Performance bounds for optimum multiuser DS-CDMA systems

In this letter we estimate the bit error probability (BEP) of optimum multiuser detection for synchronous and asynchronous code division multiple access (CDMA) systems on Gaussian and fading channels. We first compute an upper bound and a lower bound on the bit error probability for a given spreading code, then average the bounds over a few thousand sets of spreading codes. These bounds are obtained from a partial distance spectrum. On Gaussian channels, the upper bound converges to the lower bound at moderate to large signal-to-noise ratios. However, on fading channels the upper bound does not converge, hence we present our results for the lower bound only. The numerical results show that: 1) the BEP of a 31-user CDMA system with binary random spreading codes of length 31 is only two to four times higher than the BEP of the single user system; 2) the number of users that can be accommodated in an asynchronous CDMA system is larger than the processing gain; and 3) optimum multiuser detection outperforms linear detection (e.g., the decorrelating detector) by about 2.8 to 5.7 dB     

Performance analysis of space-time MMSE multiuser detection for coded DS-CDMA systems in multipath fading channels

This paper investigates the use of convolutional coding in space-time minimum mean-square-error (MMSE) multiuser-based receivers over asynchronous multipath Rayleigh fading channels. We focus on the performance gain attained through error control coding when used with binary-phase-shift-keyed modulation (BPSK) and multiuser access based on direct sequence-code-division multiple access (DS-CDMA). In our analysis, we derive an approximation for the uncoded probability of bit-error in multipath fading channels. This bit-error rate (BER) approximation is shown to be very accurate when compared to the exact performance. For a convolutionally coded system, we obtain a closed form expression for the bit-error rate upper bound. This error bound is noted to be tight as the number of quantization levels increased beyond eight. Using our theoretical results, we obtain an estimate for the achieved user-capacity that accrues due to error control coding. It is found that using convolutional coding with 3-bit soft-decision decoding, a user-capacity gain as much as 300% can easily be achieved when complete fading state information plus ideal channel interleaving are assumed.     

MMSE receivers for multirate DS-CDMA systems

Minimum-mean squared error (MMSE) receivers are designed and analyzed for multiple data rate direct-sequence code-division multiple-access (DS-CDMA) systems. The inherent cyclostationarity of the DS-CDMA signal is exploited to construct receivers for asynchronous multipath channels. Multiple- and single-bandwidth access are treated for both single and multicarrier scenarios. In general, the optimal receiver is periodically time-varying. When the period of the optimal receiver is large, suboptimal receivers are proposed to achieve a lower complexity implementation; the receivers are designed as a function of the cyclic statistics of the signals. In multiple chipping rate systems, the complexity of receivers for smaller bandwidth users can also be controlled by changing their front-end filter bandwidth. The effect of front-end filter bandwidth on receiver performance and system capacity is quantified for a variable chipping rate system. Analysis and simulation show that significant performance gains are realized by the periodically time-varying MMSE receivers over their time-invariant counterparts     

Subspace multiuser detection for multicarrier DS-CDMA

A subspace-based linear minimum mean-squared error (MMSE) multiuser detection scheme is proposed for a multicarrier direct-sequence code-division multiple-access (MC-DS-CDMA) system. Typically, a MC-DS-CDMA system employs a band-limited chip waveform. The band-limited nature of the chip waveform causes problem in applying standard subspace techniques because no non noise subspace can be formed. It is shown that channel and timing information needed for the construction of the linear MMSE detector can be identified by a multiple-signal-classification-like algorithm based on a finite-length truncation approximation of the chip waveform. In practice, since perturbed versions of the subspaces assumed in the finite-length truncation approximation are actually observed, and because of the band-limited property of the chip waveform, the accuracy of the channel estimation and, hence, the performance of the MMSE detector are degraded. This effect is investigated in this paper.     

