Communications, Information and Network Security pp 229-277 | Cite as

# Multiuser Detection and Statistical Mechanics

## Abstract

A framework for analyzing multiuser detectors in the context of statistical mechanics is presented. A multiuser detector is shown to be equivalent to a conditional mean estimator which finds the mean value of the stochastic output of a so-called Bayes retrochannel. The Bayes retrochannel is equivalent to a spin glass in the sense that the distribution of its stochastic output conditioned on the received signal is exactly the distribution of the spin glass at thermal equilibrium. In the large-system limit, the performance of the multiuser detector finds its counterpart as a certain macroscopic property of the spin glass, which can be solved using powerful tools developed in statistical mechanics. In particular, the large-system uncoded bit-error-rate of the matched filter, the MMSE detector, the decorrelator and the optimal detectors is solved, as well as the spectral efficiency of the Gaussian CDMA channel. A universal interpretation of multiuser detection relates the multiuser efficiency to the mean-square error of the conditional mean estimator output in the many-user limit.

## Keywords

Statistical Mechanic Spin Glass Spectral Efficiency Network Security Matched Filter## Preview

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