Robust Linear Receivers for Multiaccess Space–Time Block-Coded MIMO Systems: A Probabilistically Constrained Approach

Traditional multiuser receiver algorithms developed for multiple-input–multiple-output (MIMO) wireless systems are based on the assumption that the channel state information (CSI) is precisely known at the receiver. However, in practical situations, the exact CSI may be unavailable because of channel estimation errors and/or outdated training. In this paper, we address the problem of robustness of multiuser MIMO receivers against imperfect CSI and propose a new linear technique that guarantees the robustness against CSI errors with a certain selected probability. The proposed receivers are formulated as probabilistically constrained stochastic optimization problems. Provided that the CSI mismatch is Gaussian, each of these problems is shown to be convex and to have a unique solution. The fact that the CSI mismatch is Gaussian also enables to convert the original stochastic problems to a more tractable deterministic form and to solve them using the second-order cone programming approach. Numerical simulations illustrate an improved robustness of the proposed receivers against CSI errors and validate their better flexibility as compared with the robust multiuser MIMO receivers based on the worst case designs.     

Adaptive DFE Multiuser Receiver for CDMA Systems using Two-Step LMS-Type Algorithm: An Equalization Approach

This paper presents an adaptive decision feedback equalizer (DFE) based multiuser receiver for code division multiple access (CDMA) systems over smoothly time-varying multipath fading channels using the two-step LMS-type algorithm. The frequency-selective fading channel is modeled as a tapped-delay-line filter with smoothly time-varying Rayleigh-distributed tap coefficients. The receiver uses an adaptive minimum mean square error (MMSE) multiuser channel estimator based on the reduced Kalman least mean square (RK-LMS) algorithm to predict these tap coefficients (Kohli and Mehra, Wireless Personal Communication 46:507–521, 2008). We propose the design of adaptive MMSE feedforward and feedback filters by using the estimated channel response. Unlike the previously available Kalman filtering algorithm based approach (Chen and Chen, IEEE Transactions on Signal Processing 49:1523–1532, 2001), the incorporation of RK-LMS algorithm reduces the computational complexity of multiuser receiver. The computer simulation results are presented to show the substantial improvement in its bit error rate performance over the conventional LMS algorithm based receiver. It can be inferred that the proposed multiuser receiver proves to be robust against the nonstationarity introduced due to channel variations, and it is also beneficial for the multiuser interference cancellation and data detection in CDMA systems.     

Multiuser detection in fast-fading multipath environments

We propose a new framework for multiuser detection in fast-fading channels that are encountered in many mobile communication scenarios. Existing multiuser RAKE receivers, developed to combat multipath fading and multiuser interference in slow fading, suffer substantial degradation in performance under fast fading due to errors in channel state estimation. The detectors proposed in this paper employ a novel receiver structure based on time-frequency (TF) processing that is dictated by a canonical representation of the wide-sense stationary uncorrelated scatterer (WSSUS) channel model. The workhorse of the framework is a TF generalization of the RAKE receiver that exploits joint multipath-Doppler diversity. Analytical and simulated results based on realistic fast-fading assumptions demonstrate that the proposed multiuser detectors promise substantially improved performance compared to existing systems due to the inherently higher level of diversity afforded by multipath-Doppler processing     

Performance Analysis of Space-Time Coded CDMA System Over Nakagami Fading Channels with Perfect and Imperfect CSI

In this paper, the performance of multiuser CDMA systems with different space time code schemes is investigated over Nakagami fading channel. Low-complexity multiuser receiver schemes are developed for space-time coded CDMA systems with perfect and imperfect channel state information (CSI). The schemes can make full use of the complex orthogonality of space-time coding to obtain the linear decoding complexity, and thus simplify the exponential decoding complexity of the existing scheme greatly. Moreover, it can achieve almost the same performance as the existing scheme. Based on the bit error rate (BER) analysis of the systems, the theoretical calculation expressions of average BER are derived in detail for both perfect CSI and imperfect CSI, respectively. As a result, tight closed-form BER expressions are obtained for space-time coded CDMA with orthogonal spreading code, and approximate closed-form BER expressions are attained for space-time coded CDMA with quasi-orthogonal spreading code. Computer simulation for BER shows that the theoretical analysis and simulation are in good agreement. The results show that the space-time coded CDMA systems have BER performance degradation for imperfect CSI.     