Rate-compatible convolutional codes for multirate DS-CDMA systems

New rate-compatible convolutional (RCC) codes with high constraint lengths and a wide range of code rates are presented. These new codes originate from rate 1/4 optimum distance spectrum (ODS) convolutional parent encoders with constraint lengths 7-10. Low rate encoders (rates 115 down to 1/10) are found by a nested search, and high rate encoders (rates above 1/4) are found by rate-compatible puncturing. The new codes form rate-compatible code families more powerful and flexible than those previously presented. It is shown that these codes are almost as good as the existing optimum convolutional codes of the same fates. The effects of varying the design parameters of the rate-compatible punctured convolutional (RCPC) codes, i.e., the parent encoder rate, the puncturing period, and the constraint length, are also examined. The new codes are then applied to a multicode direct-sequence code-division multiple-access (DS-CDMA) system and are shown to provide good performance and rate-matching capabilities. The results, which are evaluated in terms of the efficiency for Gaussian and Rayleigh fading channels, show that the system efficiency increases with decreasing code rate     

ADAPTIVE STEP－SIZE CONSTANT MODULUS ALGORITHM FOR BLIND MULTIUSER DETECTION IN DS－CDMA SYSTEMS

Blind Adaptive Step-size Constant Modulus Algorithm (AS-CMA) for multiuser detection in DS-CDMA systems is presented.It combines the CMA and the concept of variable step-size,uses a second LMS algorithm for the step size.It adjusts the step-size according to the minimum output-energy principle within a specified range,thus overcomes the problems of bad effect of fixed step-size LMS algorithm.Compared with Adaptive Step-size LMS (AS-LMS) algorithm,through simulations,this algorithm can adapt the changes of the environment,suppress multiple access interference in the dynamic environment and the stability of Signal to Interference Ratio (SIR) is superior to that of AS-LMS.     

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.     

Iterative cyclic subspace tracking for blind adaptive multiuser detection in multirate CDMA systems

In this paper, the problem of subspace-based blind adaptive multiuser detection in multirate direct-sequence code-division multiple-access (DS-CDMA) systems adopting short (periodic) spreading codes is considered. The solution that we propose is based on the well-known formulation of the linear minimum mean-squared error and decorrelating detectors in terms of signal subspace parameters. Since in a multirate scenario the correlation properties of the observable and, hence, the signal subspace parameters are periodically time-varying, classical subspace tracking algorithms, which assume that the subspace to be tracked is time-invariant or slowly time-varying, are shown to be not useful in this situation. A new recursive cyclic subspace tracking algorithm is thus developed. This procedure, which is based on a generalization of the PASTd algorithm, is able to capture the periodical variations of the signal subspace, and thus enables subspace-based blind adaptive multiuser detection in multirate CDMA systems. The proposed algorithm has a smaller computational complexity than the recently developed cyclic recursive-least-squares procedure, and, as numerical results confirm, is capable of providing very satisfactory performance.     

Single-user sparse channel acquisition in multiuser DS-CDMA systems

Single-user channel estimation in multiuser DS-CDMA systems for the case of sparse channels with large delay spreads is addressed. In addition, practical pulse shapes are considered. In sparse channels, the efficient way to estimate the parameters is to estimate the continuous delays of each path, instead of using the typical discrete tapped delay-line model. Due to the facts that the desired delays are not drawn from a simple finite set and that band-limited pulse shapes are employed, the resulting methods require numerical optimization techniques. To facilitate estimation, it is proposed to optimize the spreading code employed during the training, or estimation, phase. The optimal single-path spreading code is derived and extended for estimation in the multipath scenario. Both single-path and multipath channel estimation are considered. The proposed algorithms are evaluated through simulation and via the determination of the Cramer-Rao lower bound on the estimation variance. Analytical approximations of key performance measures are also derived and are seen to be tight for a variety of scenarios.     

