In hands-free telephones and teleconferencing systems

the echo path to be estimated by the adaptive filter is usually sparse.The improved proportionate normalized least-mean-square (IPNLMS) algorithm can increase the convergence rate of the adaptive filter when it is used to estimate sparse systems.However

the steady-state misalignment of the IPNLMS algorithm may suffer from much larger fluctuations than that of the normalized least-mean-square (NLMS) algorithm.To address this problem

a time-varying parameter IPNLMS (TV-IPNLMS) algorithm is proposed

which uses a sigmoid function to adjust the value of the time-varying parameter according to the ratio of the mean square error (MSE) to the power of the system noise.This time-varying parameter can reduce the proportionate gains of the IPNLMS algorithm when the adaptive filter arrives at steady state.Simulation results show that the time-varying parameter method can reduce the fluctuations of the steady-state misalignment of the IPNLMS algorithms.This algorithm can be used in the fields of echo cancellation

active noise control

and so on.