Impact of diversity reception on fading channels with codedmodulation. III. Co-channel interference

For pt.II see ibid., vol.45, no.6, p.55-67, 1997. In previous work, we have studied the impact of diversity on coded digital communication systems operating over fading channels. In particular, we have shown that diversity may be thought of as a way of making the channel more similar to a Gaussian one. The present paper extends this analysis to fading channels affected by co-channel interference (CCI). Three receiver models are examined, namely, with coherent detection and perfect channel-state information (CSI), with differential; and with pilot-tone detection. We study the effect of diversity on the irreducible error floor caused by CCI and fading, and the asymptotic behavior of the channel as the diversity order increases. Our results show that, when perfect CSI is available, diversity is able to turn asymptotically the channel into a CCI-free additive white Gaussian noise (AWGN) channel with the same signal-to-noise ratio (SNR). On the other hand, differential and pilot-tone detection do not remove interference in the limit. Nevertheless, also with these detection schemes, diversity achieves significant gains when the SNR is large enough. Calculation of the channel cutoff rate provides guidelines for the design of coded systems with CCI in fading environments. A wide range of examples, validated by computer simulation, illustrates our conclusions     

Capon multiuser receiver for CDMA systems with space-time coding

We present in this paper a linear blind multiuser receiver, referred to as the Capon receiver, for code-division multiple-access (CDMA) systems utilizing multiple transmit antennas and space-time (ST) block coding. The Capon receiver is designed by exploiting signal structures imposed by both spreading and ST coding. We highlight the unique ST coding induced structure, which is shown to be critical in establishing several analytical results, including self-interference (i.e., spatially mixed signals of the same user) cancellation, receiver output signal-to-interference-and-noise ratio (SINR), and blind channel estimation of the Capon receiver. To resolve the scalar ambiguity intrinsic to all blind schemes, we propose a semi-blind implementation of the Capon receiver, which capitalizes on periodically inserted pilots and the interference suppression ability of the Capon filters, for (slowly) time-varying channels. Numerical examples are presented to compare the Capon receiver with several other training-assisted and (semi-)blind receivers and to illustrate the performance gain of ST-coded CDMA systems over those without ST coding     

Modulation and Detection for Simple Receivers in Rapidly Time-Varying Channels

We investigate the performance degradation of basic modulation schemes in a rapidly time-varying channel using a first-order autoregressive channel model. Various performance metrics are used to indicate the relative advantages of each modulation scheme. We find that noncoherent frequency-shift keying (FSK) is suitable for operating at very high mobility and high signal-to-noise ratio, ideal for some military applications. We then propose a partially coherent detector for FSK and differential phase-shift keying that exploits partial channel knowledge to enable the receiver to operate effectively in both fast and slow fading. The maximum-likelihood rule obtained for the partially coherent FSK turns out to be a linear combination of coherent and noncoherent detection rules. Results demonstrate that significant performance improvement can be achieved over the best of coherent and noncoherent FSK detection. The detector is robust to estimation errors present in the channel statistics. We also propose a few adaptive schemes that employ various combinations of modulation schemes to increase the robustness of the system in fast fading     

Combined multiuser detection and diversity reception for wirelessCDMA systems

Code division multiple-access (CDMA) techniques using interference cancellation are being explored for the capacity increase in third-generation universal mobile telecommunications systems. However, multipath fading is a major constraint on the performance of wireless CDMA systems, with multipath propagation worsening the effects of multiple-access interference, and fading on propagation paths leading to the near far problem. Multiuser detection, exploiting the knowledge of other users to cancel multiple-access interference, has the capability of eliminating the near far problem and providing a significant capacity increase in CDMA systems. On the other hand, diversity techniques effectively combat the fading effects of the channel. This paper investigates multiuser receivers that combine explicit antenna diversity, RAKE multipath diversity, and multipath decorrelating detection. Both coherent reception with maximal-ratio combining and differentially coherent reception with equal-gain combining are analyzed. The results demonstrate a significant increase in up-link capacity over the conventional RAKE receiver, at the expense of complexity. In the case of limited receiver complexity, where the number of correlators is less than the number of resolvable paths at the RAKE front-end, antenna diversity is shown to be effective in reducing residual multiple-access interference     