Preselection-based iterative multiuser detector for DS-CDMA systems

A low-complexity iterative multiuser detector is presented that uses adaptive preselection to minimise complexity while maintaining system performance very similar to that achieved when using the optimal maximum likelihood receiver.     

A dual-mode multiuser detector for DS-CDMA systems

We introduce a dual-mode multiuser detector that dynamically switches its detection mode between matched-filter and decorrelator operations based on the channel characteristics. This detector significantly reduces the overall computational requirement while maintaining similar performance as that of the decorrelator. The switching mechanism of our dual-mode detector is designed by exploiting the performance-complexity tradeoff between the decorrelator and the matched-filter. Extensions of this idea to other types of multiuser detectors are also proposed     

Modified SMC method of blind multiuser detection for DS-CDMA systems over fading channels

This paper presents the application of sequential Monte Carlo (SMC) methodology for blind detection in wireless direct sequence code division multiple access (DS-CDMA) systems over fading channels. It is known that the conventional SMC method requires a high-computational complexity that grows exponentially with the number of active users. This paper proposes a solution to this problem by employing Cholesky factorization to decompose the observed data into separate components for each user and then the parameters of each user are estimated with the SMC inference method under the decision feedback framework. Based on these concepts, an efficient blind decision feedback SMC (DF-SMC) receiver is developed for differentially encoded DS-CDMA systems. Simulation results demonstrate the promising performance of the proposed receiver for both flat fading and frequency-selective fading channels.     

A new power control function for multirate DS-CDMA systems

This paper proposes a closed-form power control function for the reverse link of a multirate single chip-rate variable processing gain DS-CDMA system in a mobile radio environment that assumes a Rayleigh fading channel with log-normal shadowing and path loss. A closed-form open-loop power control function based on a newly defined traffic exponent is proposed, and nonlinear programming is used to perform the optimization. In addition, a user model that allows users to dynamically switch traffic rates for different connection applications is implemented. Results obtained using random chip sequences demonstrate improvement in the system capacity with the new power control function compared to the conventional power control function. Furthermore, the proposed function also simplifies the power control processing     

Blind space-time multiuser channel estimation in time-varying DS-CDMA systems

A multistep linear prediction (MSLP) approach is presented for blind channel estimation for short-code direct sequence code division multiple access signals in time-varying multipath channels using a receiver antenna array. The time-varying channel is assumed to be described by a complex exponential basis expansion model. First, a recently proposed MSLP approach to blind channel estimation for time-varying single-input multiple-output (SIMO) systems is extended to time-varying multiple-input multiple-output (MIMO) systems to define a "signal" subspace. Second, the knowledge of the spreading code of a desired user is exploited in conjunction with the signal subspace to estimate the time-varying channel of the desired user up to an unknown time-invariant scale factor. Equalization/detection for the desired user can be then carried out if the information sequence is differentially encoded/decoded. Sufficient conditions for channel identifiability are investigated. Three illustrative simulation examples are provided.     

An equicorrelation-based multiuser communication scheme for DS-CDMA systems

An equicorrelation-based multiuser communication (ECBMC) scheme for direct-sequence code-division multiple-access (DS-CDMA) systems is presented. The ECBMC receiver has low computational complexity that is comparable to that of the conventional detector. By using the equality of cross correlations, the ECBMC scheme can completely eliminate multiple-access interference (MAI) in a synchronous single-path DS-CDMA network. The system performance is independent of the number of active users. The scheme is extended to include the effects of multipath fading. It is able to suppress a major portion of the MAI. This proposed ECBMC scheme is quite attractive for an MAI-dominant environment.     

Recursive algorithms for multiuser detection over DS-CDMA channels

We focus on the synthesis and the analysis of recursive receivers for direct-sequence code-division multiple-access systems aimed at achieving satisfactory performance at the price of a moderate computational complexity. At the analysis stage, some interesting properties shared by the proposed procedures are proven. Finally, the performance assessment shows that the new schemes are superior to the linear detectors, and some of them achieve a bit-error rate close to that of the optimum receiver.     

