An error probability analysis of the optimum noncoherent multiuser detector for multipath and multiantenna diversity communications over Rayleigh-fading channels

The optimum noncoherent multiuser detector is obtained for generalized diversity symbol-synchronous communication systems that employ nonorthogonal multipulse modulation. A unified approach is adopted to simultaneously address various forms of diversity such as time, frequency, multipath, and/or receiver-amenna diversity. Upper and lower bounds on the average bit-error probability of the optimum noncoherent detector are derived. While these bounds are numerically computable, they are too complicated to give insights about the relative influence of system parameters on the essential behavior of the bit-error rate. To address this issue, an asymptotic (low noise) analysis of the bit-error probability is undertaken. It is shown that the upper and lower bounds are indeed asymptotically convergent. A formula for the asymptotic efficiency of the optimum noncoherent detector is thereby derived. Interestingly, the asymptotic efficiency is found to be positive, and independent of the signal strengths of the interfering users.     

Optimum diversity combiner based multiuser detection fortime-dispersive Rician fading CDMA channels

Multiuser detection for asynchronous code division multiple access (CDMA) data transmission over the time-dispersive two-path Rician fading channel is considered. The multiuser maximum likelihood sequence detector (MLSD) is derived, and an equivalence of the fading channel to an asynchronous Gaussian intersymbol interference (AGISI) CDMA channel is established. However, the MLSD is found to be implementationally infeasible and this motivates the derivation of the optimum linear detector with near/far resistance as the performance criterion. The optimally near/far resistant linear time-invariant K-user detector is shown to consist of a cascade of a 2 K input/K output linear multiuser diversity combining filter followed by a K input/K output decorrelator that is designed for the equivalent AGISI/CDMA channel. This detector solves the near/far problem and also supports significantly higher bandwidth efficiencies for CDMA communication over the fading channel than does the conventional near/far limited single-user diversity combiner. The performance penalties incurred by multiuser detectors designed for the Gaussian channel when used over the Rician fading channel are also analytically characterized. It is shown that these penalties can be significant, making the case for the use of multiuser detectors optimized for this fading channel, particularly the optimum linear detector due to its relative implementational simplicity     

Optimum detection over Rayleigh-fading, dispersive channels, withnon-Gaussian noise

The paper discusses the problem of detecting one out of M Gaussian correlated signals in impulsive noise, modeled as a compound-Gaussian, possibly correlated process. We first show that, for uncorrelated noise, the detection problem admits one and the same optimum-in the sense of attaining minimum error probability-solution, independent of the noise statistics: the optimum detector, in fact, amounts to an estimation block, aimed at measuring the short-time noise power spectral density (PSD), whose output is fed to a bank of estimators-correlators, each keyed to one of the M admissible waveforms and to the estimated noise PSD. We also give suggestions for realizing a suboptimum receiver, with reduced complexity, which again is canonical in its structure. As for the performance analysis, we focus on binary frequency-shift keying (BFSK) signaling: we provide numerical results for two particular channel correlations and for Cauchy-distributed noise. These results indicate that, like for the general Gauss-Gauss case, the performance depends on the energy contrast, as well as on the “time-bandwidth” product of the useful signal. Moreover, noise spikiness seems to negatively affect the performance, in the sense that heavier and heavier high-amplitude tails of the noise marginal distribution give rise to higher and higher error probabilities for fixed energy contrast and time-bandwidth signal product     

Improved-performance noncoherent weighted-coefficients diversity combiner for DPSK and NC-FSK signals in nonidentical Nakagami fading channels

It is well-known that noncoherent equal-gain combining (NC-EGC) is the simplest combining technique for noncoherent and differentially coherent communication systems. However, for nonidentical Nakagami-m channels (channels having nonuniform multipath intensity profile (MIP) and/or arbitrary non-integer fading parameters), the use of NC-EGC has three main disadvantages. First, its performance serves as a lossy upper bound to that of the optimum diversity combiner. Second, it results in complicated expressions for the system average error performance. Third, it incurs noncoherent combining loss (does not aid the use of diversity) at relatively low average signal-to-noise ratio (SNR). In this letter, we propose a modified version of the NC-EGC, which is a noncoherent combiner with weighting coefficients, to overcome the disadvantages of the conventional one. We show that this alternative combiner does provide improvements over the conventional N.C-EGC for all values of average SNRs, it does not incur any noncoherent combining loss, and it leads to a design of the receiver whose average error performance can be evaluated easily.     

