Consider a Gaussian multiple-access channel shared by K users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms. The uncoded probability of error achievable by optimum multiuser detectors is investigated. It is shown that the K -user maximum-likelihood sequence detector consists of a bank of single-user matched filters followed by a Viterbi algorithm whose complexity per binary decision is O(2^{K}) . The upper bound analysis of this detector follows an approach based on the decomposition of error sequences. The issues of convergence and tightness of the bounds are examined, and it is shown that the minimum multiuser error probability is equivalent in the Iow-noise region to that of a single-user system with reduced power. These results show that the proposed multiuser detectors afford important performance gains over conventional single-user systems, in which the signal constellation carries the entire burden of complexity required to achieve a given performance level.

Minimum probability of error for asynchronous Gaussian multiple-access channels

Binary maximal-length linear feedback shift register sequences (m-sequences) have been successfully employed in communications, navigation, and related systems over the past several years. For the early applications, m-sequences were used primarily because of their excellent periodic autocorrelation properties. For many of the recent systems applications, however, the crosscorrelation properties of such sequences are at least as important as the autocorrelation properties, and the system performance depends upon the aperiodic correlation in addition to the periodic correlation. This paper presents a survey of recent results and provides several new results on the periodic and aperiodic crosscorrelation functions for pairs of m-sequences and for pairs of related (but not maximal-length) binary shift register sequences. Also included are several recent results on correlation for complex-valued sequences as well as identities relating the crosscorrelation functions to autocorrelation functions. Examples of problems in spread-spectrum communications are employed to motivate the choice of correlation parameters that are considered in the paper.

Crosscorrelation properties of pseudorandom and related sequences

We consider interference suppression for direct-sequence spread-spectrum code-division multiple-access (CDMA) systems using the minimum mean squared error (MMSE) performance criterion. The conventional matched filter receiver suffers from the near-far problem, and requires strict power control (typically involving feedback from receiver to transmitter) for acceptable performance. Multiuser detection schemes previously proposed mitigate the near-far problem, but are complex and require explicit knowledge or estimates of the interference parameters. In this paper, we present and analyze several new MMSE interference suppression schemes, which have the advantage of being near-far resistant (to varying degrees, depending on their complexity), and can be implemented adaptively when interference parameters are unknown and/or time-varying, Numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver. We conclude that MMSE detectors can alleviate the need for stringent power control. In CDMA systems, and may be a practical alternative to the matched filter receiver. >

MMSE interference suppression for direct-sequence spread-spectrum CDMA

A multiuser detection strategy for coherent demodulation in an asynchronous code-division multiple-access system is proposed and analyzed. The resulting detectors process the sufficient statistics by means of a multistage algorithm based on a scheme for annihilating successive multiple-access interference. An efficient real-time implementation of the multistage algorithm with a fixed decoding delay is obtained and shown to require a computational complexity per symbol which is linear in the number of users K. Hence, the multistage detector contrasts with the optimum demodulator, which is based on a dynamic programming algorithm, has a variable decoding delay, and has a software complexity per symbol that is exponential in K. An exact expression is obtained and used to compute the probability of error is obtained for the two-stage detector, showing that the two-stage receiver is particularly well suited for near-far situations, approaching performance of single-user communications as the interfering signals become stronger. The near-far problem is therefore alleviated. Significant performance gains over the conventional receiver are obtained even for relatively high-bandwidth-efficiency situations. >

Multistage detection in asynchronous code-division multiple-access communications

We consider an asynchronous code-division multiple-access environment in which the receiver has knowledge of the signature waveforms of all the users. Under the assumption of white Gaussian background noise, we compare detectors by their worst case bit error rate in a low background noise near-far environment where the received energies of the users are unknown to the receiver and are not necessarily similar.

Near-far resistance of multiuser detectors in asynchronous channels

Optimal phases are given for maximal length linear feedback shift-register sequences (m-sequences) of periods 31 and 63 which are to be employed as signature sequences in an asynchronous direct sequence spread-spectrum multiple access communications system. The performance measure considered is the average signal/noise ratio at the output of the correlation receiver. The data presented is applicable to various forms of direct sequence spread-spectrum modulation including binary phase-shift keying, offset quadriphase-shift keying, and minimum shift keying modulation.

Optimal phases of maximal length sequences for asynchronous spread-spectrum multiplexing

The asymptotic properties of aperiodic and related correlation parameters are investigated for random binary sequences. Performance parameters for synchronous and asynchronous multiple-access systems are comapared.

Correlation parameters of random binary sequences

Results are presented which relate the mean-squared value of the aperiodic crosscorrelation function for periodic binary sequences to their aperiodic autocorrelation function. Bounds on the mean-squared aperiodic crosscorrelation are given in terms of the mean-squared aperiodic autocorrelation.

Bounds on aperiodic cross-correlation for binary sequences

Identities are established which relate certain crosscorrelation parameters for periodic real-valued sequences to their autocorrelation functions. Applications to multiple-access communication systems and to the design of uncorrelated sequences are discussed.

M.B. Pursley

Papers

Optimal phases of maximal length sequences for asynchronous spread-spectrum multiplexing

Correlation parameters of random binary sequences

Bounds on aperiodic cross-correlation for binary sequences

New correlation identities for periodic sequences