Identification of Block-Sparse Systems using Adaptive Filtering Algorithms

Abstract

An adaptive filter is a system with a linear filter that has a transfer function controlled byvariable parameters and a means to adjust those parameters according to an optimizationalgorithm. Adaptive filters are used for linear time-variant systems where thecharacteristics of the systems keep on changing with time. Therefore, adaptive filters arerequired for some applications when some parameters of the desired processingoperation are not known in advance or are changing.In the world of adaptive algorithms, sparse system identification has received a lot ofinterest. In numerous applications, including acoustic echo cancellation, interferencereduction in industrial settings, and biomedical engineering, system identification isregularly encountered. During the last ten years, system identification has been widelyused in a variety of signal processing applications, including wireless communication,radar imaging, and echo cancellation.A sparse impulse response is one in which a significant portion of the energy orinformation is concentrated in a few number of its impulse response coefficients. Thereare few non-zero or high coefficients and numerous tap-weights with zero or tiny valuesin various cases, such as network echo cancellation, where the impulse responses aresparse. Sparse systems come in a variety of forms. The conventional one is referred to asa block-sparse system, like TV transmission channels. The non-zero coefficients ofblock-sparse systems consist of one or more clusters, and a cluster is a set of non-zero orbig coefficients, in contrast to generic impulse response sparse systems where largecoefficients are distributed at random. This thesis has taken into consideration various existing adaptive algorithms, viz, LMS, NLMS, PNLMS, ZA-NLMS, ZA-PNLMS, BS PNLMS, BS-IPNLMS to identify a block-sparse system with the help of mean squareerror and the convergence rate of the coefficients. It continues to give a proposedalgorithm with some modifcations to get a better convergence rate for the coefficients ofan unknown system which is assumed to be a block-sparse system for our research.