Minimum transmission power design for diffusion adaptive network with imperfect channels

The performance of diffusion least-mean square adaptive networks, considerably deteriorates when communication links between nodes are subject to channel noise. One way to mitigate the effect of noisy links is to amplify the transmitted information among the nodes. Although this solution reduces the effect of channel noise, however, the price for this improvement is an increase in power consumption at the nodes. In this paper our goal is to find the minimum amplifying factor at node k such that the steady-state value of mean-square deviation (MSD) at node k becomes smaller than a desired (predefined) value. We derive an expression for the desired amplifying factor at node k and provide the simulation results to clarify the derived theoretical equations.