EM-Based p-norm-like Constraint RLS Algorithm with Adaptive Regularization for Sparse System Identification

Abstract

In this paper, the recursive least squares (RLS) algorithm is considered in the sparse system identification setting. The cost function of RLS algorithm is regularized by a p-norm-like ($0\le p\le 1$) constraint of the estimated system parameters. To minimize the regularized cost function, we transform it into a penalized maximum likelihood (ML) problem that is solved by the expectation-maximization (EM) algorithm, and derive the tap-weight update through a thresholding operator whose sparsity also permits a low-complexity implementation. We further propose an error-driven adaptive regularization scheme operating on two timescales: a fast gate driven by the normalized excess a-priori error relaxes the penalty toward a lower bound, while a slow effective-support tracker sets its stationary target. Numerical simulations demonstrate the superiority of the new algorithm over the state-of-the-art sparse RLS algorithms, as well as conventional sparse RLS algorithm.

arXiv comment11 pages, 4 figures. Revised version. Submitted to IEEE ICASSP 2027