Parallel group detection for synchronous CDMA communication overfrequency-selective Rayleigh fading channels

A group detector jointly detects a group of users, and a parallel group detection scheme is a bank of J independently operating group detectors, one for each group of a J group partition of the K transmitting users of a code-division multiple-access (CDMA) channel. In this paper, two group detectors are introduced for the frequency-selective Rayleigh fading (FSRF) CDMA channel. While the optimum multiuser detector has a time complexity per symbol (TCS) of O(M ^K/K) for M-ary signaling, each of the two group detectors has a TCS of O(M(|G|)/|G|) where |G| is the group size. Hence, there are parallel group detection schemes, based on each of the two group detectors, that satisfy a wide range of complexity constraints that result from the choice of partition. Each of the two group detectors is minimax optimal in the corresponding conditional group near-far resistance measure. Furthermore, a succinct indicator of the average BER over high SNR regions is defined via the asymptotic efficiency. A lower bound and an exact formula for the asymptotic efficiency are derived for the first and second group detectors, respectively. The group detection approach for the FSRF-CDMA channel generalizes previous approaches to the complexity-performance tradeoff problem. It yields the optimum detector when the group size is K. When the group size is equal to one, the first group detector results in a new optimum linear detector and the second reduces to a recently proposed suboptimum linear detector. All other nontrivial partitions yield new multiuser detectors whose performances are commensurate with their complexities     

A new approach to greedy multiuser detection

We propose a new suboptimum multiuser detector for synchronous and asynchronous multiuser communications. In this approach, a greedy strategy is used to maximize the cost function, the maximum-likelihood (ML) metric. The coefficients of the ML metric are utilized as weights indicating in which order bits can be estimated. The complexity of the algorithm is approximately K/sup 2/ log K per bit, where K is the number of users. We analyze the performance of the greedy multiuser detection in the additive white Gaussian noise channel as well as in the frequency-nonselective Rayleigh fading channel, and compare it with the optimum detector and several suboptimum schemes such as conventional, successive interference cancellation, decorrelator, sequential, and multistage detectors. The proposed greedy approach considerably outperforms these suboptimum schemes, especially for moderate and high loads in low and moderate signal-to-noise ratio regions. The results show that when there is a significant imbalance in the values of the coefficients of the ML metric due to moderate to high noise, fading, and asynchronous transmission, near-optimum performance is achieved by the greedy detection.     

Optimum multiuser noncoherent DPSK detection in generalized diversity Rayleigh-fading channels

The jointly optimum multiuser noncoherent detector for differential phase-shift keying (DPSK) modulation over the generalized diversity Rayleigh-fading (GDRF) channel is derived and analyzed. The GDRF channel includes time/frequency/receiver antenna diversity and allows fading correlations between the various diversity branches of each user. Noncoherent detection here refers to the case where the receiver has neither knowledge of the instantaneous phases nor of the envelopes of the users' channels. Upper and lower bounds on the bit-error probability of the optimum detector are derived for a given user. For fast fading, when the fading coefficients vary from one symbol interval to the next (but are still essentially constant over one symbol interval), the detector asymptotically (for high signal-to-noise ratios (SNRs)) reaches an error floor, which is bounded from below and above for different fast fading scenarios. For slow fading, when the channel is constant for at least two consecutive symbol intervals, the upper bound is shown to converge asymptotically to the lower bound. Thus, the asymptotic efficiency of optimum multiuser DPSK detection can be determined and is found to be positive. In contrast to coherent detection, however, it is smaller than unity in general. Since the asymptotic efficiency is independent of the interfering users' signal strengths, the optimum detector is near-far resistant. While optimum multiuser detection is exponentially complex in the number of users, its performance provides the benchmark for suboptimal detectors. In particular, it is seen that the previously suggested post-decorrelative detectors can be far from satisfactory.     

