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.     

Performance Analysis of Optimum and Suboptimum Selection Diversity Schemes on Rayleigh Fading Channels With Imperfect Channel Estimates

In this paper, we present a comparative analysis on the effects of channel estimation errors on the performance of optimum and suboptimum selection diversity (SD) receivers on Rayleigh-fading channels. By modeling the estimation errors as independent complex Gaussian random variables, we derive simple closed-form expressions for the average probability of error for both optimum and suboptimum SD schemes with noisy channel estimates. With dual diversity and imperfect estimates, we establish a connection between optimum SD and maximal-ratio combining (MRC), and between suboptimum SD and equal-gain combining diversity schemes. Interestingly, we show that the optimum SD receiver structure and the resulting performance for differential binary coherent phase-shift keying (DBPSK) signaling can be obtained, in a straightforward way, as a special case of the performance of the optimum SD scheme with binary PSK signaling and channel estimation errors. For a fixed average power and bit duration, in conjunction with pilot-assisted minimum mean-square error channel estimation, we show that the optimum coherent SD scheme coincides with that of the optimum noncoherent SD scheme with binary frequency-shift keying (BFSK) signaling, whereas the coherent MRC scheme coincides with the optimum noncoherent receiver (i.e., the square-law combiner) for BFSK. The optimum number of diversity channels, under an energy-sharing mode of operation, is also studied. Finally, we formulate the problem of optimal pilot placement, consider channel estimation with a practical pilot-symbol-assisted modulation technique, and present some numerical results illustrating the comparative performances of various SD receivers     

On channel estimation and sequence detection of interleaved codedsignals over frequency nonselective Rayleigh fading channels

Due to the receiver complexity introduced by interleaving, the implementation of maximum likelihood (IML) decoding of interleaved coded signals transmitted over frequency nonselective Rayleigh fading channels has been shown to be practically impossible. As an alternative, a two-stage receiver structure has been proposed, where the channel estimation and sequence decoding are done separately. The channel estimation issue in a two-stage receiver is examined in detail in this paper. It is shown that although an optimum (maximum a posteriori (MAP)) channel estimation is not possible in practice, it can be approached asymptotically by joint MAP estimation of the channel and the coded data sequence. The implementation of the joint MAP estimation is shown to be an ML sequence estimator followed by an minimum mean-square error (MMSE) channel estimator. Approximate fill sequence estimation using pilot symbol interpolation is also studied, and through computer simulations, its performance is compared to receivers using hit sequence estimation. The effect of decision delay (DD), prediction order, and pilot insertion rate (PIR) on the reduced complexity ML sequence estimation is investigated as well. Finally, a practical receiver is proposed that makes the best compromise among the error performance, receiver complexity, DD, and power (or bandwidth) expansion due to pilot insertion     

Improved channel estimation and SIR measurement in WCDMA downlink systems

The rake receiver performance of a direct-sequence code-division multiple-access (DS-CDMA) system can significantly be degraded unless the channel condition is properly estimated. Since the channel condition is time-varying and location-dependent, it is desirable to employ an adaptive channel estimator (ACE) that can properly adjust the bandwidth of the channel estimation filter (CEF) according to the channel condition such as the maximum Doppler frequency. To this end, we propose low-complexity ACE and signal-to-interference power ratio (SIR) estimator for wide-band CDMA downlink systems with and without the use of transmit antenna diversity. The proposed schemes adjust the bandwidth of the CEF by exploiting the correlation characteristics of the received pilot signal. The analytic design is verified by computer simulation. Simulation results show that the proposed ACE and SIR estimator can significantly improve the link performance for a wide range of channel condition, particularly when the channel condition is poor.     