Suboptimum multiuser receivers for convolutionally codedasynchronous DS-CDMA systems

Motivated by the high complexity of the optimal sequence estimator for convolutionally coded asynchronous code-division multiple-access (CDMA) systems, developed by Giallorenzi and Wilson (see ibid., vol.44, no.8, p.997, 1996), and the potentially poor performance of the conventional receiver due to multiuser interference and the near-far problem, we examine relatively simple multiuser receivers which perform nearly as well as the optimal receiver. The multiuser receivers discussed are of two types. The first set of approaches are partitioned approaches that treat the multiuser interference equalization problem and the decoding problem separately. The second set of approaches are integrated approaches that perform both the equalization and decoding operations together. We study linear, decision feedback, and trellis/tree-based approaches in each category. The asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying (BPSK) receiver (termed asymptotic multiuser coding gain, or AMCG) is used as a performance criterion throughout. Also, computer simulations are used whenever the computation of the AMCG is not feasible. It is shown that a number of the approaches which are introduced achieve a high performance level with a moderate complexity     

Low-complexity blind multiuser detection of DS-CDMA signal in dispersive channels

The problem of blind multiuser detection in dispersive channels of Code-Division Multiple-Access (CDMA) in the presence of both Multiple-Access Interference (MAI) and In-terSymbol Interference (ISI) is considered. In practice, it is showed that by incorporating the desired user's signature waveform and the auxiliary vector, the information of the user can be identified using the suboptimal subspace method. The major contribution of this paper is to propose a minimum-mean-square-error detector with the suboptimal subspace-based blind technique for joint suppression of MAI and ISI in the dispersive CDMA channels.     

MMSE multiuser detection for array multicarrier DS-CDMA in fading channels

Reception of asynchronous, multicarrier direct-sequence-code division multiple access (DS-CDMA) in time-varying, multipath radio channels with use of a receiving antenna array is investigated. Interference reducing minimum mean squared error (MMSE) receivers are discussed, and by considering the time-variation of the channel, a modified structure is derived which is efficient for channels experiencing small-scale fading. A blind implementation of this receiver is then proposed. Subspace concepts are applied to formulate a tracking, composite channel vector estimator which operates effectively in fading situations, even when high levels of interference are present. Both the modified MMSE weight matrix and diversity combining weights are generated from these channel estimates. Simulations of the proposed receiver show it to have superior performance over a standard MMSE receiver which is periodically re-evaluated to permit it to follow the channel variations due to small-scale fading. Furthermore, a hybrid MMSE receiver is proposed which applies different processing methods depending on each transmitters mobility, resulting in improved performance.     

Space-time blind multiuser detection for multirate DS/CDMA signals

Multiuser detection for multirate direct-sequence code-division multiple access (DS/CDMA) has been an active area of research. For example, nonblind low-rate (LR) and high-rate (HR) decorrelators have been proposed and analyzed in the literature for synchronous dual-rate systems with single receive antenna. Inspired by the subspace-based space-time (ST) blind linear detectors for synchronous single-rate systems, this paper extends the existing results and proposes the subspace-based ST-LR and ST-HR blind linear detectors, i.e., blind decorrelators and blind minimum mean-squared error (mmse) detectors, for synchronous dual-rate DS/CDMA. It is shown that: 1) ST-LR blind linear detectors can support no less users than ST-HR blind linear detectors as long as the desired spatial signature is identifiable (assuming that all the other system parameters are the same) and 2) the bit-error rate performance of ST-LR blind decorrelator is not inferior to that of its HR counterpart. The above conclusions are generalized to synchronous multirate systems. The extension to asynchronous systems is also described. Finally, the two-stage ST dual-rate blind detectors, which combine the adaptive purely temporal dual-rate blind mmse detectors with the nonadaptive beamformer, are presented.