Tracking the time-varying sparsity of channel coefficients in shallow water acoustic communications

Sparse estimation techniques typically assume a fixed weighting between the L₁ norm of the coefficients to be estimated, and the L₂ norm of the estimation error. This weighting reflects the sparsity assumption on the distribution of coefficients being estimated, and therefore, is sensitive to potential mismatch with the actual sparsity of the distribution. In this paper, we address this issue from the perspective of tracking the delay-Doppler spread of the shallow water acoustic channel, where the sparsity of the distribution itself is unknown and changes over time. We justify the need to track the sparsity based on simulation results as well as experimental field data collected at 15 meters depth and 200 meters range under moderate to high wind conditions. We propose a heuristic update to the sparsity weighting based on the normalized prediction error, which measures the mismatch between the predicted observation based on the current estimate and the actual observation in the next time step. The proposed heuristic update for the channel sparsity is designed to adapt towards lower values of the normalized prediction error and thus, by design, ensures that the estimator performance increases, or in the worst case, stays stable as the channel sparsity undergoes changes with time.