Large-sample performance of blind and Group-blind multiuser detectors: a perturbation perspective

In blind and group-blind multiuser detection, different detectors can be designed using either the sample data covariance matrix directly or its eigencomponents. Due to finite-sample effect in practice, their performance deviates from the corresponding optimum. A perturbation technique is developed rigorously and systematically to analyze those detectors in this work. Subject to the assumption that the first-order perturbation dominates, corresponding results can be applied to a practical system of a given sample size. In particular, performance of the following typical detectors is studied for either flat or estimated multipath channels: direct-matrix-inversion (DMI) blind minimum mean-square error (MMSE) detector, subspace blind MMSE detector, direct zero-forcing (ZF) detector, subspace ZF detector, and group-blind hybrid detector. Simulation examples further verify various analytical results.     

Asymptotic analysis of blind multiuser detection with blind channel estimation

The analytical performance of the subspace-based blind linear minimum mean-square error (MMSE) multiuser detection algorithm in general multipath multi-antenna code-division multiple-access (CDMA) systems is investigated. In blind multiuser detection, the linear MMSE detector of a given user is estimated from the received signals, based on the knowledge of only the spreading sequence of that user. Typically, the channel of that user must be estimated first, based on the orthogonality between the signal and noise subspaces. An asymptotic limit theorem for the estimate of the blind linear detector (when the received signal sample size is large) is obtained, based on which approximate expressions of the average output signal-to-inference plus noise ratios (SINRs) and bit error rates (BERs) for both binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulations are given. Corresponding results for group-blind multiuser detectors are also obtained. Examples are provided to demonstrate the excellent match between the theory developed in this paper and the simulation results.     

Large-system performance analysis of blind and group-blindmultiuser receivers

We present a large-system performance analysis of blind and group-blind multiuser detection methods. In these methods, the receivers are estimated based on the received signal samples. In particular, we assume binary random spreading, and let the spreading gain N, the number of users K, and the number of received signal samples M all go to infinity, while keeping the ratios K/N and M/N fixed. We characterize the asymptotic performance of the direct-matrix inversion (DMI) blind linear minimum mean-square error (MMSE) receiver, the subspace blind linear MMSE receiver, and the group-blind linear hybrid receiver. We first derive the asymptotic average output signal-to-interference-plus-noise ratio (SINR) for each of these receivers. Our results reveal an interesting "saturation" phenomenon: The output SINR of each of these receivers converges to a finite limit as the signal-to-noise ratio (SNR) of the desired user increases, which is in stark contrast to the fact that the output SINR achieved by the exact linear MMSE receiver can get arbitrarily large. This indicates that the capacity of a wireless system with blind or group-blind multiuser receivers is not only interference-limited, but also estimation-error limited. We then show that for both the blind and group-blind receivers, the output residual interference has an asymptotic Gaussian distribution, independent of the realizations of the spreading sequences. The Gaussianity indicates that in a large system, the bit-error rate (BER) is related to the SINR simply through the Q function     

Blind Linear MMSE Receivers for MC-CDMA Systems

This paper studies blind constrained minimum output energy (CMOE)-based and subspace-based linear minimum mean-squared-error (LMMSE) detectors for multi-carrier code division multiple access (MC-CDMA) systems. By imposing quadratic weight constraint, the CMOE detector is made more robust against signature waveform mismatch, and a better performance over the standard CMOE detector is obtained. Because of separation of signal and noise subspaces, the more complicated subspace-based LMMSE detector has better performance than the CMOE detector. The recursive subspace tracking algorithms are also investigated for the subspace-based MMSE receiver. Numerical results show that the steady-state performance of the robust CMOE detector is close to the subspace-based MMSE method. The blind mode decision-directed LMMSE detection is studied where the blind detectors are used for initial adaptation. Numerical simulations illustrate that the blind mode decision-directed MMSE detection substantially improves the system performance when the frequency-selective channel is slowly-varying     