On the robustness of decision-feedback detection of DPSK and differential unitary space-time modulation in Rayleigh-fading channels

Decision-feedback differential detection (DFDD) of differential phase-shift keying (DPSK) and differential unitary space-time modulation (DUST) in Rayleigh-fading channels exhibits significant performance improvement over standard single-symbol maximum-likelihood detection. However, knowledge of channel fading correlation and signal-to-noise ratio (SNR) is required at the receiver to compute the feedback coefficients used in DFDD. In this letter, we investigate the robustness of the DFDD to imperfect knowledge of the feedback coefficients by modeling the mismatch between estimated feedback coefficients and ideal coefficients in terms of mismatch between the estimated values of fading correlation and SNR and the true values. Under the assumption of a block-fading channel when nondiagonal DUST constellations are used and a continuous fading channel otherwise, we derive exact and Chernoff bound expressions for pair-wise word-error probability and then use them to approximate the bit-error rate (BER), finding close agreement with simulation results. The relationships between BER performance and various system parameters, e.g., DFDD length and Doppler mismatch, are also explored. Furthermore, the existence of an error floor in the BER-vs-SNR curve is investigated for the infinite-length DFDD. For the special case of Jakes' fading model, it is shown that the error floor can be removed completely even when the Doppler spread is over-estimated.     

A simple DPSK receiver with improved asymptotic performance overfast Rayleigh-fading channels

In this letter we present a simple receiver for differential phase shift keying (DPSK) signals transmitted over fast, frequency flat, fading channels, which is characterized by a very low asymptotic error probability. The system performance analysis is carried out for a 2-DPSK signal     

Blind adaptive noncoherent multiuser detection for nonlinear modulation

Noncoherent multiuser detection for nonlinear modulation was previously studied and the idea of phase-independent noncoherent decorrelation was introduced and three post-decorrelative detectors were obtained and analyzed. However, their implementation requires the knowledge of the signature waveforms of all the users, which may be available only for centralized implementation. In this paper, we obtain a blind adaptive noncoherent decorrelative detector for nonlinear modulation that is suitable for distributed implementation with the knowledge of only the normalized signals of the desired user and the additive noise variance. This detector is based on the stochastic approximation method and does not require the overhead of any kind of "training." Two adaptive algorithms are developed, one guided by every signal in the desired user's signal set individually, and the other by the user's entire signal space. While this paper focuses on the particular problem of blind adaptive noncoherent decorrelative detection, it addresses a more general adaptation issue, namely, that of improving the convergence properties of an adaptive scheme by effectively using all the information that is known, and adapting only to the part of the desired solution that is truly unknown. Convergence is shown in the mean squared error sense for both the fixed step-size and time-varying step-size versions of the two algorithms.     

Time diversity in DPSK noisy phase channels

Differential phase shift keying (DPSK) in the presence of both additive white Gaussian noise and a phase impairment, modeled by a Brownian motion is considered. A time-diversity scheme is used for mitigating the effects of phase noise. This scheme renders a repetition coding approach where the transmitter sends multiple replicas of each data bit. An upper bound on the bit error probability, relying on a bivariate moment-generating function admitted by certain real functionals of the phase sample-path, is derived. The approach taken yields a trackable analysis, which rigorously adheres the phase noise effects. The impact of an incomplete statistical characterization on the tightness of the resultant bound is addressed. The theory, which is applicable to assess the design and performance of general heterodyned lightwave systems using (delay) differential demodulation (as DPSK and CP-FSK, or continuous phase frequency-shift keying), is exemplified and explicit results for the considered time-diversity DPSK scheme are provided. The optimum design of the diversity level is discussed and it is concluded that power efficient transmission is feasible even at bit rates comparable with the signal linewidth     

Noncoherent multiuser detection for nonlinear modulation over the Rayleigh-fading channel

