Numerous variable tap-length algorithms can be found in some literature and few strategies are derived from a basic theoretical formula. Thus, some algorithms lack of theoretical depth and their performance are unstable. In view of this point, the novel variable tap-length algorithm which is based on the mixed error cost function is presented in this letter. By analyzing the mixed expectation of the prior and the posterior error, the novel variable tap-length strategy is derived. The proposed algorithm has a more valid proximity to the optimal tap-length and a good convergence ability by the performance analysis. It can solve many deficiencies comprising large fluctuations of the tap-length, the high complexity and the weak steady-state ability. Simulation results demonstrate that the proposed algorithm equips good performance.

Improved fractional variable tap-length adaptive algorithm that contains Sigmoid limited fluctuation function and adaptive variable step-size of tap-length based on fragment-full error is presented. The proposed algorithm can solve many deficiencies in previous algorithm, comprising small convergence rate and weak anti-interference ability. The parameters are able to modify reasonably on the basis of different situations. The Sigmoid constrained function can decrease the fluctuant amplitude of the instantaneous errors effectively and improves the ability of anti-noise interference. Simulations demonstrate that the proposed algorithm equips better performance.