Belief Propagation Based Multi--User Detection

TL;DR

This paper demonstrates that belief propagation can be effectively used for multi-user detection in spread spectrum systems, providing an optimal detection method with proven convergence and accurate symbol estimation.

Contribution

It introduces belief propagation as an optimal detection algorithm for multi-user systems and rederives the Tse-Hanly formula without random matrix theory.

Findings

BP converges and estimates the correct conditional expectation.

BP achieves minimum mean square error detection.

Re-derivation of Tse-Hanly formula without random matrix theory.

Abstract

We apply belief propagation (BP) to multi--user detection in a spread spectrum system, under the assumption of Gaussian symbols. We prove that BP is both convergent and allows to estimate the correct conditional expectation of the input symbols. It is therefore an optimal --minimum mean square error-- detection algorithm. This suggests the possibility of designing BP detection algorithms for more general systems. As a byproduct we rederive the Tse-Hanly formula for minimum mean square error without any recourse to random matrix theory.