Enhanced MMSE channel estimation using timing error statistics for wireless OFDM systems

Estimation and tracking of the frequency-selective time-varying channel response is a challenging task for wireless communication systems incorporating coherent OFDM. In pilot-symbol-assisted (PSA) OFDM systems, the minimum mean-square-error (MMSE) estimator provides the optimum performance based on the channel statistics (channel correlation function and SNR). In OFDM systems, FFT-block timing error introduces a linear phase rotation to data modulated on individual subcarriers. An MMSE channel estimator designed only using the wireless channel statistics performs only sub-optimally when subcarrier phase rotations due to block timing errors are present. In this paper, we show that by using the block timing error statistics of the OFDM time-synchronizer the performance of the MMSE channel estimation can be significantly improved. Numerical results show that the bit-error-probability (BEP) performance degradation due to timing errors can be almost completely recovered by the proposed technique.     

Soft Decoding Assisted SNR Estimation Under Block Fading Channels for Orthogonal Modulations

The performance of the coded orthogonal modulation (OM) system under slow fading channels heavily depends on the estimation of the signal-to-noise ratio (SNR), including the fading amplitude and the noise spectral density. However, a relatively long packet of pilot symbols is often required to guarantee the accuracy of the SNR estimation, which makes it impractical in some situations. To address this problem, this paper proposes an iterative SNR estimation algorithm using the soft decoding information based on the expectation-maximization algorithm. In the proposed method, a joint iterative loop between the SNR estimator and decoder is performed, where the extrinsic information generated by the soft decoder is employed to enhance the estimation accuracy and the SNR estimated by the estimator is used to generate the soft information to the decoder. Also, no pilot symbols are needed to estimate the SNR in the proposed estimator. The Cramer–Rao lower bound (CRLB) of fully data-aided (FDA) estimation is derived to works as the final benchmark. The performance of the proposed algorithm is evaluated in terms of the normalized mean square errors (NMSEs) and the bit error rates (BERs) under block fading channels. Simulation results indicate that the NMSE of the proposed estimator reaches the CRLB of the FDA estimator and outperforms that of the approximate ML (ML-A) estimator proposed by Hassan et al. by 4.1 dB. The BER performance of coded OM system with the proposed estimation algorithm is close to the ideal case where the channel fading and the noise spectral density are known at the receiver.     

Diversity-assisted channel estimation and multiuser detection for downlink CDMA with long spreading codes

In downlink communication of a direct-sequence (DS) code-division multiple-access (CDMA) system, each user's short spreading codes are superimposed by base station's common long codes. This situation creates much difficulty in blind signal detection when multipath propagation occurs. However, when spatial/temporal diversity is available at the receiver, it is shown in this paper that subspace technique can be directly applied to estimate the common downlink multipath channel. Then, typical linear receivers, such as zero-forcing (ZF), minimum mean-square-error (MMSE) and RAKE receivers can be designed to detect the desired signal. Since the data covariance matrix is used but estimated from finite data samples, performance of both channel estimator and receivers gets perturbed. It is thus thoroughly and jointly analyzed by perturbation analysis. Justification of analysis and comparison of different receivers are also made through simulations.     

MMSE detection of multicarrier CDMA

Minimum mean-squared error (MMSE) detection of multicarrier code-division multiple-access (CDMA) signals is investigated. The theoretical performance of two different design strategies for MMSE detection are compared. In one case, the MMSE filters are designed separately for each carrier, while in the other case the optimization of the filters is done jointly. Naturally, the joint optimization produces a better receiver, but the difference in performance is shown to be substantial. The multicarrier CDMA performance is then compared to that of a single-carrier CDMA system on a frequency-selective fading channel. A mechanism is then developed to track the channel fading parameters for all the users' signals so that joint optimization of the receiver filters is possible in a time-varying channel. Simulation results show that the performance of this receiver is close to ideal theoretical results for moderate vehicle speeds. The performance begins to degrade when the normalized Doppler rate is higher than about 1%     

