  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 ($0 \leq p \leq 1$) constraint of the estimated
system parameters. In order to minimize the regularized cost function, we
transform it into a penalized maximum likelihood (ML) problem, which is solved
by the expectation-maximization (EM) algorithm. With the introduction of a
thresholding operator, the update equation of the tap-weight vector is derived.
We also exploit the underlying sparsity to implement the proposed algorithm in
a low computational complexity fashion. Numerical simulations demonstrate the
superiority of the new algorithm over conventional sparse RLS algorithms, as
well as regular RLS algorithm.
