  This letter proposes a novel sparsity-aware adaptive filtering scheme and
algorithms based on an alternating optimization strategy with shrinkage. The
proposed scheme employs a two-stage structure that consists of an alternating
optimization of a diagonally-structured matrix that speeds up the convergence
and an adaptive filter with a shrinkage function that forces the coefficients
with small magnitudes to zero. We devise alternating optimization least-mean
square (LMS) algorithms for the proposed scheme and analyze its mean-square
error. Simulations for a system identification application show that the
proposed scheme and algorithms outperform in convergence and tracking existing
sparsity-aware algorithms.
