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Iterative Semi-Blind Multiuser Detection for Coded MC-CDMA Uplink System Padam L. Kafle, Student Member, IEEE, and Abu B. Sesay, Senior Member, IEEE
Abstract—We propose two types of iterative semiblind receivers for coded multicarrier code-division multiple-access (MC-CDMA) uplink systems in the presence of both intracell and intercell interference. The first is based on minimum mean-square error criterion, and the second is a hybrid scheme, consisting of parallel interference cancellation and linear multiuser detection. These iterative receivers utilize known users’ information for the computation of log-likelihood ratios (LLRs) while blindly suppressing unknown interference. The LLRs are refined successively during the iterative process through decoding of all known users. Simulation results demonstrate that the proposed iterative semiblind methods offer substantial performance gain over conventional noniterative and nonblind iterative receivers. Index Terms—Multicarrier code-division multiple access (MCCDMA), semiblind multiuser detection, turbo codes, turbo processing.
I. INTRODUCTION
I
N AN UPLINK code-division multiple-access (CDMA) system, a semiblind approach for multiuser detection could be used to blindly suppress interference from out-of-cell users whose spreading codes are not known, while utilizing all known users’ information to suppress the intracell interference. Based on this idea, various semiblind detectors (or group-blind detectors) have been proposed for the uplink direct-sequence CDMA (DS-CDMA) [1], [2]. However, no channel coding is considered in these papers. In this letter, we consider the extension of semiblind multiuser detection to coded systems, in which more powerful joint iterative detection and decoding techniques could be utilized. We consider a multicarrier CDMA (MC-CDMA) system, which has received considerable attention for future high-speed wireless systems [3]. The main purpose of this letter is to develop iterative multiuser detection techniques for a more general scenario of coded MC-CDMA systems consisting of both in-cell and out-of-cell users. Previously proposed iterative multiuser receivers are based on a complete knowledge of the spreading codes of all users, often also assuming the availability of decoding information for all the users. The performance of these receivers degrades significantly in the presence of unknown interfering users [4]. The iterative receivers discussed here fully utilize the known users’ information for computing the log-likelihood ratios (LLRs) in the soft multiuser detection Paper approved by X. Wang, the Editor for Equalization of the IEEE Communications Society. Manuscript received February 15, 2002; revised November 26, 2002 and January 27, 2003. This paper was presented in part at the IEEE Canadian Conference on Electrical and Computer Engineering, Winnipeg, MB, Canada, May 2002, and in part at the IEEE Vehicular Technology Conference, Birmingham, AL, May 2002. The authors are with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB T2N 1N4 Canada (e-mail:
[email protected]). Digital Object Identifier 10.1109/TCOMM.2003.814206
module, as well as blindly suppressing any unknown interference. The LLRs are refined successively, during the iterative process, by using the extrinsic information available through the decoding of known users. The rest of this letter is organized as follows. In Section II, we summarize the system model. The iterative semiblind receivers are presented in Section III. Simulation results are provided in Section IV, and Section V contains the conclusions. II. SYSTEM DESCRIPTION We consider a -user MC-CDMA uplink system in which in-cell users and out-of-cell users. there are The information bits of each user are first encoded by a channel encoder and passed through a channel interleaver. The interleaved bits are then binary phase-shift keying (BPSK) moduis spread lated. Each modulated data symbol chips, , using a code sequence of , and where denotes transposition. For simplicity of notation, we consider one binary data symbol per orthogonal frequency-division multiplexing (OFDM) symbol. The transmission signal during an , which OFDM symbol is subcaris transmitted after MC-CDMA modulation, using riers. The MC-CDMA modulator consists of a serial-to-parallel conversion, frequency interleaving and inverse discrete Fourier transform (IDFT) operation followed by a guard-time insertion, using a cyclic prefix [5]. A block diagram of the transmitter, together with the iterative receiver, is shown in Fig. 1. The signal is transmitted through a multipath channel, path impulse response, which is assumed to have an . To compensate for both the delay spread of the radio channel and the asynchronism between users in a quasi-synchronous uplink system, we assume a sufficient cyclic prefix is inserted prior to the transmission, as in [6]. After matched filtering and chip-rate sampling of the received signal, the samples corresponding to the cyclic prefix are first removed and an -point discrete Fourier transform (DFT) is performed to obtain the following signals in vector form [5], [7]: (1) , is a diagonal matrix denoted as and denotes the frequency response of the channel experienced by different subcan be obtained carriers. Assuming perfect synchronization, , from an -point zero-padded DFT of , i.e., is an DFT matrix [8]. is the white Gaussian where , where denotes an noise vector with covariance matrix where
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Fig. 1.
