Adaptive Polynomial Filtering for System Identification Using Modified Sigmoid Variable Step-Size LMS Algorithm

Abstract

Adaptive polynomial filtering comprises one of the primary technologies in signal processing, and it investigates many applications in the area of industry and science. These techniques are employed in a vast range of applications, for example: adaptive echo/noise cancellation system, adaptive equalization, adaptive beamforming and system identification. The current trend in the telecommunication system design is the process of identification and minimization of undesired non-linearities, as these have adverse effects on underlying system operation. The use of nonlinear models, like Volterra series, can minimize all these non-linearities. Adaptive approaches and algorithms are extensively utilized for the estimation of Volterra kernels, under the constraint of unknown non-linear system. The accuracy of the estimation of kernels is used to investigate the precision of the system model and inverse system. This thesis propounds the adaptive polynomial filtering for system identification using variable-step-size least-mean-square (VSS-LMS) algorithms, and these VSS algorithms are compared with the fixed-step-size leastmean- square (FSS-LMS) algorithm. Different VSS-LMS algorithms are also compared with each other. These all algorithms are applied to the second-order-Volterra (SOV) filter, under the various noise constraints for different values of signal-to-noise ratio (SNR). The VSS-LMS algorithm corroborates steady state behavior during convergence. The step-size of the adaptive filter is altered in compliance with a gradient based descent algorithm to minimize the squared estimation error in the course of each iteration. It also improves tracking performance in the smoothly time-varying environments for the choice of the parameters and the boundary conditions of adaptive filter. First, we apply the sigmoid-variable-step-size least-mean-square (SVSS-LMS) algorithm to SOV filter, in which the adaptive step-size is modelled using sigmoid function. It gives fast convergence when compared with the FSS-LMS algorithm. Following this for polynomial filtering, we have used modified-sigmoid-variable-step-size least-mean-square (MSVSS-LMS) algorithm, which gives better convergence and tracking performance in comparison to SVSSLMS algorithm under similar conditions. Other VSS-LMS algorithms like Kwong-variable-stepsize least-mean-square (KVSS-LMS) algorithm (Kwong et al., 1992), Aboulnasr-variable-stepsize- least mean-square (AVSS-LMS) algorithm (Aboulnasr et al., 1997) and modified- Aboulnasr-variable-step-size least-mean-square (MAVSS-LMS) algorithm ( Kun et al., 2009) are also compared with FSS-LMS algorithm and with each other. Simulation results are also presented to demonstrate that MSVSS-LMS algorithm is a better option than SVSS-LMS and FSS-LMS algorithm in the second-order Volterra filtering applications for non-linear system identification. In non-linear signal processing scenario, MSVSS-LMS algorithm is marginally inferior to KVSS-LMS under static environment in terms of mean squared error in the convergence and tracking mode. Undoubtedly, MAVSS-LMS is the best algorithm under similar non-linear conditions, which is substantially better than AVSS-LMS and KVSS-LMS algorithm. But, MSVSS-LMS algorithm is finding applications in neural signal processing.