Application of the block sparse improved proportionate least mean square based adaptive decision feedback equalizer to mobile underwater acoustic communication channels: improvement in reverberate channel and relaxation in hyperparameter tuning

Abstract The combination of single-carrier modulation and decision-feedback equalizers with sparse adaptive algorithms is effective for compensating the temporally sparse and time-varying delay spread in underwater acoustic (UWA) channels. However, UWA often exhibits group-sparse characteristics due to reverberation from reflection at rough boundaries, for which conventional sparse models could be suboptimal. This study proposes a block-sparse improved proportionate normalized least mean squares (IPNLMS) algorithm, incorporating a mixed-norm constraint into the IPNLMS framework, and evaluates its applicability to mobile UWA with group sparsity. Performance comparisons with conventional normalized least mean squares (NLMS) and IPNLMS methods were conducted using simulation data. Experimental validation was performed with shallow-water data collected between an autonomous underwater vehicle and a moored hydrophone array. The results demonstrate that the proposed method mitigates sensitivity to hyperparameter selection and achieves superior communication performance under group-sparse channel conditions compared with conventional NLMS and IPNLMS.