A Discrete-Valued Signal Estimation by Nonconvex Enhancement of SOAV with cLiGME Model

In this paper, for the discrete-valued signal estimation, we propose a regularized least squares model but with a nonconvex enhancement of the so-called SOAV convex regularizer. To design more contrastive regularizers whose minima correspond to desired discrete values, we propose a class of nonconvex functions with Generalized Moreau Enhancement (GME) of the weighted ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-norm. Promisingly, by tuning properly the design parameters of the proposed GME regularizers, (i) we can make the nonconvexly-regularized least squares model convex; and (ii) we can use an iterative algorithm for finding a global minimizer of the proposed model. We also propose a pair of simple technical improvements, of the proposed algorithm, called respectively a generalized superiorization and an iterative reweighting. Numerical experiments demonstrate the effectiveness of the proposed model and algorithms in a scenario of MIMO signal detection.