The jointly optimum noncoherent multiuser detector is obtained for nonlinear nonorthogonal modulation over the frequency nonselective Rayleigh-fading multiple-access channel. Upper and lower bounds on the average bit-error probability are derived. While these bounds are numerically computable, they are too complicated to give insight into the relative influence of the system parameters on the essential behavior of the bit-error rate. Hence this paper develops an asymptotic analysis of the average bit-error probability. In particular, it is shown that the upper and lower bounds are asymptotically convergent. An exact formula for the asymptotic efficiency of the optimum noncoherent detector is derived. Interestingly, the asymptotic efficiency is found to be positive and independent of the signal strengths of the interfering users. In contrast, the noncoherent detector which would be optimal in a single-user channel (the "conventional detector"), when used over the multiuser channel, has an asymptotic efficiency that is identically equal to zero no matter what the powers of the interferers may be. While the performance analysis of the optimum detector provides the fundamental limit on achievable error rate, the implementational complexity of the optimum detector is exponential in the number of users. As a low-complexity alternative, a decorrelative energy detector is also proposed and analyzed in terms of error probability and asymptotic efficiency.     

MLSE for correlated diversity sources and unknown time-varyingfrequency-selective Rayleigh-fading channels

Yu and Pasupathy (see ibid., vol.43, p. 1534-44, 1995) derived a maximum-likelihood sequence estimation (MLSE) receiver structure for unknown time varying frequency-selective Rayleigh-fading channels and uncorrelated diversity sources. This receiver design is extended to the case of correlated diversity sources. Correlated diversity sources typically arise with space diversity, where constraints on antenna volume require that diversity antennae be placed too closely together. Analytic and simulated bit-error rate (BER) curves are presented for receivers which exploit and ignore the correlation. In the former case, we find a small BER improvement that reduces with decreasing correlation. However, for a fixed receiver complexity, superior performance is achieved when the correlation is ignored     

Performance of Alamouti transmit diversity over time-varying Rayleigh-fading channels

We analyze the impact of a time-varying Rayleigh-fading channel on the performance of an Alamouti transmit-diversity scheme. We propose several optimal and suboptimal detection strategies for mitigating the effects of a time-varying channel, and derive expressions for their bit-error probability as a function of the channel correlation coefficient /spl rho/. We find that the maximum-likelihood detector that optimally compensates for the time-varying channel is very tolerant to time-varying fading, attaining full diversity order even for the extreme case of /spl rho/=0. In contrast, although lower in complexity, the suboptimal schemes suffer a diversity penalty and are thus suitable only for slowly fading channels.     

Optimum diversity detection over fading dispersive channels withnon-Gaussian noise

We consider the problem of M-ary signal detection over a single-input-multiple-output (SIMO) channel affected by frequency-dispersive Rayleigh-distributed fading and corrupted by additive non-Gaussian noise, modeled as a spherically invariant random process. We derive both the optimum detection structure and a suboptimal, reduced-complexity receiver, based on the low-energy-coherence approach. Interestingly, both detection structures are canonical, i.e., they are independent of the actual noise statistics. We also carry out a performance analysis of both receivers, with reference to the case that the channel is affected by a frequency-selective fading and for a binary frequency-shift-keying signaling format. The results obtained through both a Chernoff-bounding technique and Monte Carlo simulations reveal that the adoption of diversity also represents a suitable means to restore performance in the presence of dispersive fading and impulsive non-Gaussian noise. Interestingly, it is also shown that the suboptimal receiver incurs a limited loss with respect to the optimum (unrealizable) receiving structure     

Nonparametric multiuser detection in non-Gaussian channels

Existing multiuser detection techniques in wireless systems are based on the assumption that some information on the parameters of the probability density function (pdf) of ambient noise is available. Such information may not be available in all cases, particularly for non-Gaussian and impulsive noises, or may change depending on circumstances. In this paper, we present a technique for multiuser detection that does not require any a priori knowledge about the noise parameters. This method is based on using pseudo norms for linear nonparametric regression. Analytical and simulation results show that the proposed method offers an improved, or at least comparable, performance over existing robust techniques in the absence of any information on the nature of noise in the environment. The increased computational complexity is marginal compared to existing parametric detectors. In addition, the proposed nonparametric detector is portable in the sense that it does not need to be tuned for different noise models without any considerable degradation of performance. We also show that in non-Gaussian noise, the performance of blind adaptive nonparametric multiuser detectors is better than that of robust multiuser detectors.     