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MC-CDMA uplink transmission scheme with iterative semiblind multiuser detection at the receiver.
identity matrix. is an matrix comprising the users, and is complex channel gains and spreading chips of given as
.. .
.. .
..
.
.. . (2)
III. ITERATIVE SEMIBLIND MULTIUSER DETECTION The autocorrelation matrix of the received signal vector, given in terms of its eigendecomposition as
is
(3) , contains the eigenIn the decomposition of associated with the vectors, eigenvalues, ( ) and most significant . The column space of spans contains the remaining ( ) the signal subspace. , which are associated eigenvectors
with the eigenvalues that are equal to the noise variance, i.e., [9]. in-cell Let us denote the equivalent channel matrix of , given by the first columns users as of the matrix in (2). The channel coefficients of the individual in-cell user need to be estimated at the receiver for the multiuser detection. For that purpose, a blind channel estimation based on the subspace approach [7], [10], [11] can be used. However, in the scope of this letter, we assume the channel coefficients of in-cell users have been estimated perfectly. Hence, for the is known comdiscussions hereafter, we assume the matrix pletely. that projects Similar to [2], consider the projection matrix as any signal to the subspace where
(4)
projects any signal onto the subspace The matrix We obtain the signal subspace of the matrix the following decomposition:
. by
(5)
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where
with , . We now consider two types of iterative receiver structures for joint multiuser detection and decoding based on a soft-input/soft-output (SISO) semiblind multiuser detector and individual SISO channel decoders. A. Iterative Semiblind MMSE Multiuser Detector The iterative semiblind minimum mean-square error (MMSE) multiuser detector discussed here utilizes a subspace-based semiblind approach in deriving the filter coefficients. In addition to the blind MMSE suppression of intercell interference, we also utilize the a priori probability information of known users’ code bits plus a feedback component, obtained through decoding of known users, for suppressing the intracell interference. Without loss of generality, we assume that the first user is the user of interest. Then, we consider MMSE filtering by using a feedforward to estimate the data symbol and a feedback weight vector, . weight vector, Let the vector containing soft outputs of the data symbols (obtained from the respective SISO channel decoders [13]) of all known users interfering with user 1 be denoted as . The total feedback contribution due to all interfering known users can . As in be considered as a parameter, is considered to comprise two parts, i.e., [2], the vector . The vector suppresses suppresses known interference, while , interference due to unknown users. Since for some . Let us we can assume that consider that the received signal due to the contribution of only , known users in the presence of white noise is . Then, we obtain and by where minimizing the following mean-square error (MSE): (6) The minimization of (6) with respect to following relationships between and
and :
results in the
users except the reference user. The matrix is the crosscorrelation between data symbols of known users other than the reference user, and is defined as
.. .
.. .
.. .
..
.. .
.
(12) is an operator that extracts the diagonal elements of where and from (7) and (8), and using the matrix. Solving for , we obtain
(13)
(14) , we utilize the signal subspace of the matrix To obtain in (5). We assume for some so that can be obtained by minimization of the following MSE: (15) :
Solving (15) gives the following expression for
(16) Since we have
, Similarly, and we obtain .
