A Unified Approach to Power control in Large Energy-Constrained CDMS Systems

A unified approach to power control is proposed for maximizing utility in terms of energy efficiency in code-division multiple access (CDMA) networks. The approach is applicable to a large family of multiuser receivers including the matched filter, the decorrelator, the linear minimum mean-square error (MMSE) receiver, and the (nonlinear) optimal detectors. It exploits the linear relationship between the transmit power and the output signal-to-interference-plus-noise ratio (SIR) for each user in the large-system limit. Suppose that each user seeks to selfishly maximize its own energy efficiency, a unique Nash equilibrium is shown to exist and be SIR-balanced, thus extending a previous result on linear receivers. A unified power control algorithm for reaching the Nash equilibrium is proposed, which adjusts transmit powers iteratively by computing the large-system multiuser efficiency, which is independent of instantaneous spreading sequences. The convergence of the algorithm is proved for linear receivers, and is demonstrated via simulation for the multiuser maximum likelihood detector. Moreover, the performance of the algorithm in finite-size systems is studied and compared with that of a conventional power control scheme, in which user powers depend on the instantaneous spreading sequences.     

Performance analysis of linear multiuser detectors for randomlyspread CDMA using Gaussian approximation

The performance of a linear decorrelating detector (LDD) and a minimum mean square error (MMSE) detector is analyzed for random spreading waveforms. The performance of the LDD and MMSE detectors is expressed in terms of the so-called near-far resistance, defined by a reciprocal of a diagonal component of inverse matrix. For random code division multiple access, which employs random spreading waveforms, the near-far resistance can be regarded as a random variable. Many papers have dealt with the analysis of multiuser detectors for random spreading sequences. In most cases, however, these analyses derived only the expectations or bounds for the near-far resistance. In this paper, we directly derive the approximate probability density function (PDF) of the near-far resistance and corresponding bit error rate expression for random spreading sequences. It is based on Gaussian approximation of the cross correlation between any two randomly generated spreading codes. The resulting PDF turned out to be a reversed-and-scaled version of chi-square distribution. The approximate expressions, both the PDF and the corresponding bit error rate expression, were verified via Monte Carlo simulations. The results showed that the approximation is quite close to the simulation results when the number of users is less than half the processing gain     

Timing-free blind multiuser detection in differentially encodedDS/CDMA systems

A timing-free blind multiuser detection technique is proposed for differentially encoded direct-sequence/code division multiple access (DS/CDMA) networks. Unlike previously derived blind multiuser detectors, the proposed algorithm does not rely on any information beyond the spreading code of the desired user, namely neither the complex amplitude nor the symbol timing of the signal of interest is assumed to be known to the receiver. The proposed detector structure is immune to cochannel interferers with arbitrarily large powers, and, as computer simulation results show, compares favorably with competing alternatives. Moreover, the proposed detector achieves performance quite close to that of the ideal minimum mean square error (MMSE) multiuser receiver, which requires knowledge of the spreading codes, timing offsets, and received energies for the signals of all active users     

Analysis of the linear SIC for DS/CDMA signals with random spreading

The linear successive interference canceler (LSIC) is a multiuser detector that employs the magnitude of the matched filter (MF) output as the received amplitude estimate of the detected user for use in signal reconstruction. This paper investigates the performance of the LSIC when random spreading sequences are employed. Specifically, the conditional mean and the signal-to-interference-plus-noise ratio (SINR) of the decision variable in each stage are derived to quantify the effects due to imperfect symbol and amplitude estimates. In addition, under the constraint that each user must achieve a certain SINR requirement, we examine the received powers needed for each of a specified number of users and the maximum number of users that a system can support when the LSIC is used in a base station. Computer simulations are presented to compare these results with those of several linear multiuser detectors.     

