Performance of blind and group-blind multiuser detectors

In blind (or group-blind) linear multiuser detection, the detector is estimated from the received signals, with the prior knowledge of only the signature waveform of the desired user (or the signature waveforms of some but not all users). The performance of a number of such estimated linear detectors, including the direct-matrix-inversion (DMI) blind linear minimum mean square error (MMSE) detector, the subspace blind linear MMSE detector, and the form-I and form-II group-blind linear hybrid detectors, are analyzed. Asymptotic limit theorems for each of the estimates of these detectors (when the signal sample size is large) are established, based on which approximate expressions for the average output signal-to-interference-plus-noise ratios (SINRs) and bit-error rates (BERs) are given. To gain insights on these analytical results, the performance of these detectors in an equicorrelated code-division multiple-acces (CDMA) system is compared. Examples are provided to demonstrate the excellent match between the theory developed here and the simulation 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.     

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     

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     

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.     

Performance Analysis of Blind-Adaptive-Subspace Multiuser Detectors Over Multipath Fading Channels

Perturbation analyses for various kinds of blind-adaptive-subspace multiuser detectors are presented in this paper. Closed-form expressions are derived for the minimum-mean-square-error detector, zero-forcing detector, and group-blind detector in terms of output signal-to-interference-plus-noise ratio and bit-error rate over a multipath fading channel. Numerical results show that the analytical results match well with the simulation results for both static and dynamic environments. Furthermore, the proposed analytical results can be treated as performance bounds for other blind-adaptive singular-value-decomposition-based subspace multiuser detectors     

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.     

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     

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.     

Transactions Papers - A Blind Adaptive MMSE Multiuser Detector over Multipath CDMA Channels and its Analysis

Based on the refinement-only fast subspace tracking (RO-FST) algorithm to adaptively estimate the signal sub-space, a blind adaptive SVD-based minimum-mean-square-error (MMSE) multiuser detector is proposed in this paper for asynchronous direct-sequence code-division-multiple-access (DS-CDMA) systems over multipath fading channels. Numerical results show that the proposed detector gives low computational complexity and good performance in terms of signal-to-interference-plus-noise ratio (SINR) and bit-error-rate (BER). In addition, we apply the perturbation analysis of the proposed adaptive detector to derive the closed-form expressions for the mean-square error (MSE) and SINR. The analytical results are shown to match well with the simulation results.     

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…     

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.     

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 multiuser detector based on orthogonal projection [for CDMA]

A new stable blind multiuser detector based on signal subspace orthogonal projection is presented. By carrying out a pseudoeigendecomposition (PED) analysis, a technique proposed for the first time, the signal of the interested user can be approximated by the orthogonal projection of a received multiuser signal onto the related subspace of the interested user. Simulations show that compared with the previous subspace-based MMSE blind multiuser detector, the new detector offers better performance without leading to an increase in the computational complexity     

Asymptotic performance of subspace methods for synchronousmultirate CDMA systems

Two direct sequence (DS) code division multiple access (CDMA) multirate access methods with a fixed chip rate can be employed to support multirate services: multicode (MC) access and multiple processing gain (MPG) access. In either an MC or an MPG multirate CDMA system, severe intersymbol interference (ISI) may exist due to large channel delay spread relative to the symbol interval. We generalize the blind subspace technique to such a multirate CDMA system in order to estimate possibly long channel impulse response of a desired user. Then, we build a blind minimum mean-square-error (MMSE) detector to detect the user's information. The detection performance can be significantly improved by suppressing ISI, which becomes feasible after the user's channel parameters are estimated. The asymptotic performance of the channel estimator and the detector is analyzed. In particular, for typical distributions of the inputs and channel noise, closed-form expressions for the channel estimation error and the output signal-to-interference-plus-noise ratio (SINR) of the detector are derived as functions of the number of received data samples and system parameters. Simulation results are provided to verify our analysis     

Multi-user detector for multi-carrier CDMA systems

Blind multi-user detection is of special interest for multiple access interference (MAI) mitigation in code-division multiple-access (CDMA) systems since it is impractical to assume perfect knowledge of parameters such as spreading codes, time delays and amplitudes of all the users in a rapidly changing mobile environment. In [1], the blind decorrelating detector and the minimum mean square error (MMSE) detector were developed based on subspace estimation and derived in closed forms of the signal subspace components. To combat frequency-selective fading, the subspace approach to blind multi-user detection was extended to multi-carrier CDMA (MCCDMA) systems, e.g. in [2]. In this Letter, we develop further the algorithm presented in [1, 2], and show how the condition of the signal subspace can be improved by using not only the autocorrelation, but also the pseudo-autocorrelation of the received observations, leading to improved performance in blind multi-user detection.     

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 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     

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