Linear receivers for the multiple-input multiple-output multiple-access channel

We consider a multiuser multiple-input multiple-output (MIMO) communication system using code-division multiple access (CDMA) and multiuser detection to discriminate the different users. Our focus is on the CDMA uplink of a frequency-nonselective Rayleigh fading channel. We study two types of receivers: joint receivers, which address simultaneously both spatial and multiple-access interference; and separate receivers, addressing the two types of interference individually. This approach allows assessing the benefits of adding MIMO processing capabilities to existing multiuser single-input single-output systems. For both receiver types, we analyze solutions based on linear (matched filter, decorrelator, minimum mean-square error) and maximum-likelihood receivers. For all the receivers considered, we provide closed-form expressions (as expectations of given functions) of the resulting pairwise error probabilities. Performance results are obtained in terms of frame-error rate versus E/sub b//N/sub 0/, following two different approaches. An analytic approach using large-system asymptotic methods, whereby the system parameters (number of users and antennas, spreading gain) are assumed to grow to infinity with finite limiting ratios. A computer-simulation approach is used to illustrate the differences between asymptotic and simulation results.     

Performance of antenna diversity multiuser receivers in CDMA channels with imperfect fading estimation

The performance of antenna diversity coherent and differentially coherent linear multiuser receivers is analyzed in frequency-nonselective Rayleigh fading CDMA channels with memory. The estimates of the complex fading processes are utilized for maximal-ratio combining and carrier recovery of the coherent multiuser receiver. To analyze the impact of channel estimation errors on the receiver performance, error probability is assessed directly in terms of the fading rate and the number of active users, showing the penalty imposed by imperfect channel estimation as well as the fading-induced error probability floor. The impact of fading dynamics on the differentially coherent decorrelating receiver with equal-gain combining is quantified. While performance of multiuser receivers at lower SNR is determined by both the fading dynamics and the number of active CDMA users, performance at higher SNR is given by an error probability floor which is due to fading only and has the same value as in a single-user case. The comparison of the two receiver structures indicates that the coherent decorrelating receiver with diversity reception may be preferable to the differentially coherent one in nonselective fading CDMA channels with memory.     

Blind multiuser detection in uplink CDMA with multipath fading: a sequential EM approach

We consider joint channel estimation and data detection in uplink asynchronous code-division multiple-access systems employing aperiodic (long) spreading sequences in the presence of unknown multipath fading. Since maximum-likelihood (ML) sequence estimation is too complex to perform, multiuser receivers are proposed based on the sequential expectation-maximization (EM) algorithm. With the prior knowledge of only the signature waveforms, the delays and the second-order statistics of the fading channel, the receivers sequentially estimate the channel using the sequential EM algorithm. Moreover, the snapshot estimates of each path are tracked by linear minimum mean-squared error filters. The user data are detected by a ML sequence detector, given the channel estimates. The proposed receivers that use the exact expressions have a computational complexity O(2/sup K/) per bit, where K is the number of users. Using the EM algorithm, we derive low-complexity approximations which have a computational complexity of O(K/sup 2/) per bit. Simulation results demonstrate that the proposed receivers offer substantial performance gains over conventional pilot-symbol-assisted techniques and achieve a performance close to the known channel bounds. Furthermore, the proposed receivers even outperform the single-user RAKE receiver with Nyquist pilot-insertion rate in a single-user environment.     

