ISI sparse channel estimation based on SL0 and its application in ML sequence-by-sequence equalization

In this paper, which is an extended version of our work at LVA/ICA 2010 [1], the problem of Inter Symbol Interface (ISI) Sparse channel estimation and equalization will be investigated. We firstly propose an adaptive method based on the idea of Least Mean Square (LMS) algorithm and the concept of smoothed l0 (SL0) norm presented in [2] for estimation of sparse ISI channels. Afterwards, a new non-adaptive fast channel estimation method based on SL0 sparse signal representation is proposed. ISI channel estimation will have a direct effect on the performance of the ISI equalizer at the receiver. So, in this paper we investigate this effect in the case of optimal Maximum Likelihood Sequence-by-Sequence Equalizer (MLSE) [3]. In order to implement this equalizer, we first introduce an equivalent F-model for sparse channels, and then using this model we propose a new method called pre-filtered parallel Viterbi algorithm (or pre-filtered PVA) for general ISI sparse channels which has much less complexity than ordinary Viterbi Algorithm (VA) and also with no considerable loss of optimality, which we have examined by doing some experiments in Matlab/Simulink. Indeed, simulation results clearly show that the proposed concatenated estimation–equalization methods have much better performance than the usual equalization methods such as Linear Mean Square Equalization (LMSE) for ISI sparse channels, while preserving simplicity at the receiver.