Combination weights for diffusion strategies with imperfect information exchange

Adaptive networks rely on in-network and collaborative processing among distributed agents to deliver enhanced performance in estimation and inference tasks. Information is exchanged among the nodes, usually over noisy links. This paper first investigates the mean-square performance of adaptive diffusion algorithms in the presence of various sources of imperfect information exchanges and quantization errors. Among other results, the analysis reveals that link noise over the regression data modifies the dynamics of the network evolution, and leads to biased estimates in steady-state. The analysis also reveals how the network mean-square performance is dependent on the combination weight matrices. We use these observations to show how the combination weights can be optimized and adapted. Simulation results illustrate the theoretical findings and match well with theory.