Blind adaptive multiuser detection

The decorrelating detector and the linear minimum mean-square error (MMSE) detector are known to be effective strategies to counter the presence of multiuser interference in code-division multiple-access channels; in particular, those multiuser detectors provide optimum near-far resistance. When training data sequences are available, the MMSE multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes. This paper introduces an adaptive multiuser detector which converges (for any initialization) to the MMSE detector without requiring training sequences. This blind multiuser detector requires no more knowledge than does the conventional single-user receiver: the desired user's signature waveform and its timing. The proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest     

Blind multiuser detection: a subspace approach

A new multiuser detection scheme based on signal subspace estimation is proposed. It is shown that under this scheme, both the decorrelating detector and the linear minimum-mean-square-error (MMSE) detector can be obtained blindly, i.e., they can be estimated from the received signal with the prior knowledge of only the signature waveform and timing of the user of interest. The consistency and asymptotic variance of the estimates of the two linear detectors are examined. A blind adaptive implementation based on a signal subspace tracking algorithm is also developed. It is seen that compared with the previous minimum-output-energy blind adaptive multiuser detector, the proposed subspace-based blind adaptive detector offers lower computational complexity, better performance, and robustness against signature waveform mismatch. Two extensions are made within the framework of signal subspace estimation. First, a blind adaptive method is developed for estimating the effective user signature waveform in the multipath channel. Secondly, a multiuser detection scheme using spatial diversity in the form of an antenna array is considered. A blind adaptive technique for estimating the array response for diversity combining is proposed. It is seen that under the proposed subspace approach, blind adaptive channel estimation and blind adaptive array response estimation can be integrated with blind adaptive multiuser detection, with little attendant increase in complexity     

Performance bounds for linear MMSE receivers in CDMA systems with partial channel knowledge

In code division multiple access (CDMA) systems employing linear adaptive receivers, the detector is typically estimated directly from the received signals, based on some partial knowledge about the system, e.g., signature waveforms of one or several users. We derive the Cramer-Rao lower bounds on the covariances of the estimated linear detectors, under three different assumptions on the mechanism for estimating the detectors, namely, a) finite-alphabet-based (FA) blind detectors, b) constant-modulus-based (CM) blind detectors, and c) second-order-moments-based (SO) blind detectors. These bounds translate into the upper bounds on the achievable signal-to-interference-plus-noise ratio (SINR) by the corresponding adaptive receivers. The results are asymptotic in nature, either for high signal-to-noise ratio (SNR) or for large signal sample size. The effects of unknown multipath channels on these performance bounds are also addressed. Numerical results indicate that while the existing subspace blind or group-blind detectors perform close to the SINR bound for the SO detectors, the SINR bounds for the FA and CM detectors are significantly higher, which suggests potential avenues for developing more powerful adaptive detectors by exploiting more structural information from the system.     

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.     

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     

Adaptive group-blind multiuser detection based on a new subspacetracking algorithm

Wang and Host-Madsen (see IEEE J. Select. Areas Commun., vol.17, p.1971-84, 1999) developed group-blind multiuser detectors for use in code-division multiple-access (CDMA) uplink environments in which 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. Yu and Host-Madsen (see Proc. IEEE Vehicular Technology Conf. (VTC99), Houston, TX, p.1042-46, 1999) later developed an adaptive version of this detector for synchronous CDMA channels. We develop a new low-complexity, high-performance subspace tracking algorithm and apply it to adaptive group-blind multiuser detection in asynchronous multipath CDMA channels. The detector can track changes in the number of users and their composite signature waveforms. We present steady-state performance as well as the ability of the receiver to track changes in the signal subspace. We also address the performance gain of the group-blind detector over its blind counterpart for this application     

Iterative Group-Blind Multiuser Detection and Decoding With Signal Rank Estimation for Coded CDMA Systems

In this paper, a turbo receiver structure is proposed for the uplink of coded code-division multiple-access (CDMA) systems in the presence of unknown users. The proposed receiver consists of two stages following each other. The first stage performs soft interference cancellation and group-blind linear minimum mean square error (MMSE) filtering, and the second stage performs channel decoding. The proposed group-blind linear MMSE filter suppresses the residual multiple-access interference (MAI) from known users based on the spreading sequences and the channel characteristics of these users while suppressing the interference from other unknown users using a subspace-based blind method. The proposed receiver is suitable for suppressing intercell interference in heavily loaded CDMA systems. Since the knowledge of the number of unknown users is crucial for the proposed receiver structure, a novel estimator is also proposed to estimate the number of unknown users in the system by exploiting the statistical properties of the received signal. Simulation results demonstrate that the proposed estimator can provide the number of unknown users with high accuracy; in addition, the proposed group-blind receiver integrated with the new estimator can significantly outperform the conventional turbo multiuser detector in the presence of unknown users.      

