A Low Complexity Proportionate Generlized Correntropy-Based Diffusion LMS Algorithm With Closed-Form Gain Coefficients

This brief proposes a correntropy-based proportionate diffusion algorithm with low computational complexity. The proportionate diffusion algorithms in the literature suffer from a high computational complexity due to the complicated calculation process of the coefficients of the gain matrix, i.e., by solving an optimization problem or solving a linear system of equations via a matrix inversion. In this brief, by defining a proper correntropy kernel function and suitably assuming a wise constraint, the gain matrix coefficients are derived in a closed-form formula. In fact, the correntropy kernel function is used to determine the gain coefficients. This closed-form formula significantly reduces the computational complexity of the proposed algorithm. Moreover, a condition of uniform convergence for the distributed estimation algorithm at each time instant is obtained analytically. Simulation results show the lower steady-state Normalized Mean Square Deviation (NMSD) and lower computational complexity of the proposed algorithm compared to some other competing algorithms.