Amplify-and-forward scheme in incremental LMS adaptive network with noisy links: Minimum transmission power design

The performance of adaptive networks, considerably reduces when the communication links between nodes are subject to channel noise. One way to mitigate the effect of noisy links is to use the amplify-and-forward scheme. As the amplifying factor increases, the effect of channel noise decreases at the cost of more power consumption in nodes. In this paper we focus on design of incremental least-mean square (I-LMS) adaptive network with amplify-and-forward scheme. Our goal is to find the minimum amplifying factor at node k − 1 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 − 1 and provide the simulation results to clarify the derived theoretical result.