Binary Consensus over Fading Channels: A Best Affine Estimation Approach

In this paper we consider a cooperative network that is trying to reach binary consensus over fading channels. We first characterize the impact of fading on network consensus by upper bounding the second largest eigenvalue of the underlying probability transition matrix in fading environments. Using the information of link qualities, we then propose a novel consensus-seeking protocol based on the best affine estimation of network state. We characterize the performance of our proposed strategy mathematically. We derive an approximated expression for the second largest eigenvalue in order to characterize the convergence rate. Our results show the impact of fading on network consensus. They furthermore indicate that the proposed technique can improve the consensus performance considerably.