This dissertation deals with the convergence and performance analysis of the least mean-square (LMS) algorithm and the constant modulus algorithm (CMA), which are commonly used in applications such as channel equalization and beamforming.; For the LMS algorithm, we analyze the correlation matrix of the filter coefficients estimation error and the mean-square signal estimation error in the transient phase as well as in steady-state for dependent data. We establish the convergence of the second-order statistics as the number of iterations increases, and we derive the exact asymptotic expressions for the mean-square errors. In particular, the result for the excess signal estimation error gives conditions under which the LMS algorithm outperforms the Wiener filter with the same number of taps. We also analyze a new measure of transient speed. The data is assumed to be an instantaneous transformation of a stationary Markov process satisfying certain ergodic conditions.; For the CMA, we study global convergence in the absence of channel noise as well as in the presence of channel noise. The case of fractionally spaced equalizer, and/or multiple antenna at the receiver is considered. For the noiseless case, we show that with proper initialization, and with small step-size, the algorithm converges to a zero-forcing filter with probability close to one. Under mild assumptions on the density of the received data, which allow the case of additive Gaussian noise, we prove that the algorithm diverges almost surely on the infinite time horizon. But the algorithm has desirable properties on a finite time horizon. We establish a lower bound on the expected escape time from a small neighborhood of the Wiener filters, and a lower bound on the expected number of visits to a small neighborhood of the Wiener filters.
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