  In this paper, we propose a general framework that transforms the problems of
designing sparse finite-impulseresponse linear equalizers and non-linear
decision-feedback equalizers, for multiple antenna systems, into the problem of
sparsestapproximation of a vector in different dictionaries. In addition, we
investigate several choices of the sparsifying dictionaries under this
framework. Furthermore, the worst-case coherences of these dictionaries, which
determine their sparsifying effectiveness, are analytically and/or numerically
evaluated. Moreover, we show how to reduce the computational complexity of the
designed sparse equalizer filters by exploiting the asymptotic equivalence of
Toeplitz and circulant matrices. Finally, the superiority of our proposed
framework over conventional methods is demonstrated through numerical
experiments.
