Multiuser decision-feedback receivers for asynchronous CDMA systemsover a mismatched flat Rayleigh fading channel

In this paper, the design of decision-feedback multiuser (DFM) receivers for asynchronous code-division multiple access (CDMA) systems over a mismatched flat Rayleigh fading channel is studied, and tight upper and lower bounds on the pair-wise symbol-error probability, which has been averaged over the channel fading, time delays, and phase angles, are derived for some of the DFM detection schemes. The performance bounds, which are computed by efficient analytic techniques, can serve as reliable references for CDMA system design. It is shown that the proposed system, which takes into account the effect of mismatched fading on the system design, has some gain over the system where the estimation of fading is assumed to be exact     

Tentative chip decision-feedback equalizer for multicode wideband CDMA

We investigate a chip-level minimum mean-square-error (MMSE) decision-feedback equalizer (DFE) for the downlink receiver of multicode wideband code-division multiple-access systems over frequency-selective channels. First, the MMSE per symbol achievable by an optimal DFE is derived, assuming that all interchip interference (ICI) of the desired user can be eliminated. The MMSE of DFE is always less than or at most equal to that of linear equalizers (LE). When all the active codes belong to the desired user, the ideal DFE is able to eliminate multicode interference (MCI) and approach the performance of the single-code case at high signal-to-noise ratio (SNR) range. Second, we apply the hypothesis-feedback equalizer or tentative-chip (TC)-DFE in the multicode scenario. TC-DFE outperforms the chip-level LE, and the DFE that only feeds back the symbols already decided. The performance gain increases with SNR, but decreases with the number of active codes owned by the other users. When all the active codes are assigned to the desired user, TC-DFE asymptotically eliminates MCI and achieves single-user (or code) performance at high SNR, similarly, to the ideal DFE. The asymptotic performance of the DFE is confirmed through bit error rate simulation over various channels.     

Optimal phases for a family of quadriphase CDMA sequences

Signature sequences with good even even and odd (or polyphase) correlations are crucial for asynchronous code-division multiple access (CDMA). When the data sequence is random, the even and odd (or polyphase) correlations are equally important. However, for most known signature sequences, only their even correlations were analyzed. It appears that determining the odd (or the polyphase) correlations is generally a very hard problem since the odd (or the polyphase) correlations depend on the phases of the signature sequences. Sole (1989), Boztas, Hammons, and Kumar (1992) found a family of quadriphase sequences that are asymptotically optimal. These sequences gain a factor √2 in terms of their maximum periodic even correlations when compared with the best possible binary phase-shift keying (BPSK) sequences. We find the optimal phases of these sequences. The optimality is in the sense that at these phases, the mean square values of the even, odd, and the polyphase correlations are minimal, and achieve the Welch (1974) bound-equality simultaneously. Furthermore, we show that at these phases, the average user interference of these sequences is always smaller than that of the ideal random signature sequences. Comprehensive analytical and numerical results show that good phase sequences can offer a nonnegligible amount of gain over bad phase sequences at modest and high signal-to-noise ratios     

Interference suppression for space-time coded CDMA via decision-feedback equalization

A single-user receiver structure is proposed for space-time coded code-division multiple-access (CDMA) downlink in a multiuser frequency-selective channel. This structure is a two-dimensional (2-D) decision-feedback equalizer (2D-DFE) whose filters are optimized based on the MMSE criterion to mitigate noise, intersymbol interference (ISI), and multiuser interference (MUI) with a moderate complexity. By modeling the spreading codes of the interfering users as random sequences, system performance was evaluated using the Gaussian approximation. Two models for the desired user's spreading sequence have been considered and compared. Our numerical results show that in both cases the 2D-DFE exhibits significant performance improvement over the standard space-time coded RAKE, especially in interference-limited conditions. It is also observed that the gain obtained by using DFE in a MISO channel is less that in a SISO channel and this problem can be solved by providing diversity at the receiver.     

