High-Order Maximum Likelihood Methods for Direction of Arrival Estimation

It is shown that using high-order statistics (higher than two) is beneficial in subspace-based Direction Of Arrival (DOA) estimation methods. Particularly, the high-order MUltiple SIgnal Classification (MUSIC) method, also known as $ 2q$-MUSIC method, presents more robustness to both modeling error and strong colored background noise, has better resolution, and makes it possible to process more sources with a given array, compared to the second-order MUSIC. Moreover, when the sources are uncorrelated and the number of snapshots is large, MUSIC algorithm is a realization of Maximum Likelihood (ML) DOA estimation method, with much less complexity. However, when the sources are correlated, this less complexity costs a degradation in performance compared to ML method. Besides that, there are several methods including Alternating Projection (AP), gradient ascent, Newton, and Method Of Direction Estimation (MODE), which are used to reduce the complexity of ML method, and keep its good performance. In this paper, we propose a high-order ML DOA estimation method and develop high-order extensions for the reduced complexity ML-based DOA estimation methods. The idea of using higher-order statistics in ML-based methods is novel. This can be a basis for other ML-based high-order methods. Moreover, deriving the required formulas in this paper is different from the related second-order works. Furthermore, the performance of the proposed methods are evaluated and compared. The results are also compared with $ 2q$-MUSIC method through computer simulations. The simulation results show the good performances of the proposed methods, which are obviously better than $ 2q$-MUSIC when the sources are correlated