Greedy algorithms for sparse adaptive decision feedback equalization

In this paper we propose two new adaptive decision feedback equalization (DFE) schemes for channels with long and sparse impulse responses. It has been shown that for a class of channels, and under reasonable assumptions concerning the DFE filter sizes, the feedforward (FF) and feedback (FB) filters possess also a sparse form. The sparsity form of both the channel impulse response (CIR) and the equalizer filters is properly exploited and two novel adaptive greedy schemes are derived. The first scheme is a channel estimation based one. In this scheme, the non-negligible taps of the involved CIR are first estimated via a new greedy algorithm, and then the FF and FB filters are adaptively computed by exploiting a useful relation between these filters and the CIR. The channel estimation part of this new technique is based on the steepest descent (SD) method and offers considerably improved performance as compared to other adaptive greedy algorithms that have been proposed. The second scheme is a direct adaptive sparse equalizer based on a SD-based greedy algorithm. Compared to non sparsity aware DFE, both of our schemes exhibit faster convergence, improved tracking capabilities and reduced complexity.