Mitigating error propagation in decision-feedback equalization for multiuser CDMA

This letter presents a robust decision-feedback equalization design that mitigates the error-propagation problem for multiuser direct-sequence code-division multiple-access systems under multipath fading. Explicit constraints for signal energy preservation are imposed on the filter weight vector to monitor and maintain the quality of the hard decisions in the nonlinear feedback loop. Such a measure protects the desired signal power against the detrimental effect of erroneous past decisions, thus providing the leverage to curb error propagation.     

User capacity of asynchronous CDMA systems with matched filter receivers and optimum signature sequences

For a symbol-asynchronous (but chip-synchronous) single-cell code-division multiple-access (CDMA) system, we define a system-wide quantity called the total squared asynchronous correlation (TSAC) which, for arbitrary signature sets, depends on the users' delay profile. We develop a lower bound for TSAC that is independent of the users' delays. We show that if the signature set achieves this TSAC lower bound, then the user capacity of the asynchronous CDMA system using matched filters becomes the same as that of a single-cell synchronous CDMA system; in this case, there is no loss in user capacity due to asynchronism. We present iterative signature adaptation algorithms, which, when executed sequentially by the users, appear to converge to these optimum signature sequences; however, the existence, for all user delay profiles, of signature sequences achieving this lower bound remains a significant open problem.     

随机序列直扩Rake系统在Nakagami信道下的性能

本文分析了用不同波形的二进制随机序列作扩频码的直扩系统在Nakagami下的性能，通过高斯近似，得到了系统的误比频率，最后给出了数值结果。     

Adaptive techniques for multiuser CDMA receivers

A number of CDMA receivers have been proposed that cover the whole spectrum of performance/complexity from the simple matched filter to the optimal Viterbi (1995) processor. Adaptive solutions, in particular, have the potential of providing the anticipated multiuser detection (MD) performance gains with a complexity that would be manageable for third generation systems. Our goal, in this article, is to provide an overview of previous work in MD with an emphasis on adaptive methods. We start with (suboptimal) linear receivers and discuss the data-aided MMSE receiver. Blind (nondata-aided) implementations are also reviewed together with techniques that can mitigate possible multipath effects and channel dispersion. In anticipation of those developments, appropriate discrete-time (chip rate) CDMA models are reviewed, which incorporate asynchronism and channel dispersion. For systems with large spreading factors, the convergence and tracking properties of conventional adaptive filters may be inadequate due to the large number of coefficients which must be estimated. In this context, reduced rank adaptive filtering is discussed. In this approach, the number of parameters is reduced by restricting the receiver tap vector to belong to a carefully chosen subspace. In this way the number of coefficients to be estimated is significantly reduced with minimal performance loss     

An information-theoretic framework for deriving canonical decision-feedback receivers in Gaussian channels

A framework is presented that allows a number of known results relating feedback equalization, linear prediction, and mutual information to be easily understood. A lossless, additive decomposition of mutual information in a general class of Gaussian channels is introduced and shown to produce an information-preserving canonical decision-feedback receiver. The approach is applied to intersymbol interference (ISI) channels to derive the well-known minimum mean-square error (MMSE) decision-feedback equalizer (DFE). When applied to the synchronous code-division multiple-access (CDMA) channel, the result is the MMSE (or signal-to-interference ratio (SIR) maximizing) decision-feedback detector, which is shown to achieve the channel sum-capacity at the vertices of the capacity region. Finally, in the case of the asynchronous CDMA channel we are able to give new connections between information theory, decision-feedback receivers, and structured factorizations of multivariate spectra.     

Optimal resource allocation for pilot symbol aided multiuser receivers in Rayleigh faded CDMA channels

We consider a synchronous code-division multiple-access system where each user undergoes independent frequency-flat Rayleigh fading, and where pilot symbols are periodically inserted into the data stream of each user in order to assist in the coherent demodulation of the data symbols. The motivating question for this work is: for any given set of system parameters, how often should we insert pilot symbols? Along the way to answering this question, we: (1) derive and analyze the performance of the linear minimum mean-squared-error channel estimator and (2) study the performance of a linear minimum mean-squared-error data estimator which is coupled to the channel estimator. We are able to obtain a very compact expression for the average signal-to-interference ratio in terms of the key system parameters: pilot insertion period, channel fading rate, signal-to-noise ratio, and the ratio of the number of users to the spreading gain. The average signal-to-interference ratio is numerically optimized and results are presented to illustrate the optimal rate of inserting pilot symbols for a range of system parameters.     

