A Robust and Statistically Efficient Maximum-Likelihood Method for DOA Estimation Using Sparse Linear Arrays

The recent trend of research on direction-of-arrival estimation is to localize more uncorrelated sources than sensors by using a proper sparse linear array (SLA) at the cost of robustness to source correlations even in the regime of less sources than sensors. This article is devoted to proposing one algorithm that can simultaneously tackle two challenging scenarios: 1) more uncorrelated sources than sensors and 2) highly correlated or coherent sources. In order to statistically efficiently localize a maximal number of uncorrelated sources, we use the stochastic maximum likelihood (SML) criterion and propose an effective algorithm based on elegant problem reformulations and the alternating direction method of multipliers (ADMM). Moreover, we prove that the SML is robust to source correlations under mild conditions, though it is derived under the assumption of uncorrelated sources. The proposed algorithm is usable for arbitrary SLAs (e.g., minimum redundancy arrays, nested arrays, and coprime arrays) and is named as maximum-likelihood estimation via sequential ADMM (MESA). Extensive numerical results are provided that collaborate our analysis and demonstrate the statistical efficiency and robustness of MESA against state-of-the-art algorithms. Our results also imply that it is possible to localize more sources than sensors in the presence of high source correlations.