DOA estimation using fast EM and SAGE algorithms

In this work we study direction of arrival estimation using expectation-maximization (EM) and space alternating generalized EM (SAGE) algorithms. The EM algorithm is a general and popular numerical method for finding maximum-likelihood estimates which is characterized by simple implementation and stable convergence. The SAGE algorithm, a generalized form of the EM algorithm, allows a more flexible optimization scheme and sometimes converges faster than the EM algorithm. Motivated by the componentwise convergence of the EM and SAGE algorithms, we suggest to use smaller search spaces after a few iterations. In this way, the overall computational costs can be reduced drastically. A procedure derived from the convergence properties of the EM and SAGE algorithms is proposed to determine the search spaces adaptively. By numerical experiments we demonstrate that the fast EM and the fast SAGE algorithms are computationally more efficient and have the same statistical performance as the original algorithms.