A geometric mixed norm approach to shallow water acoustic channel estimation and tracking

The shallow water acoustic channel is challenging to estimate and track due to rapid temporal fluctuations of its large delay spread. However, the impulse response and representations of its time-variability often exhibit a sparse structure that can be exploited to improve estimator performance. We propose a sparse reconstruction of the shallow water acoustic channel that employs a novel optimization metric combining the complex square root of the channel coefficients and a non-convex complex function based on the L2L2 estimation error. Our mixed norm formulation is mathematically equivalent to conventional L2L2 constrained L1L1 minimization, but fundamentally different in the non-convex topology we employ to solve for and track the optimal coefficients in real time directly over the complex field. Our estimation and tracking algorithm is designed for robustness with respect to the ill-conditioned nature of the data matrix, can smoothly handle different levels of sparsity, and is modeled to include delays due to multi-path and the Doppler spread induced by the channel. We present numerical evidence over simulated as well as field data to compare the performance of our method to conventional sparse reconstruction techniques.