Sparse direct adaptive equalization based on proportionate recursive least squares algorithm for multiple-input multiple-output underwater acoustic communications.

In this paper, the sparse direct adaptive equalization based on the recently developed proportionate recursive least squares (PRLS) adaptive filtering algorithm is investigated for multiple-input multiple-output (MIMO) underwater acoustic (UWA) communications. First, performance analysis is made for the PRLS, and simulation results show its gain over a standard recursive least squares algorithm under sparse systems. The fast implementation of the PRLS, named the proportionate stable fast transversal filters (PSFTF), is revisited to implement a direct adaptive decision-feedback equalizer which outperforms the existing PSFTF direct adaptive linear equalizer. The PSFTF direct adaptive equalizers (DAEs) are then compared with the selective zero-attracting stable fast transversal filter DAEs (SZA-SFTF-DAEs) enabled by the SZA-SFTF adaptive filtering algorithm. The SZA-SFTF algorithm is designed with the zero-attracting sparsity-promoting principle, which is in parallel to the proportionate updating principle used to design the PSFTF algorithm. Experimental results of an at-sea MIMO UWA communication trial show that PSFTF-DAEs outperform the SZA-SFTF-DAEs.