Robust Hierarchical Combination of Least Mean p-Power Algorithm Based on Binary Tree Structure

The least mean p-power (LMP) algorithm has gained popularity for its robustness in impulsive noise environments. The drawbacks of LMP include a tradeoff between convergence speed and steady-state error, as well as performance degradation in the presence of Gaussian noise. To address the problems, we propose a robust hierarchical combination of LMP (RHCLMP) algorithm based on the binary tree structure. The algorithm combines a pair of least mean square (LMS) filters and a pair of LMP filters in a hierarchical manner, which can improve convergence speed, steady-state mean square error and robustness in Gaussian and impulsive environments. In particular, we present a new mixing parameter modified by the Versoria function to reduce the computational complexity of RHCLMP. Furthermore, the theoretical analysis of the convergence and mean square performance are proposed based on the Taylor series expression. Simulation results show the effectiveness and superiority of the proposed algorithm and verify the accuracy of the theoretical analysis results.