Exploiting Rapidly Time-Varying Sparsity for Underwater Acoustic Communication

Due to the combined effects of different acoustic propagation, reflection patterns in different time-scale, time-varying underwater acoustic (UWA) channel generally exhibits hybrid sparsity, i.e., contains not only rapidly time-varying elements, but also stationary or slowly time-varying ones. While the classic sparse reconstruction algorithms such as orthogonal matching pursuit (OMP) generally do not take it into account, the existence of static multipath will unavoidably hinder the tracking of rapid time variations. In this paper, a sequential adaptive observation length orthogonal matching pursuit (SAOLOMP) approach is proposed to sequentially explore rapidly time-varying sparsity in a two-step sequential manner. Specifically, the static components are firstly separated via simultaneous orthogonal matching pursuit (SOMP) among continuous measurements. Upon the residual error of the SOMP, the measurement-wise OMP is applied for estimating the remained dynamic components. As the variation of the SOMP residual error indicates how rapidly the remained dynamic multipath components vary, the observation length of the OMP is adjusted according to the gradient of residual error to adapt to rapidly time-varying components. Finally, both types of sparse components are summed up to obtain the whole channel response. Numerical simulations as well as experimental results from field UWA communication data show that the proposed algorithm exhibits better performance in exploiting rapidly time-varying sparsity than the state-of-the-art compressive methods do under UWA channel.