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Comparative convergence analysis of EM and SAGE algorithms in DOA estimation

The convergence rates of direction of arrival (DOA) estimates using expectation-maximization (EM) and space alternating generalized EM (SAGE) algorithms are investigated. The EM algorithm is a well known recursive method for locating modes of a likelihood function which is characterized by simple implementation and stability. Unfortunately the slow convergence associated with EM makes it less attractive. The recently proposed SAGE algorithm, based on the same idea of data augmentation, preserves the advantage of simple implementation and has the potential to speed up convergence. Theoretical analysis shows that SAGE has faster convergence rate than EM under certain conditions. This conclusion is also supported by numerical experiments carried out over a wide range of SNRs and different numbers of snapshots.