Performance Measures of NLMS Adaptive Filter for Noise Estimation and Cancellation

Abstract

Interference cancellation is a technique of utmost importance in the field of signal processing. It is especially
essential for speech signal transmission and processing due to the ever-growing application of telephone and cellular
communication. Interference cancellation can be achieved by an adaptive filter, a filter which self-adjusts its transfer
function according to an optimizing algorithm. The most popular of such adaptive algorithms is the Least Mean Square
(LMS) algorithm. The normalized Least Mean Square (NLMS) algorithm can be considered as a special case of the LMS
recursion which takes into account the variation in the signal level at the filter output. The performance of these adaptive
algorithms is dependent on their filter length and the selected convergence parameter μ. NLMS algorithm is a potentially
faster converging algorithm compared to the LMS algorithm. Faster convergence, however, comes at a price of greater
residual error. More recent studies that try to relax this trade-off have been directed towards adjustable step-size
variations of the two algorithms. Rather than focusing on the convergence behavior, this paper focuses on NLMS
Adaptive filter used to minimize the noise signal. Hence, the performance of the NLMS algorithms in interference
cancellation has been presented in terms of the Simulink model of the input and output signals. The effects of the filter
length and step size parameters have been analyzed to reveal the behavior of the algorithms.