Asymptotic analysis of LMMSE multiuser receivers for multi-signature multicarrier CDMA in Rayleigh fading

This paper considers a multicarrier (MC) code-division multiple-access system where each user employs multiple signatures. The receiver is linear and minimizes the mean square error of the data estimate. Both multiple-user and single-user systems are considered, as well as single and multiple signatures per user. In each case, an asymptotic analysis is used to derive the output signal-to-interference-plus-noise ratio (SINR) as a function of the system loading, the noise power, and the fading properties of the channel. Asymptotic in this case means that the number of independent subcarriers and number of signatures per user each tends to infinity with fixed ratio. The associated bit-error rate (BER) is evaluated for binary phase-shift keying symbols. Simulations show that the asymptotic SINRs and BERs derived in each case are accurate for realistic finite systems.     

Bit-error probability analysis of linear receivers for CDMA systemsin frequency-selective fading channels

The bit-error probability of a linear receiver for code-division multiple-access communications is analyzed. The analysis is presented for the additive white Gaussian noise and fading multipath channels also with data-aided channel estimation. Two ways to approximate the averaging over the interfering data symbol combinations are considered and compared. Numerical examples are presented to demonstrate the usefulness of the analysis methods     

Performance analysis of linear multisensor multiuser receivers forCDMA in fading channels

Bit-error probability (BEP) analysis for linear multiuser receivers with multiple sensors in frequency selective Rayleigh fading channels is presented. The analysis is applied to evaluate the BEP in antenna diversity reception and in a cellular CDMA system. Diversity and multiuser receivers are compared based on the examples. It is observed that adding new diversity antenna elements improves performance even if the correlation between the antenna elements is relatively large (up to 0.7). However, the large correlation values pose a significant reduction in the diversity gain in comparison to the zero correlation. It is also seen that the macroscopic diversity improves the performance of receivers significantly in cellular CDMA networks. When comparing diversity and multiuser receivers it is concluded that multiuser receivers are necessary to provide low BEPs. It is also highly beneficial to have at least two diversity antennas available, in particular, if there is no multipath diversity provided by the channel. The results also show that the reduction of intercell multiple-access interference yields a significant performance advantage in cellular networks. It is also demonstrated that the combination of spatial diversity and a multiuser receiver provides a significant receiver performance or system capacity gain in comparison to implementing only one of them     

Performance of linear reduced-rank multistage receivers for DS-CDMA in frequency-selective fading channels

The performance of a set of linear reduced-rank multistage filter banks is studied in the context of multiuser detection for direct-sequence (DS) code-division multiple-access (CDMA) systems. The set of filter banks under consideration is comprised of the minimum mean-square error (MMSE), the minimum output energy (MOE), the best linear unbiased estimator (BLUE), and the maximum-likelihood (ML) detector. Based on a common framework for the multistage implementations of the aforementioned filter banks, the signal-to-interference plus noise ratios (SINRs) and bit-error rates (BERs) of these reduced-rank filter banks are studied for multipath Rayleigh-fading channels. A generic BER formula is provided for coherent detection and noncoherent differential detection schemes constructed under this common framework. Analysis shows that all of these performance measures are characterized by a kernel matrix K/sub mmse/ whose trace forms the output SINR of the MMSE filter bank. Through investigating the recursive structure of K/sub mmse/, the output SINRs are proven to be monotonically increasing with the number of stages and upper-bounded by a number equal to the paths of the desired user's channel. The condition for asymptotically achieving this upper bound is also provided, which leads to the notion of effective user capacity of linear reduced-rank multiuser detection as well as serves as a test for the existence of a BER floor for coherent detection. In addition, the channel mismatch due to differential detection is also shown to yield a BER floor for noncoherent detection. Based on this analysis, a simple yet effective rule for choosing the number of stages is provided for both coherent and noncoherent linear multistage multiuser detection.     