A low-complexity enhancement to suboptimal CDMA receivers

Conventional matched-filter detectors for code-division multiple-access (CDMA) systems suffer from multiple-access interference (MAI) caused by nonzero correlation between spreading codes at the receiver. A host of advanced detector structures have been proposed to reduce the effect of MAI and, hence, improve performance. However, most multiuser detectors suffer from their relatively complex implementations. A simple method is proposed to improve the performance of the conventional detector by detecting and correcting decision errors at its output without the use of forward error correcting (FEC) codes. The proposed post-detection error control method is shown to substantially improve the performance of the conventional detector, but has a much lower complexity than most other multiuser detectors.     

Adaptive multiuser interference suppression for CDM satellite systems

This paper deals with the application of linear multiuser detectors in mobile terminals of code division multiplex (CDM) satellite systems. Generally, the interference caused by other users can dramatically reduce the performance of a CDM‐based satellite communication system. Since no spreading information of other users is given and since there are no trainings sequences, a blind adaptive interference detector with low complexity is needed. In order to implement a detector for suppressing the interference from other users, different adaptation algorithms can be applied. Comparing them in terms of complexity, adaptation speed and bit error rate, the LMS (least means squares) algorithm with adaptive step size shows the best performance. However, the implementation of this algorithm in a satellite system still leads to high processing times. For this reason, two new schemes with reduced complexity are presented. A very important point is, that the adaptive algorithms are basically restricted to short spreading codes (code period equals symbol period) whereas CDM‐based satellite systems use long codes (one‐code period spans over multiple symbols). In this paper, a new scheme is presented which can be applied to long codes. By cascading multiple separated interference detectors the adaptation is done every time when the same part of the spreading sequence appears. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance analysis for the improved linear multiuser detectors in BPSK-modulated DS-CDMA systems

Recently, a new class of linear multiuser receivers for direct-sequence code-division multiple-access (CDMA) systems employing binary phase-shift keying modulation has been introduced. Unlike classical decorrelating and minimum mean-square error linear multiuser detectors, the new receivers exploit the information contained in the pseudo-autocorrelation of the observables, and are, thus, capable of achieving much better performance. We present new results on the performance analysis of this class of new receivers. In particular, with reference to a CDMA system with deterministic spreading codes, we show that the new receivers outperform the classical ones in terms of both error probability and near-far resistance. With regard, instead, to CDMA systems with random spreading, we compute the average system near-far resistance, showing that the new receivers can accommodate twice the number of users accommodated by the classical linear multiuser receivers.     

Linear and nonlinear chip-rate minimum mean-squared-error multiuserCDMA detection

A linear Kalman filter detector for code-division multiple access proposed earlier in the literature is extended to a structure that can handle arbitrary detection delays, through the mechanism of state augmentation. Because pre-detection RAKE combining is used in the detector, it is optimal for multipath channels, unlike the previous structure that performed post-detection combining. We also derive nonlinear Kalman detectors, which approximate the highly complex nonlinear minimum mean-squared-error detector, using the concept of “additional observations.” Both linear and nonlinear detectors require processing at one or more times the chip rate, and knowledge of the spreading codes of interfering users. They have the advantage over many other multiuser detection algorithms of not requiring the spreading codes to be periodic at the symbol rate, or matrix inversion. In addition, two of the detectors are able to generate and update a posteriori probabilities of the transmitted symbols, making them interesting for iterative multiuser detection     

MMSE/PIC multiuser detection for DS/CDMA systems with inter- andintra-cell interference

This paper analyzes combinations of the linear minimum mean square error (MMSE) detector and a nonlinear parallel interference canceller (PIC) for multiuser code-division multiple-access (CDMA) detection. Both the case where all users' codes are known at the receiver and the case where only some codes are known are considered. An upper bound and an approximate formula for the error probability are derived and verified through simulation. It is shown that the combined MMSE/PIC detector can have a considerable performance gain over the MMSE. It is also shown that while the MMSE detector is sensitive to large code cross-correlation values, the combined MMSE/PIC detector is robust to code cross correlations. Finally, use of the MMSE/PIC detector for cellular systems with both inter- and intra-cell interference is considered     