Group-blind multiuser detection for uplink CDMA

Previously developed blind techniques for multiuser detection in code division multiple access (CDMA) systems lead to several near-far resistant adaptive receivers for demodulating a given user's data with the prior knowledge of only the spreading sequence of that user. In the CDMA uplink, however, typically the base station receiver has the knowledge of the spreading sequences of all the users within the cell, but not that of the users from other cells. In this paper, group-blind techniques are developed for multiuser detection in such scenarios. These new techniques make use of the spreading sequences and the estimated multipath channels of all known users to suppress the intracell interference, while blindly suppressing the intercell interference. Several forms of group-blind linear detectors are developed based on different criteria. Moreover, group-blind multiuser detection in the presence of correlated noise is also considered. In this case, two receiving antennas are needed for channel estimation and signal separation. Simulation results demonstrate that the proposed group-blind linear multiuser detection techniques offer substantial performance gains over the blind linear multiuser detection methods in a CDMA uplink environment     

Receiver design in multicarrier direct-sequence CDMA communications

Multicarrier direct-sequence code-division multiple access (MC-DS-CDMA) has emerged recently as a promising candidate for the next generation broad-band mobile networks. We consider the design of multiuser receivers for MC-DS-CDMA communications over fading channels. We present a class of spreading codes that enables the simple despreading-combining receiver to achieve the performance of the optimum multiuser linear receiver. These codes are shown to be optimum for independent fading channels under a code design criterion derived. Also derived are analytic solutions of optimum spreading codes for any given channel fading statistics. Simulation results are provided to demonstrate the significant gains in performance and simplicity due to the proposed techniques     

Layered space-time multiuser detection over wireless uplink systems

In this paper, we investigate the use of layered space-time (also known as the vertical Bell Laboratories layered space-time (V-BLAST) scheme) for multiuser detection in fading channels. The multiple transmit antennas in V-BLAST are treated as individual mobile station transmitters, while the base station consists of multiple receive antennas. In the proposed system, users are organized in groups and allocated a unique spreading code within the same group. Using these codes, we are able to separate the different groups, and layered space-time algorithm is then invoked to further remove the remaining interference between users. A decorrelator-type receiver-based layered space-time detection is proposed for both complex and real constellations. For the latter case, we derive our receiver after evaluating and comparing the performance of two decorrelators based on the V-BLAST scheme. It is demonstrated that a significant performance improvement and increase in system capacity is obtained with very low spreading factors. Further results are also introduced by considering reduced complexity receivers based on serial layered space-time group multiuser detection, and parallel layered space-time group multiuser detection.     

Adaptive transmitter optimization for blind and group-blind multiuser detection

The linear subspace-based blind and group-blind multiuser detectors recently developed represent a robust and efficient adaptive multiuser detection technique for code-division multiple-access (CDMA) systems. In this paper, we consider adaptive transmitter optimization strategies for CDMA systems operating in fading multipath environments in which these detectors are employed. We make use of more recent results on the analytical performance of these blind and group-blind receivers in the design and analysis of the transmitter optimization techniques. In particular, we develop a maximum-eigenvector-based method of optimizing spreading codes for given channel conditions and a utility-based power control algorithm for CDMA systems with blind or group-blind multiuser detection. We also design a receiver incorporating joint optimization of spreading codes and transmitter power by combining these algorithms in an iterative configuration. We will see that the utility-based power control algorithm allows us to efficiently set performance goals through utility functions for users in heterogeneous traffic environments and that spreading code optimization allows us to achieve these goals with lower transmit power. The signal processing algorithms presented here maintain the blind (or group-blind) nature of the receiver and are distributed, i.e., all power and spreading code adjustments can be made using only locally available information.     

Iterative semiblind multiuser receivers for a space-time block-coded MC-CDMA uplink system

Iterative multiuser detection and space-time coding are two promising techniques to improve the capacity and performance of coded multiuser systems in wireless channels. In this paper, we present iterative multiuser detection schemes for a space-time block-coded multicarrier code-division multiple-access system with multiple transmit and receive antennas. We consider a more general case of an uplink system in the presence of both intra- and intercell interferences. We propose two types of iterative semiblind space-time receivers for such an uplink environment. The first is based on the minimum mean-square error criterion and the second is a hybrid scheme based on a combination of parallel interference cancellation and linear multiuser detection. These iterative receivers are derived, using a subspace approach, which utilizes known users' information for the computation of log-likelihood ratios (LLRs) while blindly suppressing the unknown interference. The LLRs are refined successively during the iterative process by using the extrinsic information available through decoding of all known users. A turbo code is used for channel coding. Simulation results in a frequency-selective Rayleigh-fading environment are presented to verify the performance of the proposed schemes.     