Performance Analysis of Subspace Based Downlink Channel Estimation for W-CDMA Systems Using Chaotic Codes

This paper presents blind channel estimation for downlink W-CDMA system that employs chaotic codes and Walsh codes for spreading information bits of the multiple users. In a W-CDMA system, while transmitting over multipath channels, both intersymbol interference (ISI) as a result of Inter Chip Interference and multiple access interference (MAI) cannot be easily eliminated. Although it is possible to design multiuser detectors that suppress MAI and ISI, these detectors often require explicit knowledge of at least the desired users’ signature waveform. Earlier work focused on a subspace based channel estimation algorithm for asynchronous CDMA systems to estimate the multiple users’ symbols, where only AWGN channel was considered. In our work, we study a similar subspace-based signature waveform estimation algorithm for downlink W-CDMA systems, which use chaotic codes instead of pseudo random codes, that provide estimates of the multiuser channel by exploiting structural information of the data output at the base station. In particular, we show that the subspace of the (data+noise) matrix contains sufficient information for unique determination of channels, and hence, the signature waveforms and signal constellation. We consider Rayleigh and Rician fading channel model to quantify the multipath channel effects. Performance measures like bit error rate and root mean square error are plotted for both chaotic codes and Walsh codes under Rayleigh and Rician fading channels.     

Rayleigh衰落信道中的CDMA多用户分集接收性能

本文针对频率选择性Ｒａｙｌｅｉｇｈ衰落信道，设计了一种ＣＤＭＡ多用户检测器分集结构，通过该结构，高斯信道多用户检测算法可以有效地应用到Ｒａｙｌｅｉｇｈ衰落信道中，仿真结果表明，分集合并实现的多用户中以显著改善衰落信道的误码性能，其处理多址干扰能力并不因分集而受到影响，另外，本文还对不同的合并以及不同的检测地作了性能上的比较。     

Performance bounds for optimum multiuser DS-CDMA systems

In this letter we estimate the bit error probability (BEP) of optimum multiuser detection for synchronous and asynchronous code division multiple access (CDMA) systems on Gaussian and fading channels. We first compute an upper bound and a lower bound on the bit error probability for a given spreading code, then average the bounds over a few thousand sets of spreading codes. These bounds are obtained from a partial distance spectrum. On Gaussian channels, the upper bound converges to the lower bound at moderate to large signal-to-noise ratios. However, on fading channels the upper bound does not converge, hence we present our results for the lower bound only. The numerical results show that: 1) the BEP of a 31-user CDMA system with binary random spreading codes of length 31 is only two to four times higher than the BEP of the single user system; 2) the number of users that can be accommodated in an asynchronous CDMA system is larger than the processing gain; and 3) optimum multiuser detection outperforms linear detection (e.g., the decorrelating detector) by about 2.8 to 5.7 dB     

Optimization of LDPC-coded turbo CDMA systems

We consider the analysis and design of low-density parity-check (LDPC) codes for turbo multiuser detection in multipath code division multiple access (CDMA) channels. We develop techniques for computing the probability density function (pdf) of the extrinsic messages at the output of the soft-input soft-output (SISO) multiuser detectors as a function of the pdf of input extrinsic messages, user spreading codes, channel impulse responses, and signal-to-noise ratios. Of particular interest is the soft interference cancellation plus minimum mean square error (SIC-MMSE) multiuser detector, for which the pdf of the extrinsic messages can be characterized analytically. For the case of additive white Gaussian noise (AWGN) channels, the extrinsic messages can be well approximated as symmetric Gaussian distributed. For the case of asynchronous multipath fading channels, the extrinsic messages can be approximated by a mixture of symmetric Gaussian distributions. We show that the expectation-maximization (EM) algorithm can be used to compute the parameters of this mixture. Using these techniques, we are able to accurately compute the thresholds for LDPC codes and design good irregular LDPC codes. Simulation results are in good agreement with the computed thresholds, and the designed irregular LDPC codes outperform regular ones significantly.     