An asynchronous multiuser CDMA detector based on the Kalman filter

We introduce a multiuser receiver based on the Kalman filter, which can be used for joint symbol detection and channel estimation. The proposed algorithm has the advantage of working even when the spreading codes used have a period larger than one symbol interval (“long codes”), unlike adaptive equalizer-type detectors. Simulation results which demonstrate the performance advantage of the proposed receiver over the conventional detector, the minimum mean squared error (MMSE) detector and a recursive least squares (RLS) multiuser detector are presented. A thorough comparison of the MMSE detector and the proposed detector is attempted because the Kalman filter also solves the MMSE parameter estimation problem, and it is concluded that, because the state space model assumed by the Kalman filter fits the code division multiple access (CDMA) system exactly, a multiuser detector based on the Kalman filter must necessarily perform better than a nonrecursive, finite-length MMSE detector. The computational complexity of the detector and its use in channel estimation are also studied     

On the performance of linear parallel interference cancellation

This paper analyzes the performance of the linear parallel interference cancellation (LPIC) multiuser detector in a synchronous multiuser communication scenario with binary signaling, nonorthogonal multiple access interference, and an additive white Gaussian noise channel. The LPIC detector has been considered in the literature lately due to its low computational complexity, potential for good performance under certain operating conditions, and close connections to the decorrelating detector. In this paper, we compare the performance of the two-stage LPIC detector to the original multistage detector proposed by Varanasi and Aazhang (1990, 1991) for CDMA systems. The general M-stage LPIC detector is compared to the conventional matched filter detector to describe operating conditions where the matched filter detector outperforms the LPIC detector in terms of error probability at any stage M. Analytical results are presented that show that the LPIC detector may exhibit divergent error probability performance under certain operating conditions and may actually yield error probabilities greater than 0.5 in some cases. Asymptotic results are presented for the case where the number of LPIC stages goes to infinity. Implications of the prior results for code division multiple access (CDMA) systems with random binary spreading sequences are discussed in the “large-system” scenario. Our results are intended to analytically corroborate the simulation evidence of other authors and to provide cautionary guidelines concerning the application of LPIC detector to CDMA communication systems     

最佳线性多用户信号检测器及其近似求解

本文提出了平均误比特率最小意义下的最佳线性多用户信号检测器，并给出了求解这种最佳线性多用户信号检测器的近似方法－训练单层感知器不。     

Multiuser detection for packet-switched CDMA networks with retransmission diversity

In this paper, multiuser detection is developed with exploitation of retransmission diversity. A maximum likelihood detector (MLD) that has the same order of complexity as the MLD using only the data in one transmission is developed. It is shown that the retransmission diversity increases the minimum signal distance and, therefore, significantly improves the performance of MLD. The linear MMSE, decorrelating, and MF detectors are developed under two design approaches. In the first approach,we have considered the weighted sum of outputs of a number of linear detectors, where each is implemented for one transmission. The optimum set of weights that maximizes the signal-to-interference-and-noise ratio (SINR) is obtained. In the second approach, a linear detector jointly utilizes the statistics collected from all transmissions. When the SINR of a linear detector is the same in each transmission, the retransmission diversity is shown to increase the SINR by 10log/sub 10/J dB for a packet of J transmissions. The limiting bit error rate for these three linear detectors in large networks with random spreading sequences is obtained in closed form, which enables further network throughput evaluation.     

Linear multiuser detectors for synchronous code-divisionmultiple-access channels

Under the assumptions of symbol-synchronous transmissions and white Gaussian noise, the authors analyze the detection mechanism at the receiver, comparing different detectors by their bit error rates in the low-background-noise region and by their worst-case behavior in a near-far environment where the received energies of the users are not necessarily similar. Optimum multiuser detection achieves important performance gains over conventional single-user detection at the expense of computational complexity that grows exponentially with the number of users. It is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection. Attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations, and on the optimum linear detector. It is shown that the generalized inverse detectors exhibit the same degree of near-far resistance as the optimum multiuser detectors. The optimum linear detector is obtained     

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.     