Linear predictive receivers for fading channels

The authors discuss maximum likelihood sequence detection (MLSD) based on prediction techniques for linearly modulated digital signals transmitted over fading channels. Efficient implementations of the sequence detector are investigated and a general formulation for computing the prediction coefficients is derived. Furthermore, the equivalence of different existing prediction-based receivers is shown     

Performance analysis of MMSE receivers for DS-CDMA in frequency-selective fading channels

The performance of the minimum mean-squared error (MMSE) receiver for the detection of direct sequence code division multiple access is considered in various fading channel models. Several modifications to the basic MMSE receiver structure which have been previously proposed for use on nonselective fading channels are reviewed and shown to represent different approximations to a single common form. The performance of this general structure is analyzed as well as various extensions suitable for frequency-selective fading channels. Particular attention is given to the performance advantage gained through knowledge of the fading parameters of the various transmission paths of each user's signal. It is shown that having this knowledge is not particularly useful on a flat fading channel unless the loading is very heavy and even then the difference in performance is only minimal. On the other hand, having this knowledge is crucial in a multipath fading channel and the inability to learn the fading channel parameters will lead to substantial degradation in capacity. A heuristic explanation to support this result based on a dimensionality argument is also presented.     

Capacity analysis of M-SC receivers over TWDP fading channels

An expression for the probability distribution function (PDF) of the signal-to-noise ratio of a selection combining receiver in two-wave with diffuse power fading channel is derived. Using this PDF expression, the capacity for the different adaptive transmission techniques employing selection combining (SC) are obtained. The study presents the effects of the ratio of total dominant signal power to the scattered signal power on the system capacity. The change in the capacity of the system with the diversity order for a SC receiver in the fading channel is also presented.     

Linear multipath-decorrelating receivers for CDMAfrequency-selective fading channels

Analytical expressions for the error probability of linear multipath-decorrelating receivers with coherent and differentially coherent reception are derived. Both multi-user receivers have superior performance compared to the RAKE receiver and eliminate error probability floor caused by multiple-access interference on a code-division multiple access (CDMA) reverse link. Results also emphasize benefits of using coherent multi-user reception with maximal-ratio combining in frequency-selective fading channels     

Asymptotic error probability analysis of quadratic receivers inRayleigh-fading channels with applications to a unified analysis ofcoherent and noncoherent space-time receivers

A general, asymptotic (high signal-to-noise (SNR)) error analysis is introduced for quadratic receivers in frequency-flat and multipath Rayleigh-fading channels with multiple transmit and receive antennas. Asymptotically tight expressions for the pairwise error probabilities are obtained for coherent, noncoherent, and differentially coherent space-time receivers. Not only is our unified analysis applicable to more general modulation schemes and/or channel models than previously considered, but it also reveals a hitherto unrecognized eigenvalue structure that is common to all of these problems. In addition to providing an easy recipe for computing the asymptotic pairwise error rates, we make some conclusions regarding criteria for the design of signal constellations and codes such as (a) the same design criteria apply for both correlated and independent and identically distributed (i.i.d.) fading processes and (b) for noncoherent communications, unitary signals are optimal in the sense that they minimize the asymptotic union bound     

Performance analysis of equal-gain diversity receivers over generalized Gamma fading channels

Generalized Gamma (GG) distribution is a generic model that covers many well-known fading distributions as special cases. This paper deals with the performance analysis of L-branch equal gain combining (EGC) receivers operating over GG fading channels. For these receivers and by using convergent infinite series approach, the probability of error (P_e) can be formulated in the form of an infinite series. The coefficients of P_e series can be derived by calculating complicated integrations over the fading envelope distribution. In this paper, it is shown that the required integrations for the case of GG distribution have a complex closed-form in terms of Meijer's G function, and then, a new approximation method is developed for computation of them. The proposed method only needs mean and variance of the fading envelope; hence it has low complexity and eliminates the need for calculation of complex functions. The presented numerical examples show that the developed method can approximate the required parameters and also the individual coefficients accurately and this accuracy increases with the increase of L. The proposed method is applied to analyze the probability of error performance of the L-branch EGC receiver with both coherent phase shift keying (CPSK) and frequency shift keying (CFSK) modulation schemes under different GG channel conditions. Also the effect of gain unbalance between diversity branches on the probability of error is investigated.     

