Maximum Likelihood Direction-of-Arrival Estimation via Rank-Constrained ADMM

The maximum likelihood estimation (MLE) is known to provide benchmark performance for direction-of-arrival (DOA) estimation. Due to high nonconvexity of the MLE problem, however, effective implementations of the MLE are rare in practice. In this paper, we consider DOA estimation with a uniform linear array and formulate by using re-parameterization and majorization minimization the stochastic MLE as a series of rank-constrained semidefinite programs that are solved using the alternating direction method of multipliers (ADMM). Numerical results are provided to illustrate the superior statistical performance of the proposed method as compared to existing approaches in the absence/presence of coherent sources.