A covariance shaping framework for linear multiuser detection

A new class of linear multiuser receivers, referred to as the covariance shaping multiuser (CSMU) receiver, is proposed, for suppression of interference in multiuser wireless communication systems. This class of receivers is based on the recently proposed covariance shaping least-squares estimator, and is designed to minimize the total variance of the weighted error between the receiver output and the observed signal, subject to the constraint that the covariance of the noise component in the receiver output is proportional to a given covariance matrix, so that we control the dynamic range and spectral shape of the output noise. Some of the well-known linear multiuser receivers are shown to be special cases of the CSMU receiver. This allows us to interpret these receivers as the receivers that minimize the total error variance in the observations, among all linear receivers with the same output noise covariance, and to analyze their performance in a unified way. We derive exact and approximate expressions for the probability of bit error, as well as the asymptotic signal-to-interference+noise ratio in the large system limit. We also characterize the spectral efficiency versus energy-per-information bit of the CSMU receiver in the wideband regime. Finally, we consider a special case of the CSMU receiver, equivalent to a mismatched minimum mean-squared error (MMSE) receiver, in which the channel signal-to-noise ratio (SNR) is not known precisely. Using our general performance analysis results, we characterize the performance of the mismatched MMSE receiver. We then treat the case in which the SNR is known to lie in a given uncertainty range, and develop a robust mismatched MMSE receiver whose performance is very close to that of the MMSE receiver over the entire uncertainty range.     

Autocorrelation-based blind spreading-factor detection for CDMA

Spreading factor (SF) in code-division multiple-access (CDMA) systems depends on the data rate of the user, and is, therefore, unknown a priori for a communication receiver. In this letter, the blind SF-detection problem in an additive white Gaussian noise channel is studied, and a novel one-step autocorrelation-based SF detector is proposed. Three decision rules are derived to find simple and robust SF detectors for practical communication receivers. Performance of the detectors is studied and compared with the optimal detector via Monte Carlo computer simulations. The autocorrelation-based SF detector appears to give performance close to the optimal detector, assuming perfect knowledge of signal-to-noise ratio (SNR). It is also found to be significantly more robust to SNR estimation errors than the optimal detector.     

Large system performance of linear multiuser receivers in multipathfading channels

A linear multiuser receiver for a particular user in a code-division multiple-access (CDMA) network gains potential benefits from knowledge of the channels of all users in the system. In fast multipath fading environments we cannot assume that the channel estimates are perfect and the inevitable channel estimation errors will limit this potential gain. We study the impact of channel estimation errors on the performance of linear multiuser receivers, as well as the channel estimation problem itself. Of particular interest are the scalability properties of the channel and data estimation algorithms: what happens to the performance as the system bandwidth and the number of users (and hence channels to estimate) grows? Our main results involve asymptotic expressions for the signal-to-interference ratio of linear multiuser receivers in the limit of large processing gain, with the number of users divided by the processing gain held constant. We employ a random model for the spreading sequences and the limiting signal-to-interference ratio expressions are independent of the actual signature sequences, depending only on the system loading and the channel statistics: background noise power, energy profile of resolvable multipaths, and channel coherence time. The effect of channel uncertainty on the performance of multiuser receivers is succinctly captured by the notion of effective interference     

Performance analysis of an improved MMSE multiuser receiver formismatched delay channels

Motivated by the fact that time delays in a practical direct-sequence code-division multiple-access (DS-CDMA) system can never be perfectly estimated, an improved minimum-mean squared-error (MMSE)-based receiver is proposed and analyzed. Via the simple assumption of a probability distribution for the delay estimation errors, the proposed receiver can achieve a performance superior to that of the conventional MMSE (CMMSE) receiver. The performances of this improved receiver and the CMMSE receiver are compared in terms of the mean squared error (MSE), probability of error, and asymptotic multiuser efficiency (AME). As the original definition of AME does not consider mismatched channels, the behavior of three single-user receivers bearing imperfect delay estimation is also investigated. These single-user receivers are employed to define a more appropriate AME. Finally, an efficient update mechanism to accommodate dynamic channel statistics, and thus practical implementation, is proposed     

Novel diversity receivers in the presence of Gaussian channel estimation errors

Novel diversity receivers that operate in the presence of Gaussian channel estimation errors are proposed for L independent and identically distributed fading channels. Previous work concerned with channel estimation errors has mainly examined the performance of maximal ratio combining (MRC) with estimation errors. It is shown here that MRC is not optimal when estimation errors occur. Moreover, it is shown that better diversity receivers that operate in the presence of Gaussian channel estimation errors can be obtained by using knowledge of the channel estimate statistics. Numerical results show that the derived new diversity receivers can perform as much as 2.0 dB in signal-to-noise ratio better than the conventional MRC receiver in some cases.     

