On Ways to Improve Adaptive Filter Performance

(ABSTRACT) Adaptive filtering techniques are used in a wide range of applications, including echo cancellation, adaptive equalization, adaptive noise cancellation, and adaptive beamforming. The performance of an adaptive filtering algorithm is evaluated based on its convergence rate, misadjustment, computational requirements, and numerical robustness. We attempt to improve the performance by developing new adaptation algorithms and by using " unconventional " structures for adaptive filters. Part I of this dissertation presents a new adaptation algorithm, which we have termed the Normalized LMS algorithm with Orthogonal Correction Factors (NLMS-OCF). The NLMS-OCF algorithm updates the adaptive filter coefficients (weights) on the basis of multiple input signal vectors, while NLMS updates the weights on the basis of a single input vector. The well-known Affine Projection Algorithm (APA) is a special case of our NLMS-OCF algorithm. We derive convergence and tracking properties of NLMS-OCF using a simple model for the input vector. Our analysis shows that the convergence rate of NLMS-OCF (and also APA) is exponential and that it improves with an increase in the number of input signal vectors used for adaptation. While we show that, in theory, the misadjustment of the APA class is independent of the number of vectors used for adaptation, simulation results show a weak dependence. For white input the mean squared error drops by 20 dB in about () 1 / 5 + M N iterations, where N is the number of taps in the adaptive filter and () 1 + M is the number of vectors used for adaptation. The dependence of the steady-state error and of the tracking properties on the three user-selectable parameters, namely step size µ , number of vectors used for adaptation () 1 + M , and input vector delay D used for adaptation, is discussed. While the lag error depends on all of the above parameters, the fluctuation error depends only on µ. Increasing D results in a linear