Analysing the impact of system dimension on the performance of a variable-tap-length adaptive algorithm

Abstract

The variable-tap-length algorithms try to find out the optimum number of adaptive filter coefficients that are necessary to model an unknown plant. The most recent variable-tap-length algorithms claim themselves to be independent of the order of the unknown channel, even though the convergence rate of an adaptive finite impulse response filter that is used for identifying an unknown plant in a system identification framework may be affected by the characteristics of the input signal and time-varying filter parameters. The system dimension may vary notably from one application to others, such as acoustic echo cancellation in a big conference hall needs thousands of filter weights, whereas feedback cancellation in hearing-aids requires less than a hundred coefficients. Hence, there is a need to analyze the convergence of the variable-tap-length algorithm for these time-varying applications of adaptive filters of different dimensions. In this paper, we develop and propose a novel technique to measure the convergence and transient behavior of the variable-tap-length adaptive algorithm. Using this analysis, we also arrive at conclusion that the median rate of convergence declines with the rise in system dimension to a limit determined by the reference input. It is proved that the limiting point can be obtained by the level of the autocorrelation of the input signal.