Blind equalization and multiuser detection in dispersive CDMAchannels

The problem of blind demodulation of multiuser information symbols in a high-rate code-division multiple-access (CDMA) network in the presence of both multiple-access interference (MAI) and intersymbol interference (ISI) is considered. The dispersive CDMA channel is first cast into a multiple-input multiple-output (MIMO) signal model framework. By applying the theory of blind MIMO channel identification and equalization, it is then shown that under certain conditions the multiuser information symbols can be recovered without any prior knowledge of the channel or the users' signature waveforms (including the desired user's signature waveform), although the algorithmic complexity of such an approach is prohibitively high. However, in practice, the signature waveform of the user of interest is always available at the receiver. It is shown that by incorporating this knowledge, the impulse response of each user's dispersive channel can be identified using a subspace method. It is further shown that based on the identified signal subspace parameters and the channel response, two linear detectors that are capable of suppressing both MAI and ISI, i.e., a zero-forcing detector and a minimum-mean-square-error (MMSE) detector, can be constructed in closed form, at almost no extra computational cost. Data detection can then be furnished by applying these linear detectors (obtained blindly) to the received signal. The major contribution of this paper is the development of these subspace-based blind techniques for joint suppression of MAI and ISI in the dispersive CDMA channels     

Two Schemes of Blind MMSE Multiuser Receiver for Space-Time Coded CDMA Systems

1　IntroductionIthasbeenshownthatthecapacityofwirelesscommunicationsystemscanbeincreaseddramatical lybyemployingmultipletransmittingandreceivingantennas.Space timecodinghasbeenpaidmoreat tentionrecentlybecauseitisaneffectivewaytoex ploitspatialandtemporaldiversity[1～2 ] .Despitealossincodingadvantage,space timeblockcodingcanofferthemaximumdiversitygainbasedononlythelinearprocessingatthereceiver[3～ 4] andhasbeenproposedtobeusedin 3Gsystems.InterferencesuppressionismorechallenginginCDMAsyste…     

On the average near-far resistance for MMSE detection of directsequence CDMA signals with random spreading

The performance of a near-far-resistant, finite-complexity, minimum mean squared error (MMSE) linear detector for demodulating direct sequence (DS) code-division multiple access (CDMA) signals is studied, assuming that the users are assigned random signature sequences. We obtain tight upper and lower bounds on the expected near-far resistance of the MMSE detector, averaged over signature sequences and delays, as a function of the processing gain and the number of users. Since the MMSE detector is optimally near-far-resistant, these bounds apply to any multiuser detector that uses the same observation interval and sampling rate. The lower bound on near-far resistance implies that, even without power control, linear multiuser detection provides near-far-resistant performance for a number of users that grows linearly with the processing gain     

A robust rank estimation algorithm of group-blind MMSE multiuser detectors for CDMA systems

We propose an adaptive rank-estimation method for the additive white or colored Gaussian noise model. The main contribution of this paper has three parts. (1) We investigate the rank mismatch problem in the group-blind multiuser detector of Wang and Host-Madsen (see IEEE J. Select. Areas Commun., vol.17, p.1971-1984, Nov. 1999), and find that underestimating the rank causes significant performance degradation, whereas, rank overestimation can achieve performance gain in the low signal-to-noise-ratio (SNR) region. However, rank overestimation can lead to inaccurate channel estimation, which degrades the detector performance significantly in the high SNR region. (2) We propose a heuristic criterion for initial rank estimation which is robust for nonwhite noise cases. (3) In order to mitigate the rank mismatch problem, we introduce a hypothesis testing criterion for rank and signal subspace decisions, which selects the most probable rank for the group-blind detectors. Simulation results show that the performance of the group-blind detector using this adaptive rank estimation algorithm is comparable to the group-blind with perfect knowledge of the rank, and even better in the low-to-medium SNR region.     

