Binary Consensus Over Fading Channels

In this paper, we consider a cooperative network that is trying to reach consensus on the occurrence of an event, by communicating over time-varying network topologies with fast fading channels. We mathematically characterize both the asymptotic and transient behaviors of the network. We show that the network converges to a memoryless state asymptotically, which is undesirable. However, the network can still be in consensus for a long period of time. In order to characterize the transient behavior, we then derive a tight approximation for the second largest eigenvalue of the underlying average probability transition matrix in fading environments. We show the impact of channel unreliability and network topology on consensus performance and shed light on the underlying tradeoffs in terms of speed of convergence and memoryless asymptotic behavior.