Maximum likelihood methods for direction-of-arrival estimation

Five methods of direction-of-arrival (DOA) estimation which can be derived from the maximum-likelihood (ML) principle are considered. The ML method (MLM) results from the application of the ML principle to the statistics of the observed raw data. The standard multiple signal classification (MUSIC) procedure, called MUSIC-1, is obtained as a brute-force approximation of the MLM. An improved MUSIC procedure, named MUSIC-2, is obtained by applying the ML principle to the statistics of certain linear combinations of the sample noise space eigenvectors. A procedure which compromises between the good performance of the MLM and the computational simplicity of MUSIC is a method of direction estimation (MODE-1) which is derived as a large sample realization of the MLM. A fifth method, called MODE-2, is obtained by using the ML principle on the statistics of certain linear combinations of the sample eigenvectors. MODE-2 is computationally less demanding than the MLM (it is of the same complexity as MODE-1) and statistically more efficient. A numerical comparison of these five DOA estimation methods is presented. It confirms the analytic results on their theoretical performance levels