Real-valued DOA estimation with unknown number of sources via reweighted nuclear norm minimization

Traditional MUSIC-like methods for direction-of-arrival (DOA) estimation require the number of sources a priori and suffer from the heavy computational burden caused by complex-valued operations and exhaustive spectral search. In this paper, we propose two novel real-valued estimation methods without knowing the number of sources to overcome these weaknesses. Specifically, we first transform the complex-valued second-order statistics (covariance matrix) into real-valued one by unitary transformation and taking its real (or imaginary) part, respectively. We then formulate a real-valued low rank recovery problem to reveal the relation between the real-valued covariance matrices and source number. Finally, we propose a computationally efficient approach to solve the optimization problem via reweighted nuclear norm minimization. Simulation results show that without knowing the number of sources, the proposed methods exhibit superior estimation performance and can substantially reduce the complexity, as compared to the state-of-the-art techniques.