Multiuser Detection by MAP Estimation with Sum-of-Absolute-Values Relaxation

TL;DR

This paper introduces a convex optimization approach using SOAV relaxation for multiuser detection in M2M communications, effectively handling interference with prior discrete signal information.

Contribution

It proposes a novel MAP estimation relaxation to SOAV optimization, enabling efficient detection in star-topology M2M systems with discrete signals.

Findings

Outperforms LMMSE and LASSO in simulations

Efficient solution via proximal splitting algorithm

Closed-form proximity operator provided

Abstract

In this article, we consider multiuser detection that copes with multiple access interference caused in star-topology machine-to-machine (M2M) communications. We assume that the transmitted signals are discrete-valued (e.g. binary signals taking values of $\pm 1$), which is taken into account as prior information in detection. We formulate the detection problem as the maximum a posteriori (MAP) estimation, which is relaxed to a convex optimization called the sum-of-absolute-values (SOAV) optimization. The SOAV optimization can be efficiently solved by a proximal splitting algorithm, for which we give the proximity operator in a closed form. Numerical simulations are shown to illustrate the effectiveness of the proposed approach compared with the linear minimum mean-square-error (LMMSE) and the least absolute shrinkage and selection operator (LASSO) methods.