Improved Robust Techniques for Multiuser Detection in Non-Gaussian Channels

In many physical channels where multiuser detection techniques are to be applied, the ambient channel noise is known through experimental measurements to be decidedly non-Gaussian, due largely to impulsive phenomena. This is due to the impulsive nature of man-made electromagnetic interference and a great deal of natural noise. This paper presents a robust multiuser detector for combating multiple access interference and impulsive noise in code division multiple access (CDMA) communication systems. A new M-estimator is proposed for "robustifying" the detector. The approach is corroborated with simulation results to evaluate the performance of the proposed robust multiuser detector compared with that of the linear decorrelating detector, and the Huber and the Hampel M-estimator based detectors. Simulation results show that the proposed detector with significant performance gain outperforms the linear decorrelating detector, and the Huber and the Hampel M-estimator based detectors. This paper also presents an improved robust blind multiuser detection technique based on a subspace approach, which requires only the signature waveform and the timing of the desired user to demodulate that user's signal. Finally, we show that the robust multiuser detection technique and its blind adaptive version can be applied to both synchronous and asynchronous CDMA channels.     

Group-blind intersymbol multiuser detection for downlink CDMA with multipath

Group-blind multiuser detectors for uplink code-division multiple-access (CDMA) were recently developed by Wang and Host-Madsen. These detectors make use of the spreading sequences of known users to construct a group constraint to suppress the intracell interference. However, such techniques demand the estimation of the multipath channels and the delays of the known users. In this paper, several improved blind linear detectors are developed for CDMA in fading multipath channels. The proposed detectors utilize the correlation information between consecutively received signals to generate the corresponding group constraint. It is shown that by incorporating this group constraint, the proposed detectors can provide different performance gains in both uplink and downlink environments. Compared with the previously reported group-blind detectors, our new methods only need to estimate the multipath channel of the desired user and do not require the channel estimation of other users. Simulation results demonstrate that the proposed detectors outperform the conventional blind linear multiuser detectors.     

Blind adaptive multiuser detector for nonlinearly modulated satellite mobile CDMA systems

This paper presents a novel blind adaptive noncoherent decorrelative multiuser detector for nonlinearly modulated satellite mobile Code Division Multiple Access （CDMA） systems. By using the known signature waveforms of the counterpart earth station in the blind adaptive multiuser detector, the system performance has been improved obviously. The computation results about the convergence properties of the new detector and the previous detectors demonstrate that the proposed multiuser detector has better performance than previous multiuser detectors for nonlinearly modulated CDMA systems.     

Receiver design for multicarrier CDMA using frequency-domain oversampling

Based on the frequency-domain oversampling and minimum mean-square error (MMSE) principles, we propose three linear single-user detectors for downlink multicarrier codedivision multiple-access (MC-CDMA) systems. We begin with an optimal linear MMSE detector, which is computationally demanding. To reduce the complexity, a two-stage MMSE detector and a diagonal one-stage MMSE detector are developed subsequently. Simulation results show that the proposed detectors can efficiently suppress the multiple access interference (MAI) caused by frequency-selective fading, near-far effect, frequency offset, and nonlinear power amplification.     

Nonlinear group-blind multiuser detection

A nonlinear group-blind technique is developed for joint detection of some given users' data in a CDMA uplink environment with the presence of unknown interference. This method performs the so-called “slowest-descent search” over a likelihood function of the desired users, starting from the estimate closest to the unconstrained maximizer of the likelihood function, and along mutually orthogonal directions where this likelihood function drops to the slowest. Simulation results show that this new nonlinear technique offers substantial performance improvement over the previously proposed linear group-blind multiuser detectors with little attendant increase in computational complexity. The problem of group-blind multiuser detection in the presence of both unknown interference and impulsive ambient noise is also treated under the framework of slowest-descent search, with the aid of a novel subspace-based robust interference cancellation scheme. It is seen that this robust group-blind method significantly outperforms the robust blind multiuser detection scheme proposed previously