Design and Analysis of Sparsifying Dictionaries for FIR MIMO Equalizers

In this paper, we propose a general framework that transforms the problems of designing sparse finite-impulse-response linear equalizers and nonlinear decision-feedback equalizers, for multiple antenna systems, into the problem of sparsest approximation 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.