Decision-feedback blind adaptive multiuser detector for synchronousCDMA system

We develop a blind adaptive multiuser detector for synchronous code-division multiple access (CDMA) with a noise-whitening filter. The triangular structure of the noise-whitened model ensures complete resolution of detection ambiguities. To further improve the symbol error probability performance, we introduce decision feedback in our detector similar to the decorrelating derision-feedback detector (DDFD), thus forming the decision-feedback blind adaptive multiuser detector (DFBD). Simulations indicate that the performance of the DFBD is very close to that of the DDFD in additive white Gaussian noise (AWGN) channels. In Rician fading channels, the DFBD can track the slowly varying channels well and has a symbol error probability performance approaching that of the DDFD, which requires the knowledge of users' energies. The blind adaptive and decision-feedback blind adaptive multiuser detectors proposed here do not, however, require that knowledge     

Optimum Multiuser Detector for Multipath Slow Fading Asynchronous CDMA Channels

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Blind turbo multiuser detection for long-code multipath CDMA

We consider the problem of demodulating and decoding multiuser information symbols in an uplink asynchronous coded code-division multiple-access (CDMA) system employing long (aperiodic) spreading sequences, in the presence of unknown multipath channels, out-cell multiple-access interference (OMAI), and narrow-band interference (NBI). A blind turbo multiuser receiver, consisting of a novel blind Bayesian multiuser detector and a bank of MAP decoders, is developed for such a system. The effect of OMAI and NBI is modeled as colored Gaussian noise with some unknown covariance matrix. The main contribution of this paper is to develop blind Bayesian multiuser detectors for long-code multipath CDMA systems under both white and colored Gaussian noise. Such detectors are based on the Bayesian inference of all unknown quantities. The Gibbs sampler, a Markov chain Monte Carlo procedure, is then used to calculate the Bayesian estimates of the unknowns. The blind Bayesian multiuser detector computes the a posteriori probabilities of the channel coded symbols, which are differentially encoded before being sent to the channel. Being soft-input soft-output in nature, the proposed blind Bayesian multiuser detectors and the MAP decoders can iteratively exchange the extrinsic information to successively refine the performance, leading to the so-called blind turbo multiuser receiver     

Suboptimum soft-output detection algorithms for coded multiuser systems

In this paper, we consider coded asynchronous multiuser signals in an additive white Gaussian noise channel. Since optimum joint multiuser detection (MUD) and forward error correction (FEC) decoding is characterized with a very high computational complexity, we consider disjoint MUD and FEC decoding. The optimum disjoint multiuser detector is the soft-output maximum a posteriori detector that provides sequences of a posteriori probabilities to the corresponding FEC decoders. It involves backward and forward recursions resulting in high complexity and processing delay. In this paper, we consider several suboptimum soft output disjoint multiuser detectors that involve only forward recursions and have reduced complexity and delay.     

Near optimum tree-search detection schemes for bit-synchronousmultiuser CDMA systems over Gaussian and two-path Rayleigh-fadingchannels

Simple reduced tree-search detection schemes of the breadth-first type are applied to suboptimal joint multiuser detection in bit-synchronous code-division multiple access (CDMA) systems over both Gaussian and two-path Rayleigh-fading channels. It is pointed out that in contrast to the case of the optimal multiuser detector, the choice of the receiver filter severely influences the performance of suboptimal multiuser detectors. Simulation results supported by analysis show that breadth-first tree-search algorithms using a decorrelating noise whitening receiver filter perform better than similar receivers, which solely use a matched filter (MF) for virtually all nonsingular spreading code sets studied. Most of the code sets are randomly generated. The M- and T-algorithm detectors based on decorrelating noise whitening filter (WF) outputs can achieve near optimum performance at a very low complexity compared to the optimal detector, although the proposed detectors are more complex than some known suboptimum detectors. Furthermore, the use of combining techniques is considered for a two-path Rayleigh-fading channel, and a semi-synchronous CDMA structure is proposed. It is shown that if maximum ratio combining (MRC) is employed, the decorrelating noise WF still exists. The corresponding suboptimal combining detector with a decorrelating noise WF outperforms a similar noncombining detector     

