Real-Valued Sparse Bayesian Learning for Off-Grid Direction-of-Arrival (DOA) Estimation in Ocean Acoustics

Real-valued sparse representation methods have recently become popular for directions of arrival (DOAs) of unknown and possibly correlated signals using an array of sensors. Such a representation is useful when it is not straightforward to extend sparse representation algorithms, which are specifically designed in the real domain, to the complex domain or when the array output is represented in the sparse covariance domain. However, most existing real-valued sparse representation methods simply separate the real and imaginary parts of the signals, which are possibly complex, and treat them independently, rather than simultaneously, to impose the sparsity constraint. We use a unitary transformation-based real-valued sparse representation approach to convert the problem of estimating the DOAs from complex to the real domain for a uniform linear array. A fully automatic sparse Bayesian learning principle-based algorithm is then proposed to estimate the DOAs by simultaneously imposing the sparsity constraint on both the real and imaginary parts of the signals. This is in contrast to conventional deterministic sparse signal processing methods, which require tuning of regularization parameters, making them unsuitable to be used in practice where the ground truth is usually unknown. Since in practice, the DOAs of signals may not be exactly aligned with the predefined angular grids, we use an off-grid model to infer the off-grid DOAs. Using the singular value decomposition directly on the array output, the proposed real-valued DOA estimation can also be carried out in the same dimensional space as the original complex domain, which results in a reduction of computational complexity. Moreover, since in ocean acoustics, signals are usually wideband, we extend our proposed narrowband algorithm to the wideband case, where we estimate one spatial power spectrum by simultaneously exploiting sparsity from all frequency bins. Finally, we demonstrate the application of the proposed algorithms by analyzing both narrowband and wideband correlated multipath signals from a shallow water high-frequency (namely, HF97) ocean acoustic experiment.