Transient analysis of diffusion least‐mean squares adaptive networks with noisy channels

In this paper, we study the effect of noisy channels on the transient performance of diffusion adaptive network with least‐mean squares (LMS) learning rule. We first drive the update equation of diffusion LMS which incorporates the effects of noisy channels. Then, using the framework of fundamental weighted energy conservation relation, we derive closed‐form expressions for learning curves in terms of mean‐square deviation and excess mean‐square error. We also find the mean and mean‐square stability bounds of step‐size for diffusion LMS with noisy channels. We show that although noisy channels affect the performance of the diffusion LMS network, the stability bounds of the step‐size are the same form as in the ideal channels case. The derived closed‐form expressions are shown to provide a good match with values found by simulation. Copyright © 2011 John Wiley & Sons, Ltd.