The article studies the steady-state performance of a diffusion least-mean squares (LMS) adaptive network with imperfect communications where the topology is random (links may fail at random times) and the communication in the channels is corrupted by additive noise. Using the established weighted spatial–temporal energy conservation argument, the authors derive a variance relation which contains moments that represent the effects of noisy links and random topology. The authors evaluate these moments and derive closed-form expressions for the mean-square deviation, excess mean-square error and mean-square error to explain the steady-state performance at each individual node. The mean stability analysis is also provided. The derived theoretical expressions have good match with simulation results. Nevertheless, the important result is that the noisy links are the main factor in performance degradation of a diffusion LMS algorithm running in a network with imperfect communications.
