Exploiting Time-Varying Sparsity for Underwater Acoustic Communication Under Delay and Doppler Spreading Channel

Underwater acoustic (UWA) communication is a critical part of information exchange among marine equipment in the Internet of Underwater Things (IoUT). The impact of the marine environment on UWA communication manifests through physical channels, which exhibit multipath propagation, Doppler spread, and time-varying characteristics. The dynamic compressed sensing (DCS) framework, represented by Kalman Filtered CS (KF-CS) algorithm, is introduced to dynamically adapt support sets by real-time tracking of observations. Meanwhile, channel modeling in Delay-Doppler (DD) domain offers a more stable representation for doubly-selective UWA channels, revealing a potential for channel estimation. In this paper, we transform the time-domain channel estimation into the DD domain channel estimation, and formulate the DD domain channel estimation under the DCS framework to exploit the time-varying sparsity of the UWA channel in the DD domain. In addition, to solve the DD model, the classic algorithms need to search for the sparse solution in the extremely large two-dimensional space of the entire UWA channel. Since only a few multipath arrivals within the large time-delay spread of the entire UWA channel have the Doppler value, we propose the multipath arrivals-Doppler function-based DCS channel estimation approach (DCS-MAD) to solve the DD model. The proposed DCS-MAD can remodel the traditional DD model as multipath arrivals and Doppler model, and search for the sparse solution in the two-dimensional space of multipath arrivals, instead of on the entire channel, so as to effectively reduce system complexity and better focus on Doppler value estimation at the UWA channel’s multipath arrivals. Specifically, we first estimate the multipath arrival delay of the UWA channel using the DCS algorithm. Then, the two-dimensional space search is performed specifically at the multipath arrivals and Doppler domains under the DCS framework to exploit the time-varying sparsity. Finally, the results of numerical simulation and sea experiments validate the superiority of the proposed schemes, compared to the benchmark algorithms.