Effects Of Source Distributions And Correlation On Fractionally Spaced Blind Constant Modulus Algori

A common assumption in blind equalization schemes using the Constant Mod-ulus Algorithm (CMA) is that the source sequence is drawn from an independent, uniform distribution. Much of the analysis demonstrating the global convergence of CMA to an open-eye setting uses such an assumption. Also, much of this analysis has been performed in the baud-spaced equalizer setting, in which an innnite order equalizer is necessarily assumed to avoid the existence of local minima. However , recent results in the literature show that a nite fractionally-spaced equalizer allows for perfect equalization of moving average channels (under certain channel conditions known as equalizability). Furthermore, CMA has been shown to converge to a perfect equalizing setting under independent, uniformly distributed source. This thesis work investigates the eeect of source statistics on the location of CMA stationary points in the fractionally-sampled equalizer case under the conditions of equalizability. The work identiies the stationary points as the solution set of a system of multivariate polynomial equations with monomial coeecients given by the source moments. The work is divided into three main areas. First, an investigation of the properties of the CMA error surface is performed assuming source independence. This section revisits some previously known results and then extends them by quantifying aspects of the error surface based on the source kurtosis. The relevancy of the results here point to the tradeoos between coding gain (a function of the source distribution) and the error surface curvature (with its eeects on convergence). Next, features of a topological nature of the CMA error surface are discussed. Such properties, which hold independent of source statistics assumptions, form a bridge to the third section describing stationary point locations under temporal source correlation. The mathematical tools used here (e.g. Groebner bases and Homotopy Methods) are just starting to appear in applications in signal processing. The results include a Monte-Carlo study of the eeects of source correlation due to periodic inputs as well as an example of source sequences resulting from Markov models. iii To MeeYoung iv Acknowledgements I wish to express my sincere gratitude to MeeYoung for the endless support she has given me over the years. Her dedication, cheerfulness, and patience has made all this possible. Her sidekick for the past 18 months, Pascal, deserves high praise for being such a joyful baby and giving me the drive to nish. Thanks are also due to my mother and father, not just …

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