A new diffusion variable spatial regularized LMS algorithm

Abstract This paper develops a new diffusion (Diff) least mean squares (LMS) algorithm for the identification of a network of systems that have distinct parameters at each node. The mean and mean squares behavior of the Diff-LMS algorithm in the so called multitask environment is studied in order to obtain an explicit expression of the estimation bias and variance in terms of the spatial regularization (SR) parameter. An optimal SR formula for the Diff LMS algorithm is then derived via minimizing the estimation error. An approximation is made to the formula such that a new practical Diff variable SR LMS (Diff-VSR-LMS) algorithm is obtained. This paper also provides a framework for the design of other LMS-like algorithms that incorporate diffusion technology to solve multitask problems. The theoretical analysis is evaluated via computer simulations and the performance of the proposed algorithm is compared with conventional Diff LMS algorithms under the multitask environment.