Designing an optimized linear adaptive filtering algorithm

Abstract

For any system, sparse or dispersive, z2 proportionate algorithm of Proportionate Normalized Least Mean Square (PtNLMS) class, gives the best convergence rate compare to any other weiner filter based iterative algorithms. Though, to implement this algorithm practically, is impossible due to lack of information about the unknown system weight vector wopt, which has been directly used in the formation of the gain proportionality function in z2 proportionate algorithm. For that to formulate, an approximate adaptive model for proportionate gain function is developed using the fuzzy logic. Then using this new proposed approach, formulated the proportionality gain function for some standard adaptive algorithms like NLMS, PNLMS and their convex combinations. Later on, another algorithm of PtNLMS class is developed by formulating the deterministic adaptive gain function, which gives huge improvement in terms of the convergence rate of adaptive filter and provides better stability compare to some adavanced algorithm like IPNLMS.