Multiuser receivers for randomly spread signals: fundamental limitswith and without decision-feedback

Synchronous code-division multiple-access (CDMA) communication systems with randomly chosen spreading sequences and capacity-achieving forward error correction coding are analyzed in terms of spectral efficiency. Emphasis is on the penalties paid by applying single-user coding in conjunction with suboptimal multiuser receivers as opposed to optimal joint decoding which involves complexity that is exponential in the number of users times the code word length. The conventional, the decorrelating, and the (re-encoded) decorrelating decision-feedback detectors are analyzed in the nonasymptotic case for spherical random sequences. The re-encoded minimum mean-squared error (MMSE) decision-feedback receiver achieving the same performance as joint multiuser decoding for equal power users is shown to be suboptimal in the case of equal rates     

Optimal sequences for CDMA under colored noise: a Schur-saddlefunction property

We consider direct sequence code division multiple access (DS-CDMA), modeling interference from users communicating with neighboring base stations by additive colored noise. We consider two types of receiver structures: first we consider the information-theoretically optimal receiver and use the sum capacity of the channel as our performance measure. Second, we consider the linear minimum mean square error (LMMSE) receiver and use the signal-to-interference ratio (SIR) of the estimate of the symbol transmitted as our performance measure. Our main result is a constructive characterization of the possible performance in both these scenarios. A central contribution of this characterization is the derivation of a qualitative feature of the optimal performance measure in both the scenarios studied. We show that the sum capacity is a saddle function: it is convex in the additive noise covariances and concave in the user received powers. In the linear receiver case, we show that the mini average power required to meet a set of target performance requirements of the users is a saddle function: it is convex in the additive noise covariances and concave in the set of performance requirements     

Optimal sequences and sum capacity of synchronous CDMA systems

The sum capacity of a multiuser synchronous CDMA system is completely characterized in the general case of asymmetric user power constraints-this solves the open problem posed by Rupf and Massey (see ibid., vol.40, p.1261-6, 1994) which had solved the equal power constraint case. We identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them     

Blind startup of MMSE receivers for CDMA systems

This paper presents a novel technique for blindly starting up a minimum-mean-squared-error (MMSE) receiver for a user newly entering a code-division multiple-access (CDMA) system. It is assumed that only one user at a time is admitted into the system and that data before and after the onset of the new transmission are available. The technique is based on the generalized eigendecomposition of the two corresponding autocorrelation matrices (before and after the new user is admitted). In general, the two autocorrelation matrices differ by a low-rank matrix contributed by the autocorrelation of the new user signal. This fact yields the useful property that the generalized eigenvectors corresponding to the minimum eigenvalue span the noise subspace of the low-rank signal term. Exploiting this subspace relation, the signature of the new user can be identified. If, in particular, the difference between the two autocorrelation matrices is exactly a rank-one matrix, then there is only one maximum eigenvalue, and the corresponding eigenvector coincides with the MMSE receiver corresponding to the rank-one signal term. These properties are also applicable to long-code CDMA systems to provide an optimal multipath combining method     

Blind adaptive algorithms for minimum variance CDMA receivers

Constrained optimization methods have received considerable attention as a means to derive blind multiuser receivers with low complexity. The receiver's output variance is minimized subject to appropriate constraints which depend on the multipath structure of the signal of interest. When multipath is present, the constraint equations can be written in parametric form, and the constraint parameters jointly optimized with the linear receiver's parameters. We develop adaptive solutions for this joint, constrained optimization problem. Both stochastic gradient and recursive least-square-type algorithms are developed. The performance of the proposed methods is compared with other blind and trained methods and turns out to be close to the trained minimum mean-square-error receiver     

User capacity for synchronous multirate CDMA systems with linear MMSE receivers

The performance of linear minimum mean-square error (MMSE) multiuser receivers in a dual-rate synchronous direct-sequence code-division multiple-access (DS-CDMA) system is investigated using the random spreading sequence analysis. Multicode (MC) systems and different variants of variable spreading length (VSL) systems are studied. User capacity regions are obtained for these systems.     

