A robust normalized variable tap-length normalized fractional LMS algorithm

In system identification, the selection of the optimum taplength of an adaptive filter is desirable to balance the conflicting requirements of computational cost and the steady-state performance. The performance of the original fractional tap-length least-mean-square LMS (FT-LMS) algorithm is severely degraded with a change in the variance of the input excitation signal, as well as with a change in the variance of the tap-coefficients of the unknown system. In this paper, a normalized LMS style variable tap-length (VTL) algorithm is proposed. The main idea is to efficiently normalize the step-size in the update equation for the tap-length. Furthermore, the idea of fractional gradient is incorporated with the weight-update equation of the adaptive filter. Extensive computer simulations are carried out, which demonstrate that the proposed algorithm gives robust performance in the time-varying environment.