. By substituting
(17) (7) (8) We assume statistical independence among data symbols of different users. The a priori probabilities of data symbols of all known interfering users, approximated from the decoder’s soft outputs, are utilized. Also, by using the fact that the data and noise are uncorrelated, we obtain (9) (10) (11) is a vector with all zero entries except one where in its th position. The vector contains the data symbols of all known
By combining (13) and (17), we obtain the following feedforward coefficients:
(18) Next, we consider the computation of the LLRs passed on to the individual channel decoders. The output of the semiblind MMSE multiuser detector for user 1 is (19) We assume the output signal to be approximately Gaussian as in [12], with equivalent amplitude , which for user 1 is given by (20)
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The variance of the effective noise component can be approximated by neglecting knowledge of the a priori information and the residual interference after MMSE filtering to obtain
Form I: Assuming accurate cancellation after the soft PIC, the signal vector, in (25) contains contributions due to unknown users and the user of interest only. We, therefore, use the instead of (23) following constrained criterion for
(21) Extensive simulation studies indicate insignificant performance loss with this approximation. The LLRs derived from the multiuser detection module for the data symbol of the reference user is then given by
subject to
(26)
, with and . Using an approach similar to the one for obtaining (17), we get
We again consider
(22)
B. Iterative Semiblind Hybrid Multiuser Detectors We now consider another form of the iterative receiver by combining the zero-forcing criteria and parallel interference cancellation (PIC) of known interference with blind MMSE suppression of unknown interference. These hybrid detectors are based on extensions of the hybrid group-blind detector of [2] to iterative forms. For the first iteration, it is similar to the Form I hybrid group-blind detector of [2], as no a priori information on data symbols is available. For subsequent iterations, we discuss two variants of the hybrid receivers, which utilize decoding information of known users. As no a priori information of data symbols is available at the beginning, we use the following MMSE criterion subject to zero forcing of known users:
subject to
(23)
This yields the following filter coefficients for the first iteration [2]
(27) and are obtained from the eigendecomposition where matrix, as in (5), in which we use given of the is the new sample autocorrelation by (4), and matrix that has to be estimated. By using the constraint of (26), . Finally, we obtain the following coefwe have ficients for the Form I hybrid receiver after the first iteration: (28) Form II: In order to further suppress the residual intracell interference after the soft PIC, we can use instantaneous MMSE filtering [12]. However, as we only have knowledge of channel and spreading codes of in-cell users, we combine the blind MMSE suppression of unknown users (using the signal subspace of ) with the instantaneous MMSE filtering for residual intracell interference. denote the contribution Let the vector due to residual intracell interference and channel noise when soft PIC is applied only to the received signal components due , as to known users (i.e., ). We again assume in Section III-A, where (29)
(24)
(30) Once the soft outputs from decoding of known users are available, it is more beneficial to subtract the interference components of other known users from the received signal vector instead of applying the zero-forcing criteria. The soft interference cancellation, utilizing soft bit estimates, can suppress interference without noise enhancement as well as avoid error propagation. Hence, after the first iteration, we utilize soft PIC and blind MMSE suppression for the subsequent iterations of joint detection and decoding. By using soft-bit estimates of interfering known users, we first obtain the following signal vector after PIC:
(25) We now consider two forms of the hybrid receivers, Form I and Form II.
Using standard minimization techniques for (29), we obtain the as solution for (31) We have the following relations for
and
:
(32) (33) where
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Similar to the previous derivations, solving (30) yields , given by (27). Hence, combining (31) – (33) and (27), we obtain
(34) Finally, the LLRs for both hybrid detectors are computed as in , and passed on to (22), by using the output signal, the individual channel decoders. We use a turbo code for channel coding with log-maximum a posteriori (MAP) for decoding [13]. The soft channel decoder for the multiuser provides code extrinsic information, detection, details of which are referred to [12], [13]. Each expec, required for comtation of data symbol, matrix and the vectors in (14), (18), puting the and (25), is obtained by using the following expectation [12]: (35) However, these expectations, based on the soft decoding decisions, are only approximations, which are affected by the correlations between the decisions arising during the iterations.
Fig. 2.
BER performance of the iterative semiblind MMSE receiver.
IV. PERFORMANCE RESULTS We consider a rate-1/2 turbo code consisting of two punctured ) recursive systematic convolutional codes ( for channel coding, with a fixed pseudorandom interleaver of size 640 information bits. Each user uses a different channel interleaver generated randomly with a block size of 1280 code bits. Orthogonal Walsh–Hadamard codes of length are used for MC-CDMA spreading. A total of users, consisting of six in-cell users and three out-of-cell users, are considered. paths, assuming uniform A multipath channel with power delay profile, is used for each user. The channel gains are generated by using complex Gaussian distribution, which are normalized so that each user’s signal arrives at the receiver with , similar to [2] and [12]. Channel equal power, i.e., coefficients are assumed to be static during a block of 256 bits, which is the size of the signal frame used for computing the sample autocorrelation matrix of the received signal. Four decoding iterations are used in the turbo decoders for each of the joint multiuser detection and decoding iterations. A total of three iterations of detection and decoding are considered in the simulations. Performance is evaluated by estimating bit-error rates (BER) versus signal-to-noise ratios (SNRs) per information bit ). ( Fig. 2 presents the BER performance for the iterative MMSE semiblind receiver. The channel state information (CSI) of in-cell users is assumed to be known. The curves are shown for the users with the best and the worst BER performance (min. and max. BER) among in-cell users. Performance at the first iteration corresponds to the performance of the conventional noniterative MMSE semiblind receiver. We observe significant improvements in performance from iterative processing. Performance of the complete blind MMSE multiuser detection followed by turbo decoding is shown for comparison.
