Narrowband and Wideband Off-Grid Direction-of-Arrival Estimation via Sparse Bayesian Learning

The sparse Bayesian learning based relevance vector machine (SBLRVM) algorithm is a promising algorithm to estimate the directions-of-arrival (DOAs) of multiple narrowband signals. The parameters involved in the DOA estimation model are automatically estimated by the algorithm that makes it more attractive than the deterministic sparsity based DOA estimation algorithms in which fine-tuning of parameters is necessary. However, one limitation of the algorithm is that it assumes the DOAs of the signals to be exactly aligned with the angular grids, which may not be true in practice. In this paper, we first propose an off-grid version of the narrowband SBLRVM algorithm. Next, we propose an off-grid wideband SBLRVM algorithm. The algorithms assume that the true scenario DOAs of the signals are not exactly aligned with the angular grids and the parameters of the algorithms are automatically estimated by the expectation maximization approach. In the wideband DOA estimation algorithm, we estimate one spatial power spectrum by simultaneously exploiting sparsity from all frequency bins. We demonstrate the application of the proposed algorithms by analyzing data from the shallow water HF$\mathbf {97}$ ocean acoustic experiment. The estimated DOAs of a narrowband tonal from the experiment by using our proposed narrowband DOA estimation algorithm are consistent with the nonadaptive conventional beamformer. Processing a wideband chirp from the experiment shows that estimating one spatial power spectrum by simultaneously exploiting sparsity from all frequency bins using the proposed wideband DOA estimation algorithm is a more valuable processor than an incoherent combination of the power spectra from the individual frequency bins estimated using the proposed narrowband DOA estimation algorithm. Moreover, since our proposed algorithms are off-grid algorithms, an empirical analysis for the choice of the discretization interval of the angular spread is not required as opposed to the on-grid DOA estimation algorithms. This results in a reduced computational complexity.