Distributed linear prediction in the presence of noise and multipath

We are considering problem of estimating autoregressive signal coefficients over a network of agents. Noise and/or multipath are disturbing reception of the signals in network nodes. The autoregressive signals have different powers and delays at different nodes. Least-mean-square algorithms are used in nodes for the estimation as well as the cooperation strategy based on the adapt-then-combine diffusion. Several combining algorithms are used to implement cooperation and their convergence rates and steady-state levels are compared using mean-square weight deviations. Conditions to get benefits from the cooperations are discussed. Possibilities for performance improvements are supported by numerical experiments.