Effect of eigenvalue spread in noise cancellation of two sensory systems using adaptive algorithms

Abstract

The least mean square (LMS) algorithm is the basic generic search algorithm and simple to implement, also it has stable and has robust performance. Therefore, numerous adaptive algorithms have been derived from LMS. But maximum research is limited to convergence rate maximization in the algorithms of LMS family. Eigenvalue spread changes the convergence of any adaptive algorithms as it also affects the selection of step size. When spectral power of input signal is non-stationary, the residual error is more in all the cases. The performance analysis of adaptive algorithms for eigenvalue spread is still ignored by researchers. In this paper the effect of eigenvalue spread on different popular algorithm of LMS family has been studied. For this, many noises of different eigenvalue spread were mixed with a voice signal i.e. pronunciation of the word “This activity is truly unproductive” to make primary signal. Then simulation has done to analyze the effect of eigenvalue spread in MATLAB for different algorithms. Eigenvalue spread is calculated for all contaminated primary signals then steady state error or residual errors have also been calculated for LMS, VSSLMS, and QLMS. Their performance is compared by changing the surrounding noisy environment as car noise, water raining noise, thonder noise, and aeroplane noise. To analyses the effect of eigenvalue on adaptive algorithms, a table is prepared on the basis of residual error and eigenvalue spread for chosen algorithms. This analysis will help to select the algorithm for devices, which need to work in changing surrounding environment.