Design of Sparse Filters for Channel Shortening

Channel shortening equalizers are used in acoustics to reduce reverberation, in error control decoding to reduce complexity, and in communication receivers to reduce inter-symbol interference. The cascade of a channel and channel shortening equalizer ideally produces an overall impulse response that has most of its energy compacted into fewer adjacent samples. Once designed, channel shortening equalizers filter the received signal on a per-sample basis and need to be adapted or re-designed if the channel impulse response changes significantly. In this paper, we evaluate sparse filters as channel shortening equalizers. Unlike conventional dense filters, sparse filters have a small number of non-contiguous non-zero coefficients. Our contributions include (1) proposing optimal and sub-optimal low complexity algorithms for sparse shortening filter design, and (2) evaluating impulse response energy compaction vs. design and implementation stage computational complexity tradeoffs for the proposed algorithms. We apply the proposed equalizer design procedures to (1) asymmetric digital subscriber line channels and (2) underwater acoustic communication channels. Our simulation results utilize measured channel impulse responses and show that sparse filters are able to achieve the same channel energy compaction with half as many coefficients as dense filters.