A statistical-mechanics approach to large-system analysis of CDMAmultiuser detectors

We present a theory, based on statistical mechanics, to evaluate analytically the performance of uncoded, fully synchronous, randomly spread code-division multiple-access (CDMA) multiuser detectors with additive white Gaussian noise (AWGN) channel, under perfect power control, and in the large-system limit. Application of the replica method, a tool developed in the literature of statistical mechanics, allows us to derive analytical expressions for the bit-error rate, as well as the multiuser efficiency, of the individually optimum (IO) and jointly optimum (JO) multiuser detectors over the whole range of noise levels. The information-theoretic capacity of the randomly spread CDMA channel and the performance of decorrelating and linear minimum mean-square error (MMSE) detectors are also derived in the same replica formulation, thereby demonstrating validity of the statistical-mechanical approach     

Adaptive space-time feedforward/feedback detection for high datarate CDMA in frequency-selective fading

We investigate linear and nonlinear space-time minimum mean-square-error (MMSE) multiuser detectors for high data rate wireless code-division multiple-access (CDMA) networks. The centralized reverse-link detectors comprise a space-time feedforward filter and a multiuser feedback filter which processes the previously detected symbols of all in-sector users. The feedforward filter processes chip-rate samples from a bank of chip-matched filters which operate on the baseband outputs from an array of antennas. We present an adaptive multiuser recursive least squares (RLS) algorithm which determines the MMSE adjusted filter coefficients with less complexity than individual adaptation for each user. We calculate the outage probabilities and isolate the effects of antenna, diversity, and interference suppression gains for linear and nonlinear filtering and for CDMA systems with varying levels of system control (e.g., timing control, code assignment, cell layout). For eight users transmitting uncoded 2-Mb/s quadrature phase-shift keying with a spreading gain of eight chips per symbol over a fading channel with a multipath delay spread of 1.25 μs, the performance of a three-antenna feedforward/feedback detector was within 1 dB (in signal-to-noise ratio per antenna) of ideal detection in the absence of interference. By training for 10% of a 5-ms frame, RLS adaptation enabled the same detector to suffer less than a 0.5-dB penalty due to the combined effects of imperfect coefficients and error propagation. The advantage of nonlinear feedforward/feedback detection over linear feedforward detection was shown to be significantly larger for a CDMA system with enhanced system control     

Multiuser macrodiversity detection in asynchronous DS-CDMA systems

The authors present a performance analysis for the reverse link of a wireless DS-code division multiple access (CDMA) system that exploits macrodiversity reception while adopting the maximum likelihood (ML) multiuser detector for the basic detection. This appears to be the first analytical treatment of the ML multiuser macrodiversity detector in asynchronous DS-CDMA systems. They also include the effects of frequency selective fading, imperfect synchronization, and imperfect channel state information. Power control and connection control companion algorithms are presented to assess the value of this detector in a system context. The authors have shown that the ML multiuser-macrodiversity detector is capable of reducing the bit-error rate for many users by several orders of magnitude compared with multiuser detectors that operate on each antenna separately.     

Fractionally sampled decorrelator for CDMA Rayleigh fading channels

A coherent multiuser decorrelating detector for an asynchronous CDMA, time-varying Rayleigh fading channel is proposed and analysed. The detector uses fractionally sampled correlators outputs at time instants corresponding to users relative delays to simultaneously achieve two goals: the novel realisation of a one-shot decorrelator with lower computational complexity; and to exploit a form of the time diversity for improved error performance compared to symbol spaced sampling     

Optimally near-far resistant multiuser detection in differentiallycoherent synchronous channels

The noncoherent demodulation of differentially phase-shift keyed signals transmitted simultaneously via a synchronous code-division multiple-access (CDMA) channel is studied under the assumption of white Gaussian background noise. A class of noncoherent linear detectors is defined with the objective of obtaining the optimal one. The performance criterion considered is near-far resistance that denotes worst-case multiuser asymptotic efficiency over near-far environments. It is shown that the optimal linear detector is a noncoherent decorrelating detector. The commonality between the properties of the decorrelating detectors for coherent and noncoherent channels is established. In particular, it is shown that no other differential phase-shift keying (DPSK), multiuser detector achieves a higher near-far resistance than does the noncoherent decorrelator     