Multisampling decision-feedback linear prediction receivers for differential space-time modulation over Rayleigh fast-fading channels

Novel decision-feedback (DF) linear prediction (LP) receivers, which process multiple samples per symbol interval in conjunction with optimal sample combining, are proposed for differential space-time modulation (DSTM) over Rayleigh fast-fading channels. Performance analysis demonstrates that multisampling DF-LP receivers outperform their symbol-rate sampling counterpart in fast fading substantially. In addition, an asymptotically tight upper bound on the pairwise error probability is derived. In view of this bound, the design criterion of DSTM for fast fading is the same as that for block-wise static fading. To avoid the estimation of the second-order statistics of the channel, a polynomial-model-based DF-LP receiver is proposed. It can approach the performance of the optimum DF-LP receiver at high signal-to noise ratios, provided fading is moderate.     

Robust constrained linear receivers for CDMA wireless systems

For code-division multiple access (CDMA) communication systems, many constrained linear receivers have been developed to suppress multiple access interference. The linearly constrained formulations are generally sensitive to multipath fading and other types of signal mismatch. We develop robust linear receivers by exploring appropriate constraints. Multiple linear constraints are exploited to preserve the output energy that is scattered in multipath channels. In addition, a quadratic inequality constraint on the weight vector norm is used to improve robustness with respect to imprecise signal modeling. These constraints can be applied to the minimum output energy (MOE) detector to mitigate the signal mismatch problem and to the decision directed minimum mean square error (MMSE) detector to prevent error propagation and eliminate the need for training sequences at startup. Adaptive implementations for the proposed detectors are presented using recursive least square (RLS) updating in both the direct form and the partitioned linear interface canceller (PLIC) structure. Simulations are performed in a multipath propagation environment to illustrate the performance of the proposed detectors     

Optimal sequences and sum capacity of symbol asynchronous CDMA systems

The optimal signature sequences that maximize the sum capacity of a direct sequence code-division multiple-access (CDMA) system are characterized in the general case of symbol delay profile and user power constraints. It is shown that the optimal sum capacity of the symbol asynchronous system equals that of the symbol synchronous system with the same user power constraints. With the optimal signature sequence set, the maximum sum capacity is achieved with white Gaussian input signals. The existence of the optimal signature sequence set is proved by the proposal of an explicit construction method for arbitrary user delay profiles and power constraints.     

Multiuser receivers for CDMA systems in Rayleigh fading channels

Multiuser demodulation in relatively fast fading channels is analyzed. The optimal maximum likelihood sequence detection (MLSD) receiver is derived and a general suboptimal receiver to approximate the MLSD is proposed. The performance of the parallel interference cancellation (PIC) and decorrelating receivers is compared. The PIC receiver is demonstrated to achieve better performance in known channels than the decorrelating receiver, but it is observed to be more sensitive to the channel coefficient estimation errors than the decorrelator. At high channel loads the PIC receiver suffers from bit error rate (BER) saturation, whereas the decorrelating receiver does not. The performance of data-aided (DA) and decision-directed (DD) multiuser channel estimation is also compared. DA channel estimation is shown to be more robust than DD channel estimation, which may suffer from BER saturation caused by hangups at high signal-to-noise ratios (SNRs). The impact of channel estimation filter impulse response on the BER is studied by comparing optimal and suboptimal channel estimation filters. The implementation complexity of the decorrelating and PIC receivers is compared in terms of required floating point operations and clock cycles in a practical communication scenario. It is observed that the PIC receiver is only moderately more complex to implement than the conventional matched filter bank receiver, whereas the decorrelating receiver is significantly more complex