Combination coefficients for fastest convergence of distributed LMS estimation

Diffusion strategies for learning across networks which minimize the transient regime mean-square deviation across all nodes are presented. The problem of choosing combination coefficients which minimize the mean-square deviation at all given time instances results in a quadratic program with linear constraints. The implementation of the optimal procedure is based on the estimation of weight deviation vectors for which an algorithm is proposed. Additionally, the optimization that uses relaxed constraints is considered. The proposed methods were validated through simulations for different estimation distribution strategies and input signals. The results show a potential for significant improvement of the convergence speed.