  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.
