Binary Consensus Over Fading Channels

Abstract

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.

An integrated diversity and fusion framework for binary consensus over fading channels

“…We showed that by incorporating the information of link qualities, the network will be in consensus with a higher probability but still holds the undesirable asymptotic behavior. In [11], we considered binary consensus over rapidly changing network topologies with fading channels. We mathematically characterized the impact of fading, noise, network connectivity and time-varying topology on consensus performance.…”

“…We study two decision-making strategies that differ in terms of using the available transmissions: fusion and diversity. In the first strategy, the given resources are used to increase the flow of information in the network, whereas the second strategy aims to increase robustness to link error by channel coding [11]. We characterize the underlying trade-offs between these two strategies for binary consensus over a not fully connected and time-invariant network topology.…”

“…In section III-B of [11], we mathematically analyzed the asymptotic behavior of the basic BAE for binary consensus over fully connected network topology. We showed that the network loses its memory of the initial state asymptotically due to the impact of link errors, which is undesirable.…”

Binary consensus through binary communication

“…The performance of such a binary consensus protocol for a fully connected network in the presence of Gaussian communication noise is considered in [9]. Extensions of the binary consensus protocol of [9] to accommodate for noise and link qualities are given in [10]- [12] and the fully connected network assumption is relaxed in [13]. Application of a binary consensus protocol for distributed detection of primary users in cognitive radio networks is presented in [14].…”

“…Traditionally, average consensus algorithms are based on local disagreement between nodes [17], [18], while the binary consensus protocols are based on the local average among the nodes [9], [13]. The proposed binary consensus protocol involves an internal learning state associated with each node whose values are updated based on both local disagreement and local average of the binary votes.…”