Exploring Statistic Features for Computationally-Efficient Maximum-Likelihood Algorithms in Signal Processing and Communications Applications

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The problem of estimating the parameters in a Gaussian mixture probability density function has been prevalent in the literature for nearly a century. During the last two decades, the method of maximum likelihood has become the predominant approach to this problem. In this thesis work, we try to combat the well-known maximum likelihood (ML) problem by designing the simplified alternative objective functions together with the computationally efficient solutions. Rather than the simple but drawback-prone gradient search algorithms for the ML problems, we propose new iterative procedures for two particular signal processing/communications applications, namely source localization and blind equalization, whose underlying problem is maximum likelihood. Our new iterative methods for solving ML are based on expectation maximization (EM) algorithms. The associated theories and practice including robustness, computational complexity, system performance are also presented in this dissertation.