Asymmetric Mixing Matrix Optimization for Faster Average Consensus in Wireless Sensor Networks

Achieving fast and accurate average consensus is pivotal for numerous collaborative tasks in wireless sensor networks (WSNs). Towards this end, this paper explores the design of asymmetric mixing matrices for achieving faster average consensus rate in WSNs. We firstly demonstrate that the optimal symmetric mixing matrices may achieve much slower consensus rate compared to an asymmetric mixing matrix, and formulate the design of the asymmetric mixing matrix as a non-convex spectral radius minimization problem. To address this challenge, a locally optimal iterative spectral norm-based method is proposed. Furthermore, to reduce the computational complexity while maintaining an acceptable level of performance gains, we also introduce two suboptimal methods based on the Frobenius norm and the numerical radius upper bounds, respectively. Through extensive simulation results across both fixed and random network topologies, we demonstrate that our proposed asymmetric schemes outperform existing benchmark optimal symmetric and best constant schemes in terms of the spectral radius and the consensus time performance.