Modified RLMS and SHARF Algorithms for Rapid Convergence

A general infinite impulse response (IIR) or recursive adaptive filter co-efficient vector update equation is given by where μ(k) is the adaptation gain sequence, and f(k) is the correction vector. In this paper, we show that improvements in filter convergence can be obtained by appropriately modifying either μ(k) or f(k). In the former case, we force Dvoretzky conditions (from stochastic approximation theory) on μ(k) during the search period, whereas the latter uses delayed error signals (i e, modified f (k)) resulting in a parallel processing technique.We have incorporated these proposed modifications in recursive least mean square (RLMS) and simple hyperstable adaptive recursive filter (SHARF) algorithms. From simulation studies, it has been observed that the modification on f(k) gave improved results for the SHARF, and the RLMS converged quickly with the modification on μ(k). Results of simulation studies are presented in the form of learning curves and parameter tables.