Randomly Spread CDMA: Asymptotics via Statistical Physics

TL;DR

This paper analyzes the asymptotic behavior of randomly spread CDMA systems using statistical physics methods, revealing how multiuser detection can be decoupled into equivalent single-user Gaussian channels with quantifiable degradation.

Contribution

It introduces a replica-based analytical framework for large-system CDMA, deriving fixed-point equations for multiuser efficiency applicable to various detectors and MIMO channels.

Findings

Detection outputs converge to a deterministic function of Gaussian variables.

Multiuser channels can be decoupled into single-user Gaussian channels.

Explicit formulas for error rates and mutual information are derived.

Abstract

This paper studies randomly spread code-division multiple access (CDMA) and multiuser detection in the large-system limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before single-user decoding. The generic detector can be particularized to the matched filter, decorrelator, linear MMSE detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically non-Gaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a "hidden" Gaussian statistic independent of the interferers. Thus the multiuser channel can be decoupled: Each user experiences an equivalent single-user Gaussian channel, whose signal-to-noise ratio suffers a degradation due to the multiple-access interference. The uncoded error performance (e.g., symbol-error-rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixed-point equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to MIMO channels such as in multiantenna systems.