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We consider the problem of decentralized frequency and phase synchronizationin distributed phased arrays via local broadcast of the node electrical states.Frequency and phase synchronization between nodes in a distributed array isnecessary to support beamforming, but due to the operational dynamics of thelocal oscillators of the nodes, the frequencies and phases of their outputsignals undergo the random drift and jitter in between the update intervals.Furthermore, frequency and phase estimation errors contribute to the totalphase errors, leading to a residual phase error in the array that degradescoherent operation. Recently, a classical decentralized frequency and phasesynchronization algorithm based on consensus averaging was proposed with whichthe standard deviation of the residual phase errors upon convergence wasreduced to $10^{-4}$ degrees for internode update intervals of $0.1$ ms,however this was obtained for arrays with at least $400$ nodes and a highconnectivity ratio of $0.9$. In this paper, we propose a message passing basedaverage consensus (MPAC) algorithm to improve the synchronization of theelectrical states of the nodes in distributed arrays. Simulation results showthat the proposed MPAC algorithm significantly reduces the residual phaseerrors to about $10^{-11}$ degrees, requiring only $20$ moderately connectednodes in an array. Furthermore, MPAC converges faster than the DFPC-basedalgorithms, particularly for the larger arrays with a moderate connectivity.

A Message Passing Based Average Consensus Algorithm for Decentralized Frequency and Phase Synchronization in Distributed Phased Arrays