Abstract
In this paper, we propose a general framework that transforms the problems of designing sparse finite-impulse response channel-shortening equalizers and target impulse response filters for multiple antenna systems into the problems of sparsest-approximation of a vector in different dictionaries. Additionally, we compare several choices of the sparsifying dictionaries in terms of the worst-case coherence metric, which determines their sparsifying effectiveness. Furthermore, a reduced complexity design approach is proposed, which is realized by exploiting the asymptotic equivalence of Toeplitz and circulant matrices. Finally, the significance of our proposed approach is demonstrated through numerical experiments.