Improved hybrid variable and fixed step size least mean square adaptive filter algorithm with application to time varying system identification

In this paper a new simplified adaptive filter algorithm is introduced which is based on the hybrid operation of variable step-size and fixed step-size least mean square adaptive algorithm. In this proposed algorithm the variable step-size is used in the first stage, the algorithm adopts the fixed step size least mean square (LMS) whenever an acceptable mean square error threshold is reached that ensures the required steady state error and stability. The simulation results obtained show that the new algorithm outperforms the standard least mean square (LMS) in the desired transient-response, and outperforms the normalized least mean square (NLMS) algorithm in the desired transient and the steady-state response. It is shown that this new algorithm is able to track time-varying systems with better performance response. Also, the computational-complexity for this algorithm is reduced as compared with the ordinary least mean square (LMS).