GLOBAL OPTIMIZATION ALGORITHMS FOR ADAPTIVE INFINITE IMPULSE RESPONSE FILTERS By CHING-AN LAI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy GLOBAL OPTIMIZATION ALGORITHMS FOR ADAPTIVE INFINITE IMPULSE RESPONSE FILTERS By Ching-An Lai December 2002 Chair: José C. Principe Major Department: Electrical and Computer Engineering The major goal of this dissertation is to develop global optimization algorithms for adaptive IIR filters. Since the performance surface of adaptive IIR filters is nonconvex with respect to the filter coefficients, conventional gradient-based algorithms can easily be trapped at an unacceptable local optimum. We need to exploit global optimization methods in adaptive IIR filtering and overcome the problem of converging to the local minima, preserving stability throughout adaptation. One approach for adaptive IIR filtering suggests a stochastic approximation with convolution smoothing (SAS). We modify the perturbing noise by multiplying it with its cost function. The modified algorithm results in better performance when compared to the original algorithm. We also analyze the global optimization behavior of the proposal algorithm by analyzing the transition probability density of escaping from a local minimum. A gradient estimation error can be used to act as the perturbing noise, provided it is properly normalized. Consequently, another approach for global IIR filter optimization is the normalized LMS (NLMS) algorithm. The behavior of the NLMS algorithm with decreasing step size is similar to that of the LMS-SAS algorithm from a global optimization perspective.