Novel Approaches to Nonlinear Adaptive Filtering and Their Applications to Communications

Practical systems often encounter nonlinearities which call for techniques for the compensation of nonlinear systems and/or signals. Volterra filters, Extended Kalman Filter (EKF), and more recently Support Vector Machines (SVM) are among the most nonlinear filtering popular techniques. However, these approaches have drawbacks of increased training complexity or mediocre performance when the underlying system is highly nonlinear. In this thesis, novel approaches to nonlinear filtering and classification are proposed which have less training complexity and the Unscented Kalman Filter is discussed as an alternative to the EKF. Set-membership normalized least-mean-squares (SM-NLMS) is an adaptive solution for estimating the parameter vector satisfying the bounded error criterion, which is the fundamental idea of set-membership filtering (SMF). An attractive feature of all SM algorithms is the data-dependant selective update i.e., the parameter estimates are updated only if the prediction error of the filter exceeds a pre-defined bound. This feature is combined with the emph{kernel trick} to extend the SM-NLMS algorithm for nonlinear problems, resulting in a kernel-SM algorithm. UKF is based on the concept of Unscented Transformation (UT), which is a deterministic sampling method to determine the statistics of a random variable undergoing nonlinear transformation. The greater accuracy of UKF leads to better recursive estimates and robustness with respect to divergence compared to EKF. Applications of the kernel-SM algorithms and the UKF to equalization of nonlinear inter-symbol interference (ISI) channels and predistortion of nonlinear high power amplifiers (HPA) show very encouraging results.