Comparative convergence analysis of EM and SAGE algorithms in DOA estimation

In this work, the convergence rates of direction of arrival (DOA) estimates using the expectation-maximization (EM) and space alternating generalized EM (SAGE) algorithms are investigated. The EM algorithm is a well-known ite rative method for locating modes of a likelihood function and is characteri zed by simple implementation and stability. Unfortunately, the slow converg ence associated with EM makes it less attractive for practical applications . The SAGE algorithm proposed by Fessler and Hero, based on the same idea o f data augmentation, has the potential to speed up convergence and preserve s the advantage of simple implementation. We study both algorithms within t he framework of array processing. Theoretical analysis shows that SAGE has faster convergence speed than EM under certain conditions on observed and a ugmented information matrices. The analytical results are supported by nume rical simulations carried out over a wide range of signal-to-noise ratios ( SNRs) and various source locations.