Near optimum tree-search detection schemes for bit-synchronousmultiuser CDMA systems over Gaussian and two-path Rayleigh-fadingchannels

Simple reduced tree-search detection schemes of the breadth-first type are applied to suboptimal joint multiuser detection in bit-synchronous code-division multiple access (CDMA) systems over both Gaussian and two-path Rayleigh-fading channels. It is pointed out that in contrast to the case of the optimal multiuser detector, the choice of the receiver filter severely influences the performance of suboptimal multiuser detectors. Simulation results supported by analysis show that breadth-first tree-search algorithms using a decorrelating noise whitening receiver filter perform better than similar receivers, which solely use a matched filter (MF) for virtually all nonsingular spreading code sets studied. Most of the code sets are randomly generated. The M- and T-algorithm detectors based on decorrelating noise whitening filter (WF) outputs can achieve near optimum performance at a very low complexity compared to the optimal detector, although the proposed detectors are more complex than some known suboptimum detectors. Furthermore, the use of combining techniques is considered for a two-path Rayleigh-fading channel, and a semi-synchronous CDMA structure is proposed. It is shown that if maximum ratio combining (MRC) is employed, the decorrelating noise WF still exists. The corresponding suboptimal combining detector with a decorrelating noise WF outperforms a similar noncombining detector     

Impact of Imperfect Power Control and Channel Estimation on the Performance of Multiuser Detectors in Synchronous DS-CDMA System

Simulation performance comparison of various linear multiuser and parallel interference cancellation (PIC) detectors in the presence of imperfect power control and channel estimation is presented. Results show that imperfect power control degrades even the performance of a single-user detector. Therefore, tight power control is highly indispensable for suboptimal detectors to maintain a good performance. When power control is not perfect, interference cancellation detectors can outperform linear multiuser detectors. Among cancellation detectors, the conventional [1] and partial PIC [2] detectors are fairly sensitive to channel estimation error, while the LMS PIC [3] is quite robust in this regard.     

Finite memory-length linear multiuser detection for asynchronousCDMA communications

Decorrelating, linear, minimum mean-squared error (LMMSE), and noise-whitening multiuser detectors for code-division multiple-access systems (CDMA) are ideally infinite memory-length (referred to as IIR) detectors. To obtain practical detectors, which have low implementation complexity and are suitable for CDMA systems with time-variant system parameters (e.g., the number of users, the delays of users, and the signature waveforms), linear finite-memory-length (referred to as FIR) multiuser detectors are studied in this paper. They are obtained by truncating the IIR detectors or by finding optimal FIR detectors. The signature waveforms are not restricted to be time-invariant (periodic over symbol interval). Thus, linear multiuser detection is generalized to systems with spreading sequences longer than the symbol interval. Conditions for the stability of the truncated detectors are discussed. Stable truncated detectors are shown to be near-far resistant if the received powers are upper bounded, and if the memory length is large enough (but finite). Numerical examples demonstrate that moderate memory lengths are sufficient to obtain the performance of the IIR detectors even with a severe near-far problem     

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     

A Soft-Input Soft-Output Decorrelating Block Decision-Feedback Multiuser Detector for Turbo-Coded DS-CDMA Systems

Previously, a decorrelating decision-feedback multiuser detector for direct-sequence code-division multiple-access (DS-CDMA) systems normally produces only hard-decision outputs of users' data. In turbo-coded DS-CDMA systems, such a multiuser detector does not match well with the soft-input soft-output nature of a turbo-decoding algorithm, thereby resulting in some extent of performance loss. In this paper, a soft-input soft-output decorrelating block decision-feedback multiuser detector is proposed to perform joint multiuser detection and turbo decoding in an iterative manner. This multiuser detector partitions the received users' data into a number of blocks appropriately and then detects the users' data on a block-by-block basis, where the soft-decision outputs are generated based on the maximum a posteriori criterion and the decision outputs of a stronger block (with a higher energy) are fed back for use in making decisions of those weaker ones. Computer simulation results show that the proposed iterative multiuser detector with turbo decoding significantly improves the bit error rate performance of a DS-CDMA receiver.