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 iterative method for locating modes of a likelihood function and is characterized by simple implementation and stability. Unfortunately, the slow convergence associated with EM makes it less attractive for practical applications. The SAGE algorithm proposed by Fessler and Hero (1994), based on the same idea of data augmentation, has the potential to speed up convergence and preserves the advantage of simple implementation. We study both algorithms within the framework of array processing. Theoretical analysis shows that SAGE has faster convergence speed than EM under certain conditions on observed and augmented information matrices. The analytical results are supported by numerical simulations carried out over a wide range of signal-to-noise ratios (SNRs) and various source locations