Performance of M-PSK with GSC and EGC with Gaussian weighting errors

Using a moment-generating function (MGF)-based approach, we study the performance of M-ary phase-shift keying (M-PSK) with generalized selection combining (GSC) and equal gain combining (EGC) in fading channels (including Rayleigh, Rician, Nakagami-m, and Nakagami-q fading) with independent and identically distributed (i.i.d) branches. Analytical expressions for the error and outage probabilities, the signal-to-noise-ratio (SNR) statistics, and the channel capacity of M-PSK diversity receivers are derived, taking into account the effects of Gaussian weighting errors and all relevant system and channel parameters. Unlike the case of perfect channel-state information (CSI), the outage probability for the case of imperfect channel estimation (ICE) is not only a function of the normalized SNR with respect to the SNR threshold, but also a function of the operating SNR itself. The SNR loss of the M-PSK GSC and EGC receivers due to ICE and the relation between the receiver input and output SNRs for ICE are derived. Our results show that, even with ICE, GSC and EGC are effective in improving the output SNR and significantly reduce the error floor and the channel-capacity loss caused by ICE.     

Soft‐output MMSE V‐BLAST receiver with MMSE channel estimation under correlated Rician fading MIMO channels

For wireless multiple‐input multiple‐output (MIMO) communications systems, both channel estimation error and spatial channel correlation should be considered when designing an effective signal detection system. In this paper, we propose a new soft‐output MMSE based Vertical Bell Laboratories Layered Space‐Time (V‐BLAST) receiver for spatially‐correlated Rician fading MIMO channels. In this novel receiver, not only the channel estimation errors and channel correlation but also the residual interference cancellation errors are taken into consideration in the computation of the MMSE filter and the log‐likelihood ratio (LLR) of each coded bit. More importantly, our proposed receiver generalizes all existing soft‐output MMSE V‐BLAST receivers, in the sense that, previously proposed soft‐output MMSE V‐BLAST receivers can be derived as the reduced forms of our receiver when the above three considered factors are partially or fully simplified. Simulation results show that the proposed soft‐output MMSE V‐BLAST receiver outperforms the existing receivers with a considerable gain in terms of bit‐error‐rate (BER) performance. Copyright © 2011 John Wiley & Sons, Ltd.     

A Decision Aided CDMA Receiver with Partially Adaptive Decorrelating Multi-User Interference Cancellation

A CDMA receiver with enhanced multiple access interference (MAI) suppressionis proposed for a pilot symbols assisted system over multipath channels. Thedesign of the receiver involves the following procedure. First, blind adaptivecorrelators are constructed at different fingers based on the scheme ofgeneralized sidelobe canceller (GSC) to collect the multipath signals andsuppress MAI. A low-complexity partially adaptive (PA) realization of the GSCcorrelators is proposed which incorporates multi-user information for reducedrank processing. By a judiciously designed decorrelating procedure, a new GSCstructure is obtained in which the MAI are decorrelated and suppressedindividually. The next step is then a simple coherent combining of thecorrelator outputs with pilot aided channel estimation. Finally, furtherperformance enhancement is achieved by an iterative scheme in which the signalis reconstructed and subtracted from the GSC correlators input data, leadingto faster convergence of the receiver. The proposed low-complexity PA CDMAmulti-user receiver is shown to be robust to multipath fading and channelerrors, and achieve nearly the same performance of the ideal maximum SINR andMMSE receivers by using a small number of pilot symbols.     

