A one-shot LDD with pre-SDC/post-MRC for random CDMA overasynchronous Rayleigh channels

It is well known that conventional detectors of direct sequence-code division multiple access systems are interference-limited. Multiuser detection has been considered as a promising approach to combat this problem. Since an optimal multiuser detector is too complex to implement, several suboptimal multiuser detector techniques have been developed. The one-shot linear decorrelating detector (LDD) was proposed to reduce the computational complexity and delay required in the conventional LDD, but it still require high complexity. Another one-shot LDD with low complexity was proposed. To improve its performance, this detector uses a maximal ratio combining (MRC) at the two outputs of the left piece of the present bit and the right piece of the next bit in an one-shot window; this detector is called as a one-shot LDD with post-MRC. In spite of the aid of MRC, the performance of the one-shot LDD with post-MRC is worse than the one-shot LDD. To overcome this problem, we propose the one-shot LDD with pre-SDC/post-MRC that employs selection diversity combining (SDC) with multiple antenna elements in front of the one-shot LDD with post-MRC. In asynchronous random code division multiple access systems over fading channels, the largest signal-to-noise ratio (SNR) of SDC, near-far resistance (NFR) of the one-shot LDD, and the output SNR of MRC are random variables. We derive the probability density functions (PDFs) for these random variables and calculate the bit error rate) of the proposed detector using the obtained PDFs. In a comparison of mathematical analysis and computer simulation results, we observe good agreement     

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     

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     

Linear Differentially Coherent Multiuser Detection for Multipath Channels

By combining multipath processing, differential signal detection, and multiuser detection techniques, we develop a class of near-far resistant linear detectors for differentially coherent multipath signals. We derive and establish performance relationships among the following detectors: an optimally near-far resistant detector, a suboptimum detector which does not require knowledge of the signal coordinates, and a minimum mean square error (MMSE) detector which achieves near-optimum asymptotic efficiency. We present an adaptive multiuser detector which converges to the MMSE detector without training sequences and which requires less information than the conventional single user rake receiver.     

Low Complexity Polynomial Expansion Multiuser Detector for CDMA Systems

The polynomial expansion (PE) multiuser detector can iteratively approximate the linear decorrelating and MMSE multiuser detectors. This is a very promising approach since the complexity of the PE detector is considerably less than that of the decorrelating and MMSE detectors. The concept of the PE multiuser detector is a weighted matrix polynomial for which optimal weighting has been suggested in the literature. Unfortunately, the optimal weights apply only to a specific correlation matrix. As soon as the correlation between the users changes (and hence also the correlation matrix), a new set of optimal weights has to be calculated. The calculation of these weights is computationally very intense. In this paper, an approach is presented where the weights are predefined and apply for all matrices. Furthermore, a normalization factor is needed to ensure convergence. It will be shown how this factor has to be chosen to obtain the optimal convergence speed. For the optimal normalization factor the minimum and maximum eigenvalues are needed. A low complexity and accurate method to estimate these eigenvalues is derived which can be applied to all correlation matrices and therefore to any code division multiple access (CDMA) scenario. Hence, the matrix-dependent optimal normalization factor can easily be calculated and ensures a good bit error rate (BER) performance, even if the correlation between the users changes quickly (e.g., in time-variant channels). Furthermore, it will be shown how to enhance the PE detector such that it has a high near-far resistance. Additionally, for the first time it can be proven that the approximation error of the proposed detector diminishes exponentially with the number of iterations. Finally, simulations verify the fast convergence of the proposed PE detector and its flexible usage in a variety of scenarios.     

Analysis of an Approximate Decorrelating Detector

In this paper an approximate decorrelating detector is analyzed on the basis of a first order approximation to the inverse crosscorrelation matrix of signature waveforms. The approximation is fairly accurate for systems with low crosscorrelations and is exact in the two-user synchronous case. We present an exact as well as approximate analysis of the bit-error-rate performance of this detector on a channel that is subject to flat fading, and also specifically for the case of random signature waveforms. The detector outperforms the conventional matched filter receiver in terms of BER. The approximate decorrelator (while not being near-far resistant like the decorrelating detector) is fairly robust to imperfections in power control. Power trade-off regions are identified which characterize the significant advantage that the approximate decorrelator provides over the matched filter receiver. The reduced complexity of the approximate decorrelator and performance gains over the conventional matched filter makes it a viable alternative for implementation in practical CDMA systems, in particular in those where the signature waveforms span many symbol intervals.     

Near-far resistance of multiuser detectors in asynchronous channels

Consideration is given to an asynchronous code-division multiple-access environment in which receiver has knowledge of the signature waveforms of all the users. Under the assumption of white Gaussian background noise, the authors compare detectors by their worst case bit error rate in a near-far environment with low background noise, where the received energies of the users are unknown to the receiver and are not necessarily similar. Conventional single-user detection in a multiuser channel is not near-far resistant, and the substantially higher performance of the optimum multiuser detector requires exponential complexity in the number of users. The authors explore suboptimal demodulation schemes which exhibit a low order of complexity while not exhibiting the impairment of the conventional single-user detector. It is shown that there exists a linear detector whose bit-error-rate is independent of the energy of the interfering users. It is also shown that the near-far resistance of optimum multiuser detection can be achieved by a linear detector. The optimum linear detector for worst-case energies is found, along with existence conditions, which are always satisfied in the models of practical interest     

异步CDMA系统中的CM多用户检测器

本文将恒模（CM）算法应用于异步CDMA系统的多用户信号检测。该CM检测器只要求了解目标用户的信息，运算较简单，且由于采用了自适应方法，检测器无需估计信号的幅度。分析及仿真结果均表明，CM检测器的误码性能和抗-近效应能力均优于传统检测器，且对于用户数目的变化有很好的适应性。     

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.     

