Recursive Least Squares With Minimax Concave Penalty Regularization for Adaptive System Identification

We develop a recursive least squares (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 to a local optimum of the static least squares version of our algorithm and provide bounds for the estimation error. We study the performance of the recursive version numerically. Using simulation studies of Rayleigh fading channel, Volterra system and multivariate time series model, we demonstrate that our recursive algorithm outperforms, in the mean-squared error (MSE) sense, the standard RLS and the
$\ell _{1}$
-regularized RLS.