Maximum likelihood DOA estimation and detection without eigendecomposition

Most popular techniques for the narrowband direction of arrival (DOA) problem rely on an eigenvalue decomposition (EVD) computation to determine both the number of signals and their respective DOAs. An alternative algorithm is presented that solves both the DOA detection and estimation problems without resorting to an EVD. The algorithm is shown to be asymptotically equivalent to the (stochastic) maximum likelihood method, and hence yields asymptotically minimum variance DOA estimates. In addition, the asymptotic distribution of the algorithm´s cost function is derived and is shown to be composed of the sum of two differently scaled chi-squared random variables. A hypothesis test for determining the number of signals based on this result is presented