Joint frequency-domain differential detection and equalization for DS-CDMA signal transmissions in a frequency-selective fading channel

It has been revealed that direct sequence code-division multiple access (DS-CDMA) can achieve a good bit-error rate (BER) performance, comparable to multicarrier CDMA (MC-CDMA), by using coherent frequency-domain equalization (FDE) instead of coherent Rake combining. However, coherent FDE requires accurate channel estimation. Pilot-assisted channel estimation is a practical solution, but its accuracy is sensitive to the Doppler spread. In this paper, a frequency-domain differential encoding and detection scheme is proposed for a DS-CDMA mobile radio. Joint frequency-domain differential detection and equalization (FDDDE) based on minimum mean-square error (MMSE) criterion is presented, where a simple decision feedback filter is used to provide a reliable reference signal for MMSE-FDDDE. Also presented is an approximate BER analysis. It is confirmed by both approximate BER analysis and computer simulation that MMSE-FDDDE provides good BER performance close to the coherent MMSE-FDE and shows high robustness against the Doppler spread; it outperforms coherent MMSE-FDE for large Doppler spreads. The proposed MMSE-FDDDE can also be applied to MC-CDMA. A performance comparison between uncoded DS- and MC-CDMA shows that DS-CDMA with MMSE-FDDDE achieves better BER performance than MC-CDMA with MMSE-FDDDE for small spreading factors.     

相关Nakagami信道下信道估计器对RAKE接收机性能影响研究

在实际环境中RAKE接收机在接收信号时都要进行信道系数估计,以便进行相干合并。文章研究了不采用导频信号与采用导频信号两种估计器,具有估计误差情况下,在相关Nakagami信道下的RAKE接收机的性能,并且通过特征函数法得到了误码率公式的闭合表达式。比较了两种估计器对系统性能的影响,最后给出了数值结果,可以看出,当导频信号能量与信号能量相等,且导频数目比较多时（大于5）,采用导频信号的系统性能优于直接估计信道系数的系统。直接估计信道系数的系统性能在信噪比大于5dB后,其性能远远优于导频信号的估计系统。     

Joint detection with coherent receiver antenna diversity in CDMAmobile radio systems

In code division multiple access (CDMA) mobile radio systems, both intersymbol interference and multiple access interference arise which can be combated by using either elaborate optimum or favorable suboptimum joint detection (JD) techniques. Furthermore, the time variation of the radio channels leads to degradations of the receiver performance. These degradations can be reduced by applying diversity techniques. Using coherent receiver antenna diversity (CRAD) is especially attractive because only the signal processing at the receiver must be modified. In the present paper, the application of CRAD to the more critical uplink of CDMA mobile radio systems with suboptimum JD techniques is investigated for maximal-ratio combining. The authors study six different suboptimum JD techniques based on decorrelating matched filtering, Gauss-Markov estimation, and minimum mean square error estimation with and without decision feedback. These six suboptimum JD techniques which are well-known for single antenna receivers are extended for the application to CRAD. A main concern of the paper is the determining of the SNR performance of the presented JD techniques for CRAD and the achievable average uncoded bit error probabilities for the transmission over rural area, typical urban and bad urban mobile radio channels are determined     

An improved blind adaptive MMSE receiver for fast fading DS-CDMAchannels

Blind adaptive minimum mean-squared errors (MMSE) receivers for multiuser direct-sequence code-division multiple access (DS-CDMA) systems that assume knowledge of the steering vector, i.e., the cross-correlation between the desired output and the input signal, are known for their robustness against channel fading as they do not attempt to explicitly track the channel of the user of interest. However, these receivers often have higher excess mean squared error and, hence, poorer performance than training-sequence based adaptive MMSE receivers. In this paper, an improved correlation matrix estimation scheme for blind adaptive MMSE receivers is provided. The new scheme takes advantage of the fact that the desired linear receiver can be expressed as a function of the interference correlation matrix only, rather than the total data correlation matrix. A theoretical analysis is performed for the flat fading case which predicts that the new estimation scheme will result in significant performance improvement. Blind adaptive MMSE receivers with the new estimation scheme appear to achieve performance comparable to the training-sequence based adaptive MMSE receivers. Detailed computer simulations for the fast multipath fading environment verify that the proposed scheme yields strong performance gains over previous methods