Low-Complexity Sparse FIR Channel Shortening

The complexity of maximum-likelihood (ML) or maximum-a-posteriori (MAP) detectors grows exponentially with the number of channel impulse response (CIR) taps. This makes the implementation of ML or MAP detectors over broadband channels with long CIRs prohibitively complex. Channel shortening is a widely-used technique to solve this problem by implementing a front-end finite impulse response (FIR) filter to shorten the CIR. In this paper, we propose a novel approach based on compressive sensing theory to design low-complexity FIR channel shortening filters. The superiority of our new approach is proven analytically and illustrated via simulations.