Sequential High-Resolution Direction Finding From Higher Order Statistics

The classical higher order MUSIC-like methods based on a simultaneous search for all directions of arrival (DOA's) show: i) a capacity for processing underdetermined mixtures of sources; ii) a high robustness with respect to both a Gaussian noise with unknown spatial coherence and modeling errors; and iii) a better resolution than algorithms based on second order statistics. However, these methods have some limits: for a finite number of samples, they show poor performance for sources exhibiting quasi-colinear DOA's. In order to overcome this drawback, two new sequential MUSIC-like algorithms are proposed in this paper, namely the 2q-D-MUSIC and the 2q-RAP-MUSIC (q >= 2) algorithms. These methods are based on a sequential optimization of proposed generalized noise and signal 2q-MUSIC metrics, respectively. That allows us to learn and then to take into account the level of correlation between sources. A comparative study, both in terms of performance and numerical complexity, is performed showing the interest of the proposed techniques when some sources are angularly close. Eventually, an upper bound of the maximum number of sources which can be processed by the 2q-MUSIC-like techniques is given for all. This improves recent work on the 2qth-order virtual arrays.