Achieving near-optimum asymptotic efficiency and fading resistanceover the time-varying Rayleigh-faded CDMA channel

We study multiuser receiver design and analysis for synchronous code-division multiple-access (CDMA) channels with time-varying Rayleigh fading. Starting from an error probability criterion, we first derive a near-optimum receiver for this channel that admits a detector-estimator decomposition, has certain asymptotic optimality properties and a complexity which is independent of the length of the observation interval. The performance of this detector is analytically characterized and contrasted with that of the optimal multiuser detector for the time-invariant (or static) CDMA Rayleigh-fading channel when it is implemented over the time-varying channel. Notable among our conclusions is the fact that, unlike the static channel multiuser detector, the time-varying channel detector is able to withstand not only the estimated interference from the other system users, but also, the residual interference (that cannot be estimated) arising out of imperfect estimation of the interferer fading parameters. Using estimation error covariance information, this detector shows flexibility in accommodating a wide range of interferer fading conditions     

Selective Multiuser Detection for Cellular CDMA Systems

Multiuser detection-oriented CDMA systems have been anticipated to significantly improve system capacity in third-generation W-CDMA-based systems. However, they are greatly limited by the computational complexity of multiuser receivers. In this work, we propose a new, computationally efficient approach to multiuser detection (MUD), consisting in MUD of the subset of preselected users, and conventional detection of the rest of users, called selective multiuser detection (SMD). It allows for full exploitation of available processing power at the receiver by use of MUD and provides remedy for computational complexity of MUD techniques when the number of active users increases beyond the processing capability. We propose and examine three different criteria for selection of users to be processed by the multiuser receiver and analyze the capacity for the single-cell and the multicell CDMA cellular system. The capacity improvement with respect to the conventional CDMA detector combines the gain from MUD and reduction of other-cell interference. We apply the analysis to two SMD schemes using decorrelator and successive interference canceller (SIC) as the multiuser receiver. The results indicate that the SMD is a promising alternative for MUD-oriented CDMA systems with large numbers of active users.     

Partial sampling MMSE interference suppression in asynchronousmulticarrier CDMA system

Linear minimum mean square error (LMMSE) receivers for asynchronous multicarrier code division multiple access (MC-CDMA) system under frequency-selective Rayleigh fading channel is studied. The performance of this LMMSE receiver is evaluated and shown to be superior to that of the other two schemes, equal-gain combining (EQC) and maximum-ratio combining (MRC). However, a perfect timing estimation of the desired user is needed for these receivers, as a misaligned sampling interval of these receivers results in severely self intersymbol interference (ISI) and intercarrier interference (ICI) for the desired signal at the output. In order to remove the timing acquisition requirement of a receiver for an asynchronous MC-CDMA system, we proposed a novel partial sampling MMSE (PS-MMSE) receiver. Numerical result shows that the PS-MMSE receiver without timing knowledge provides significantly stronger interference suppression capability than the LMMSE receiver with known timing. Moreover, a so-called reduced complexity partial sampling MMSE (RPS-MMSE) receiver is proposed to make the number of the receiver's taps independent of the number of subcarriers. Results show that with a proper grouping parameter, a much less complicated RPS-MMSE receiver achieves almost the same performance as the PS-MMSE receiver. Thus, one is able to implement an MMSE receiver without a prior timing requirement to perform multiuser detection for the MC-CDMA system in an asynchronous scenario at the expense of a slight complexity increase     

A multiuser approach to narrowband cellular communications

We compare three receivers for coded narrowband transmission affected by fading and co-channel interference. The baseline receiver is based on conventional diversity reception with maximal-ratio combining. A multiuser approach allows us to derive a maximum-likelihood multiuser receiver and its reduced-complexity suboptimal version. Finally, a decorrelating diversity receiver, which seeks a tradeoff between performance and complexity, is studied. Closed-form performance parameters are derived for all the proposed receivers in the case of coded coherent PSK and independent frequency nonselective Rayleigh fading