A new variable step-size normalized PBS_LMS algorithm

This paper presents a novel variable step-size normalized PBS_LMS algorithm for adaptive filters. The fixed step-size PBS_LMS algorithm, which significantly decreases the number of calculations for updating tap-weight vector and increases the speed of convergence rate in comparison with conventional LMS algorithm, has proposed previously. However, the fixed step-size PBS_LMS algorithm as fixed step-size LMS algorithm usually results in a trade-off between the residual error and the convergence speed of the algorithm. Now in this paper the properties of Normalized LMS algorithm are used in the conventional PBS_LMS algorithm to approach the Normalized PBS_LMS algorithm with fast convergence rate. Then variable step-size is used parallel with the Normalized PBS_LMS algorithm to minimize the steady state mean square error. The function of mean square error variation is used to detecting the rate of convergence for increasing the step-size parameter to approach this goal. The computer simulations validate that the Normalized PBS_LMS algorithm can approach the faster convergence rate than the PBS_LMS algorithm. In addition, these simulations show the lower mean square error and tracking ability in Variable Step-Size Normalized PBS_LMS algorithm in comparison with the Normalized PBS_LMS algorithm.