Deterministic and Bayesian Sparse Signal Processing Algorithms for Coherent Multipath Directions-of-Arrival (DOAs) Estimation

In this paper, we propose novel deterministic and Bayesian methods to identify the directions-of-arrival (DOAs) of coherent multipath signals assuming that a very few number of multipath signals are present and multiple snapshots are available. For both types of methods, we exploit both sparsity and the underlying structure of coherent signal propagation. For the deterministic case, we formulate the problem of estimating the DOAs of coherent multipath signals as a biconvex optimization problem and then solve it by an alternating convex search approach. This is in contrast to the widely used $\ell _1$ sparse signal recovery convex optimization problem, which only exploits sparsity of the signal under consideration. For the Bayesian case, we propose two novel algorithms based on the mean field variational Bayesian expectation maximization approach. The first algorithm assumes that the true scenario DOAs of the multipath signals are exactly aligned with the angular grids. We next extend the on-grid model to deal with the off-grid problem, which is the second proposed Bayesian algorithm of this paper. These two Bayesian algorithms are in contrast to the widely used sparse Bayesian learning relevance vector machine algorithm, which only exploits sparsity in spatial domain. A simulation study is carried out in terms of root-mean-squared error in the DOA estimates to compare the performances of different algorithms. Finally, we demonstrate the application of the proposed off-grid Bayesian algorithm by analyzing data from the shallow water HF $\mathbf {97}$ ocean acoustic experiment.