Noncoherent detection in asynchronous multiuser channels

The noncoherent demodulation of multiple differentially phase-shift-keyed signals transmitted simultaneously over an asynchronous code-division multiple-access (CDMA) channel with white Gaussian background noise is considered. A class of bilinear detectors is defined with the objective of obtaining the optimal bilinear detector. The optimality criterion considered is near-far resistance that denotes worst-case asymptotic efficiency over the signal energies and phases which are unknown at the receiver. The optimal bilinear detector is therefore obtained by solving a minimax optimization problem. In the finite packet length case, this detector is shown to be a time-varying multiinput multioutput linear decorrelating filter followed by differential decision logic. In the limit as packet lengths go to infinity, the time-varying decorrelating detector is replaced by a time-invariant multiinput multioutput decorrelating filter. Several properties of the optimally near-far resistant detector are established     

Robust multiuser detection in non-Gaussian channels

In many wireless systems where multiuser detection techniques may be applied, the ambient channel noise is known through experimental measurements to be decidedly non-Gaussian, due largely to impulsive phenomena. The performance of many multiuser detectors can degrade substantially in the presence of such impulsive ambient noise. We develop robust multiuser detection techniques for combating multiple-access interference and impulsive noise in CDMA communication systems. These techniques are based on the M-estimation method for robust regression. Analytical and simulation results show that the proposed robust techniques offer significant performance gain over linear multiuser detectors in impulsive noise, with little attendant increase in computational complexity. We also develop a subspace-based technique for blind adaptive implementation of the robust multiuser detectors, which requires only the signature waveform and the timing of the desired user in order to demodulate that user's signal. The robust multiuser detection technique and its blind adaptive version can be applied to both synchronous and asynchronous CDMA channels     

Performance comparison of selection combining schemes for binary DPSK on nonselective Rayleigh-fading channels with interference

This paper is concerned with the error performance analysis of binary differential phase shift keying (DPSK) with differential detection over the nonselective Rayleigh-fading channel with selection diversity reception and with an additive, correlated, Gaussian interference process in each diversity channel. The fading process is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The selection schemes investigated are: 1) the selection combining (SC) scheme based on signal-to-noise power ratio (SNR); 2) the SC scheme based on signal-plus-noise (S+N); and 3) the SC scheme based on maximum output (MO). New, exact, closed-form bit-error probability (BEP) expressions are derived, and a performance comparison among the three SC schemes and combining diversity reception is given. The results obtained reduce to previously known results when the correlated interference process is absent, and when the fading process does not fluctuate over the duration of several symbol intervals. The results indicate that the performance of each scheme depends on the tradeoff between the number of diversity branches, the SNR, the interference level, and the correlation of the interference process. However, the SC-(S+N) scheme generally performs worse than the SC-SNR scheme, the SC-MO scheme and combining diversity reception scheme. The findings presented here are not only of fundamental theoretical value, but are also of practical interest to the designers of future mobile communication systems.     

Signed-rank nonparametric multiuser detection in non-Gaussian channels

We present a novel nonparametric multiuser detector for non-Gaussian channels that is based on the signed-rank norm for linear regression. Analytical and simulation results show that the proposed detector offers similar or better performance as compared to the minimax robust detector, but without requiring any a priori information on the noise. The complexity of this detector is lower than that of the pseudo-norm nonparametric detector stated previously by the authors. This is due to the fact that in contrast to the latter, it is not necessary to compute the intercept parameter for the signed-rank detector proposed in this correspondence. We analyze the behavior of the blind version of this detector and show that it outperforms the blind minimax detector. We also show that this detector has a bounded influence function and hence it is robust.     

Space-time multiuser detection in multipath CDMA channels

The problem of multiuser detection in multipath CDMA channels with receiver antenna array is considered. The optimal space-time multiuser receiver structure is first derived, followed by linear space-time multiuser detection methods based on iterative interference cancellation. Blind adaptive space-time multiuser detection techniques are then proposed, which require prior knowledge of only the spreading waveform and the timing of the desired user's signal. Single-user-based space-time processing methods are also considered and are compared with the multiuser approach. It is seen that the proposed multiuser space-time processing techniques offer substantial performance gains over the single-user-based methods, especially in a near-far situation