Multiuser detection of asynchronous CDMA with frequency offset

This article presents a near-far resistant detection scheme for asynchronous code-division multiple access with frequency offset. Based on a one-shot technique and Taylor expansion, a zeroth-order and a first-order one-shot linear decorrelating detector (LDD) are proposed. The zeroth-order LDD has simple architecture but suffers performance degradation for large frequency offset. The first-order one-shot LDD, with increased complexity, has very good near-far resistant property even for large frequency offset. Two versions of the first-order one-shot LDD are investigated according to different Taylor expansion approaches. The feasibility of the proposed detectors is demonstrated by computer simulations     

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     

一种简化的解相关检测器及其性能分析

基于矩阵求逆的一阶近似提出了一种简化的解相关检测器,当用户间的相关系数较小时,这种检测器可以相当准确地逼近解相关检测器,文中分析了这种检测器的误码率性能。数值结果表明该检测器的性能远优于传统的多用户检测器,具有较好的抗远近性能,与解相关检测器相比,它的复杂度大大降低,使其有可能用于实际的 Ｃ Ｄ Ｍ Ａ 通信系统中。     

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     

Analysis and Performance Evaluation of Linear Multiuser Detectors in the Downlink of DS-CDMA Systems Applying Spectral Decomposition

This paper studies the performance of linear multiuser detectors for direct-sequence code division multiple access systems at different loading levels and users' powers, using singular value decomposition (SVD) techniques in the downlink of Rayleigh flat-fading and additive white Gaussian channels. The performance of the matched filter (MF), decorrelator (zero-forcing), and minimum mean-squared error (MMSE) detectors are studied and compared. Analytical and simulation results are also presented in terms of the bit error rate. From this analysis, a simple linear multiuser detector is developed that exploits the structure of the system's spreading codes matrix from the SVD viewpoint. Also, the numerical performance of this proposed detector is compared to that of the conventional detector (MF) as a function of the signal-to-noise ratio. Finally, the performance limits are established in terms of the singular values of the spreading codes matrix. Extensive simulation results validate the analysis presented in the paper for equal or unequal users' powers.     

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.     

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.     

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.     

Average bit-error-rate performance of band-limited DS/SSMA communications

Direct-sequence spread-spectrum multiple-access (DS/SSMA) communications, strictly band-limited transmitter chip waveforms with excess bandwidth in the interval between zero and one, pseudo-random spreading sequences, an additive white Gaussian noise channel, and matched filter receivers are considered. First, a new expression for the average bit error rate (BER) is derived for systems with quaternary phase-shift keying (QPSK) spreading, the conventional matched filter receiver, a coherent detector for binary phase-shift keying (BPSK) data symbols, and chip waveforms that result in no interchip interference. The expression consists of a well known BER expression based on the standard Gaussian approximation to multiple-access interference and a few correction terms. It enables accurate BER evaluations without any numerical integration for various choices of system parameters of interest. The accuracy of the expression is guaranteed as long as the conditional Gaussian approximation to the cross-correlation coefficients between the desired user's spreading sequence and the interfering users' spreading sequences is valid. The expression well reflects the effect of filtering on the system performance. Extensions of the expression are discussed for systems with QPSK spreading and different detection schemes, systems with BPSK spreading, and systems with different transmit and receive filters. Monte Carlo simulation results are also provided to verify the accuracy.     

Performance analysis of O/sup 3/BPSK LDD for asynchronous CDMA systems in the presence of synchronization errors

A convenient signaling scheme, termed orthogonal on-off binary phase-shift keying (O/sup 3/BPSK), along with a simple one-shot linear decorrelating detector (LDD), was proposed by F.C. Zheng and S.K. Barton (see ibid., vol.47, p.969-76, 1998; Proc. IEEE PIMRC'94, p.194-8, 1994) as a technique for near-far resistant detection in asynchronous direct-sequence code-division multiple-access (DS/CDMA) systems. The temporally adjacent bits from different users in the received signals are decoupled by using on-off signaling, and the data rate is maintained with no increase in the transmission rate by adopting an orthogonal structure. The paper examines the effects of three classes of synchronization errors (time-delay errors, carrier phase errors, and carrier frequency errors) on the performance of the O/sup 3/BPSK LDD in an asynchronous CDMA near-far environment. It is shown that the performance of the O/sup 3/BPSK LDD has an advantage over that of the isolation bit insertion detector in the presence of synchronization errors. In addition, numerical results show that the O/sup 3/BPSK LDD still offers a good near-far resistant property as long as synchronization errors do not exceed some practical limit.