Adaptive Estimation over Networks with Link Failures and Channel Noise

Analysis of adaptive networks in the simultaneous presence of noise and topology randomness is an important physical layer issue that has not been considered in previous work. Hence, in this paper, we study the steady-state performance of a diffusion least-mean square (LMS) adaptive network where the network topology is random and the communication channel is corrupted by additive noise. We use the weighted spatialtemporal energy conservation approach to derive closed-form expressions for the mean-square deviation (MSD), excess mea-square error (EMSE) and mean-square error (MSE) to explain the steady-state performance at each individual node. Simulations of the derived mathematical equations show that the main factor in performance degradation of the diffusion LMS algorithm is the presence of noise.