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Alternative algorithm for maximum likelihood DOA estimation and detection

The majority of algorithms developed for the narrowband direction of arrival (DOA) estimation problem rely on an eigenvalue decomposition (EVD) 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 have asymptotically equivalent performance to that of the (unconditional) maximum likelihood method, and hence it yields asymptotically minimum variance DOA estimates. The computational complexity required to update the DOA estimates in response to additional data from the array is investigated, and the algorithm is shown to be somewhat simpler than other methods with comparable performance. 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 then presented.