Diffusion LMS with communication constraints

Diffusion LMS is a distributed algorithm that allows a network of nodes to solve estimation problems in a fully distributed manner by relying solely on local interactions. The algorithm consists of two steps: a consultation step whereby each node combines in a convex manner information collected from its neighbors and an adaptation step where the node updates its local estimate based on local data and on the data exchanged with the neighbors. Various forms of diffusion algorithms are possible such as combine-then-adapt (CTA) and adapt-then-combine (ATC) forms, in addition to probabilistic implementations where consultations are performed only with a subset of the neighbors chosen at random. In this paper we propose an alternative protocol to reduce the communications cost during the consultation process. Each node is limited to selecting only one of its neighbors for consultation, and we propose a dynamic technique that enables the node to pick from among its neighbors that neighbor that is likely to lead to the best mean-square deviation (MSD) performance. In other words, rather than picking nodes at random, the proposed algorithm is meant to enable nodes to perform the selection in a more informed manner. The paper describes the proposed method and illustrates its behavior via simulations.