Power-delay analysis of consensus algorithms on wireless networks with interference

Abstract

We study the convergence of the average consensus algorithm in wireless networks in the presence of interference. For regular lattices with periodic boundary conditions, we characterise the convergence properties of an optimal Time Division Multiple Access (TDMA) protocol that maximises the speed of convergence on these networks. We provide analytical upper and lower bounds for the convergence rate for these networks. Our results show that in an interference-limited scenario, the fastest converging interconnection topology for the consensus algorithm crucially depends on the geometry of node placement. In particular, we prove that asymptotically in the number of nodes, increasing the transmit power to allow long-range interconnections improves the convergence rate in one-dimensional tori, while it has the opposite effect in higher dimensions.