Fig. 3. BER performance of the Form I and Form II iterative semiblind hybrid receivers.
The semiblind scheme clearly outperforms the complete blind scheme. Also, the performance of the conventional nonblind iterative MMSE receiver is shown, in which the unknown interference is simply regarded as additional noise. The iterative semiblind receiver again outperforms the conventional MMSE (nonblind) scheme. Single user performance is also shown, which serves as the lower bound for these multiuser detectors. Fig. 3 shows the performance of the hybrid semiblind iterative receivers. The CSI of in-cell users is assumed to be available. The Form II hybrid receiver outperforms the Form I hy-
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brid receiver, mainly because of the additional MMSE filtering used to suppress the residual interference. The Form II receiver performs in a similar way as the semiblind MMSE receiver (in Fig. 2) after the third iteration. V. CONCLUSION In this letter, we have proposed iterative receiver structures for joint semiblind multiuser detection and decoding in the uplink environment of a coded MC-CDMA system. Two schemes were developed, one based on the MMSE criterion, and the other is a hybrid scheme based on a combination of PIC and linear multiuser detection. With these techniques, iterative processing can be optimally applied, under different criteria, to the uplink in the presence of both known and unknown interference. Simulation results show that the proposed iterative semiblind methods offer substantial performance gains over the conventional noniterative receivers and nonblind iterative receivers. Although the receiver structures are described for a coded MC-CDMA system, it can be easily extended to a coded DS-CDMA uplink with appropriate modifications of the signal model and channel estimation technique. REFERENCES [1] A. Høst-Madsen and K. S. Cho, “MMSE/PIC multi-user detection for DS-CDMA systems with inter- and intra-cell interference,” IEEE Trans. Commun., vol. 47, pp. 291–299, Feb. 1999. [2] X. Wang and A. Høst-Madsen, “Group-blind multiuser detection for uplink CDMA,” IEEE J. Select. Areas Commun., vol. 17, pp. 1971–1984, Nov. 1999.
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[3] S. Hara and R. Prasad, “Design and performance of multicarrier CDMA system in frequency selective Rayleigh fading channels,” IEEE Trans. Veh. Technol., vol. 48, pp. 1584–1595, Sept. 1999. [4] E. S. Esteves and R. A. Scholtz, “Bit-error probability of linear multiuser detectors in the presence of unknown multiple access interference,” in Proc. IEEE GLOBECOM’ 97, 1997, pp. 599–603. [5] P. L. Kafle and A. B. Sesay, “On the performance of MC-CDMA with interleaved concatenated coding and interference cancellation for high-rate data transmission,” in Proc. IEEE ICC’02, Apr.-May 2002, pp. 694–698. [6] A. C. McCormick, P. M. Grant, and J. S. Thompson, “Hybrid uplink multi-carrier CDMA interference cancellation receiver,” Inst. Elect. Eng. Proc. Commun., vol. 148, pp. 119–124, Apr. 2001. [7] C. J. Escudero, D. I. Iglesia, M. F. Bugallo, and L. Castedo, “Analysis of a subspace channel estimation technique for multicarrier CDMA systems,” in Proc. IEEE Workshop on Statistical Signal and Array Processing, Aug. 2000, pp. 10–14. [8] P. L. Kafle and A. B. Sesay, “Iterative semiblind space–time multiuser detection for MC-CDMA uplink system,” in Proc. IEEE Vehicular Technology Conf. (VTC-Fall 2002), Sept. 2002, pp. 1617–1621. [9] G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. Baltimore, MD: Johns Hopkins Univ. Press, 1989. [10] S. E. Bensley and B. Aazhang, “Subsapce-based channel estimation for code-division multiple-access communication systems,” IEEE Trans. Commun., vol. 44, pp. 1009–1020, Aug. 1996. [11] H. Liu and G. Xu, “A subspace method for signature waveform estimation in synchronous CDMA systems,” IEEE Trans. Commun., vol. 44, pp. 1346–1354, Oct. 1996. [12] 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. [13] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, “The Telecommunication and Data Acquisition Progress Report,” Jet Propulsion Laboratory, Pasadena, CA, 42–127, 1996. [14] X. Wang and H. V. Poor, “Bind multiuser detection : A subspace approach,” IEEE Trans. Inform. Theory, vol. 44, pp. 677–690, Mar. 1998.
