In this paper, we firstly propose an adaptive method based on the idea of Least Mean Square (LMS) algorithm and the concept of smoothed
(SL0) norm presented in  for estimation of sparse Inter Symbol Interface (ISI) channels which will appear in wireless and acoustic underwater transmissions. 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) . In order to implement this equalizer, 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. 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 with the use of PVA.