  We study the performance of diffusion least-mean-square algorithms for
distributed parameter estimation in multi-agent networks when nodes exchange
information over wireless communication links. Wireless channel impairments,
such as fading and path-loss, adversely affect the exchanged data and cause
instability and performance degradation if left unattended. To mitigate these
effects, we incorporate equalization coefficients into the diffusion
combination step and update the combination weights dynamically in the face of
randomly changing neighborhoods due to fading conditions. When channel state
information (CSI) is unavailable, we determine the equalization factors from
pilot-aided channel coefficient estimates. The analysis reveals that by
properly monitoring the CSI over the network and choosing sufficiently small
adaptation step-sizes, the diffusion strategies are able to deliver
satisfactory performance in the presence of fading and path loss.
