Optimal topology design for energy efficient consensus in broadcast wireless sensor networks

Average consensus algorithms are an essential tool in wireless sensor networks for multiple estimation tasks, being the convergence time and the energy consumption of these algorithms critical for their usability. Most existing work in the related literature focuses on improving these two parameters, assuming generally unicast communications, which are neither realistic nor efficient given the wireless nature of these networks. Instead, broadcast communications allow a greater instantaneous exchange of information between the network nodes, accelerating the consensus and saving energy in communications. In this work, we propose two methods that optimize the network topology to simultaneously improve the total power consumption per iteration, the maximum power consumption per node and the convergence time in a broadcast scenario. The first method is applied to continuous systems, while the second one is more suitable for discrete systems. Numerical results are presented to show the validity and efficiency of the proposed methods.