Asymptotic analysis of optimum and suboptimum CDMA downlink MMSE receivers

In this paper, we investigate the performance of two linear receivers for code-division multiple-access (CDMA) downlink transmissions over frequency-selective channels, the users having possibly different powers. The optimum minimum mean-square error (MMSE) receiver is first considered. Because this receiver requires the knowledge of the code vectors attributed to all the users within the cell when these vectors are time varying, its use may be unrealistic in the forward link. A classical suboptimum receiver, consisting in a chip rate equalizer followed by a despreading with the code of the user of interest, is therefore studied and compared to the optimum MMSE receiver. Performance of both receivers is assessed through the signal-to-interference-plus-noise ratio (SINR) at their outputs. The analytical expressions of these SINRs depend in a rather nonexplicit way on the codes allocated to the users of the cell, and are therefore not informative. This difficulty is dealt with by modeling the users code matrix by a random matrix. Because the code matrices used in the forward link are usually isometric, the code matrix is assumed to be extracted from a Haar-distributed random unitary matrix. The behavior of the SINRs is studied when the spreading factor and the number of users converge to /spl infin/ at the same rate. Using certain results of the free probability theory, we establish the fact that the SINRs converge almost surely toward quantities that depend only on the complex amplitudes of propagation channel paths. We then use the expressions of these SINR limits to discuss the influence of the various parameters on the performance of the receivers.     

Reduced-rank multistage receivers for DS-CDMA in frequency-selective fading channels

Multistage (MS) implementation of the minimum mean-square error (MMSE), minimum output energy (MOE), best linear unbiased estimation (BLUE), and maximum-likelihood (ML) filter banks (FBs) is developed based on the concept of the MS Wiener filtering (MSWF) introduced by Goldstein et al. These FBs are shown to share a common MS structure for interference suppression, modulo a distinctive scaling matrix at each filter's output. Based on this finding, a framework is proposed for joint channel estimation and multiuser detection (MUD) in frequency-selective fading channels. Adaptive reduced-rank equal gain combining (EGC) schemes for this family of FBs (MMSE, MOE, BLUE, and ML) are proposed for noncoherent blind MUD of direct-sequence code-division multiple-access systems, and contrasted with the maximal ratio combining counterparts that are also formed with the proposed common structure under the assumption of known channel-state information. The bit-error rate, steady-state output signal-to-interference plus noise ratio (SINR), and convergence of the output SINRs are investigated via computer simulation. Simulation results indicate that the output SINRs attain full-rank performance with much lower rank for a highly loaded system, and that the adaptive reduced-rank EGC BLUE/ML FBs outperform the EGC MMSE/MOE FBs, due to the unbiased nature of the implicit BLUE channel estimators employed in the EGC BLUE/ML schemes.     

Multiuser receivers for CDMA systems in Rayleigh fading channels

Multiuser demodulation in relatively fast fading channels is analyzed. The optimal maximum likelihood sequence detection (MLSD) receiver is derived and a general suboptimal receiver to approximate the MLSD is proposed. The performance of the parallel interference cancellation (PIC) and decorrelating receivers is compared. The PIC receiver is demonstrated to achieve better performance in known channels than the decorrelating receiver, but it is observed to be more sensitive to the channel coefficient estimation errors than the decorrelator. At high channel loads the PIC receiver suffers from bit error rate (BER) saturation, whereas the decorrelating receiver does not. The performance of data-aided (DA) and decision-directed (DD) multiuser channel estimation is also compared. DA channel estimation is shown to be more robust than DD channel estimation, which may suffer from BER saturation caused by hangups at high signal-to-noise ratios (SNRs). The impact of channel estimation filter impulse response on the BER is studied by comparing optimal and suboptimal channel estimation filters. The implementation complexity of the decorrelating and PIC receivers is compared in terms of required floating point operations and clock cycles in a practical communication scenario. It is observed that the PIC receiver is only moderately more complex to implement than the conventional matched filter bank receiver, whereas the decorrelating receiver is significantly more complex     

Performance of RAKE receivers in Nakagami fading channel witharbitrary fading parameters

A new expression for the bit error rate of RAKE receivers with either coherent or noncoherent/differentially coherent binary demodulation schemes in a Nakagami fading channel is derived. The analysis assumes an arbitrary number of diversity branches with arbitrary fading parameters     

