Complexity of linear finite-impulse-response (FIR)
equalizers is proportional to the square of the number of nonzero
taps in the filter. This makes equalization of channels with long
impulse responses using either zero-forcing or minimum mean
square error (MMSE) filters computationally expensive. Sparse
equalization is a widely-used technique to solve this problem. In
this paper, a general framework is provided that transforms the
problem of sparse linear equalizers (LEs) design into the problem
of sparsest-approximation of a vector in different dictionaries. In
addition, some possible choices of sparsifying dictionaries in this
framework are discussed. Furthermore, the worst-case coherence
of some of these dictionaries, which determines their sparsifying
strength, are analytically and/or numerically evaluated. Finally,
the usefulness of the proposed framework for the design of sparse
FIR LEs is validated through numerical experiments.