IEEE Commun. Mag., vol. 35, no. 12, pp. 126–133, Dec. 1997. [3] I. E. Telatar, “Capacity of multi-antenna Gaussian channels,” European Trans. Telecommun., vol. 10, no. 6, 1999. [4] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Pers. Commun., pp. 311–335, 1998. [5] D. Gesbert, M. Shafi, D. Shiu, P. J. Smith, and A. Naguib, “From theory to practice: An overview of MIMO space-time coded wireless systems,” IEEE J. Select. Areas Commun., vol. 21, no. 3, pp. 281–302, 2003. [6] C. Berrou and A. Glavieux, “Near optimum error correcting coding and decoding: Turbo-codes,” IEEE Trans. Commun., vol. 44, no. 10, pp. 1261–1271, Oct. 1996.

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