Minimax Concave Penalty Regularized Adaptive System Identification

TL;DR

This paper introduces a recursive algorithm with a minimax concave penalty for adaptive sparse system identification, demonstrating improved mean-squared error performance over standard methods in various signal models.

Contribution

It presents a novel RLS-type algorithm with MCP regularization for sparse channel estimation, including convergence proof and steady-state error bounds.

Findings

Outperforms standard RLS in MSE on simulated channels

Achieves better sparsity recovery than L1-regularized RLS

Converges to a local optimum with proven bounds

Abstract

We develop a recursive least square (RLS) type algorithm with a minimax concave penalty (MCP) for adaptive identification of a sparse tap-weight vector that represents a communication channel. The proposed algorithm recursively yields its estimate of the tap-vector, from noisy streaming observations of a received signal, using expectation-maximization (EM) update. We prove the convergence of our algorithm to a local optimum and provide bounds for the steady state error. Using simulation studies of Rayleigh fading channel, Volterra system and multivariate time series model, we demonstrate that our algorithm outperforms, in the mean-squared error (MSE) sense, the standard RLS and the $\ell_1$-regularized RLS.