On noncoherent receivers for DSTM in spatially correlated fading

In this letter, we derive a multiple-symbol differential detection (MSDD) and a novel MSDD-based decision-feedback differential detection (MS-DFDD) receiver for differential space-time modulation transmitted over spatially correlated multiple-input multiple-output fading channels. We show that MS-DFDD outperforms previously proposed DFDD schemes that are based on scalar and vector prediction (SP-DFDD and VP-DFDD). In addition, we prove that at high signal-to-noise ratio (SNR) VP-DFDD is equivalent to SP-DFDD and thus fails to properly exploit the spatial fading correlations.     

Recursive receivers for diversity channels with correlated flat fading

This paper addresses the design and performance of time-recursive receivers for diversity based communication systems with flat Rayleigh or Ricean fading. The paper introduces a general state-space model for such systems, where there is temporal correlation in the channel gain. Such an approach encompasses a wide range of diversity systems such as spatial diversity, frequency diversity, and code diversity systems which are used in practice. The paper describes a number of noncoherent receiver structures derived from both sequence and a posteriori probability-based cost functions and compares their performance using an orthogonal frequency-division multiplex example. In this example, the paper shows how a standard physical delay-Doppler scattering channel model can be approximated by the proposed state-space model. The simulations show that significant performance gains can be made by exploiting temporal, as well as diversity channel correlations. The paper argues that such time-recursive receivers offer some advantages over block processing schemes such as computational and memory requirement reductions and the easier incorporation of adaptivity in the receiver structures.     

Multistage linear receivers for DS-CDMA systems

A new family of multistage low-complexity linear receivers for direct sequence code division multiple access (DS-CDMA) communications is introduced. The objective of the proposed design is to mitigate the effect of multiple access interference (MAI), the most significant limiting factor of user capacity in the conventional DS-CDMA channel. The receivers presented here employ joint detection of multiple users and therefore require knowledge of all the signature codes and their timing. In addition, for a multipath environment, reliable estimates of the received powers and phases are assumed available for maximal ratio RAKE combining. Each stage of the underlying design recreates the overall modulation, noiseless channel, and demodulation process. The outputs of these stages are then linearly combined. The combining weights can be chosen to implement different linear detectors, including the decorrelating and minimum mean square error (MMSE) detectors. In this paper, we focus on implementing the MMSE detector. Simulation results illustrate that significant performance gains can be achieved in both synchronous and asynchronous systems.This work was presented in part at IEEE Communication Theory Workshop, April 23–26, 1995, and at IEEE MILCOM '95, November 5–8, 1995.This work was submitted in partial fulfillment of Ph.D. requirements at The City University of New York.     

Asymptotic performance analysis of arbitrary rectangular QAM over fading channels

In this paper, the asymptotic performance of arbitrary rectangular Quadrature Amplitude Modulation (QAM) signals over fading channels is investigated. A novel unified asymptotic average Symbol Error Probability (SEP) expression is derived in terms of diversity and coding gain. The validity and accu-racy of the analytical result are verified by means of computer simulations. Furthermore, the results pre-sented are very easy to be extended to the systems with multi-channel diversity receivers.     

Performance analysis of a class of GSC receivers over nonidentical Weibull fading channels

The performance of a class of generalized-selection combining (GSC) receivers operating over independent but nonidentically distributed Weibull fading channels is studied. We consider the case where the two branches with the largest instantaneous signal-to-noise ratio (SNR), from a total of L available, GSC(2, L) are selected. By introducing a novel property for the product of moments of ordered Weibull random variables, convenient closed form expressions for the moments of the GSC(2,L) output SNR are derived. Using these expressions, important performance criteria, such as average output SNR and amount of fading, are obtained in closed form. Furthermore, employing the Pade/spl acute/ approximants theory and the moment-generating function approach, outage and bit-error rate performance are studied. An attempt is also made to identify the equivalency between the Weibull and the Rice fading channel, which is typically used to model the mobile satellite channel. We present various numerical performance evaluation results for different modulation formats and channel conditions. These results are complemented by equivalent computer simulated results which validate the accuracy of the proposed analysis.