Design of sparse filters for channel shortening

Channel shortening filters have been used in acoustics to reduce reverberation, in error control decoding to reduce complexity, and in communication systems to reduce inter-symbol interference. The cascade of a channel and a channel shortening filter would produce an overall impulse response that has more of the energy in the channel impulse response compacted into fewer adjacent samples. Once designed, channel shortening filters operate on a per-sample basis. In this paper, we evaluate sparse FIR filters, which use more design complexity and less per-sample processing complexity, for channel shortening. Our contributions include (1) proposing a new sparse FIR filter design method for channel shortening, and (2) evaluating design tradeoffs in energy compaction vs. implementation complexity for sparse and non-sparse FIR filters. Our simulation results for ADSL channels show that sparse designs could achieve the same energy compaction with half as many coefficients than non-sparse FIR filters for low filter orders.