Randomly spread CDMA: asymptotics via statistical physics

This paper studies randomly spread code-division multiple access (CDMA) and multiuser detection in the large-system limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before single-user decoding. The generic detector can be particularized to the matched filter, decorrelator, linear minimum mean-square error (MMSE) detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically non-Gaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a "hidden" Gaussian statistic independent of the interferers. Thus, the multiuser channel can be decoupled: Each user experiences an equivalent single-user Gaussian channel, whose signal-to-noise ratio (SNR) suffers a degradation due to the multiple-access interference (MAI). The uncoded error performance (e.g., symbol error rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixed-point equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to multiple-input multiple-output (MIMO) channels such as in multiantenna systems.     

Multiuser detection in asynchronous CDMA frequency-selective fading channels

Multipath fading severely limits the performances of conventional code division multiple-access (CDMA) systems. Since every signal passes through an independent frequency-selective fading channel, even modest cross-correlations among signature sequences may induce severe near-far effects in a central multiuser receiver. This paper presents a systematic approach to the detection problem in CDMA frequency-selective fading channels and proposes a low complexity linear multiuser receiver, which eliminates fading induced near-far problem.We initially analyze an optimal multiuser detector, consisting of a bank of RAKE filters followed by a dynamic programming algorithm and evaluate its performance through error probability bounds. The concepts of error sequence decomposition and asymptotic multiuser efficiency, used to characterize the optimal receiver performance, are extended to multipath fading channels.The complexity of the optimal detector motivates the work on a near-far resistant, low complexity decorrelating multiuser detector, which exploits multipath diversity by using a multipath decorrelating filter followed by maximal-ratio combining. Analytic expressions for error probability and asymptotic multiuser efficiency of the suboptimal receiver are derived that include the effects of multipath fading, multiple-access interference and signature sequences correlation on the receiver's performance.The results indicate that multiuser detectors not only alleviate the near-far problem but approach single-user RAKE performance, while preserving the multipath diversity gain. In interference-limited scenarios multiuser receivers significantly outperform the RAKE receiver.This paper was presented in part at the Twenty-Sixth Annual Conference on Information Sciences and Systems, Princeton, NJ, March 1992 and MILCOM'92, San Diego, CA, October 1992. This work was performed while author was with the Department of Electrical and Computer Engineering, Northeastern University, Boston, USA.     

Adaptive joint multiuser detection and channel estimation in multipath fading CDMA channels

The problem of joint multiuser detection and channel estimation in frequency-selective Rayleigh fading CDMA channels is considered. First the optimal multiuser detector for such channels is derived, which is seen to have a computational complexity exponential in the product of the number of users and the length of the transmitted data sequence. Two suboptimal detectors are then developed and analyzed, both of which employ decorrelating filters at the front-ends to eliminate the multiple-access interference and the multipath interference. The symbol-by-symbol detector uses a Kalman filter and decision feedback to track the fading channel for diversity combining. The per-survivor sequence detector is in the form of the Viterbi algorithm with the trellis updates being computed by a bank of Kalman filters in the per-survivor fashion. Both suboptimal detectors require the knowledge of all waveforms of all users in the channel and the channel fading model parameters. Adaptive versions of these suboptimal detectors that require only the knowledge of the waveform of the user of interest are then developed. The adaptive receivers employ recursive-least-squares (RLS) minimum-mean-square-error (MMSE) filters at the front-end to mitigate the interference, and use a bank of linear predictors to track the fading channels. It is shown that the front-end RLS-MMSE filters can be implemented using systolic arrays to exploit massively parallel signal processing computation, and to achieve energy efficiency. Finally, the performance of the suboptimal detectors and their adaptive versions are assessed by simulations. This revised version was published online in July 2006 with corrections to the Cover Date.