Frequency and Phase Synchronization in Distributed Antenna Arrays Based on Consensus Averaging and Kalman Filtering

A decentralized approach for joint frequency and phase synchronization in distributed antenna arrays is presented. The nodes in the array locally broadcast their frequencies and phases to their neighboring nodes, and use consensus averaging to align these parameters across the array. The architecture is fully distributed, requiring no centralization. Each node has a local oscillator and we consider a signal model where intrinsic frequency and phase errors of the local oscillators on each node caused by the frequency drift and phase jitter as well as the frequency and phase estimation errors at the nodes are included and modeled using practical statistics. A decentralized frequency and phase consensus (DFPC) algorithm is proposed which uses an average consensus method in which each node in the array iteratively updates its frequency and phase by computing an average of the frequencies and phases of their neighboring nodes. Simulation results show that upon convergence the DFPC algorithm can align the frequencies and phases of all the nodes up to a residual phase error that is governed by the oscillators and the estimation errors. To reduce this residual phase error and thus improve the synchronization between the nodes, a Kalman filter based decentralized frequency and phase consensus (KF-DFPC) algorithm is presented. The total residual phase error at the convergence of the KF-DFPC and DFPC algorithms is derived theoretically. The synchronization performances of these algorithms are compared to each other and to the diffusion least mean square (DLMS), the diffusion KF (DKF) algorithm, and the Kalman consensus information filter (KCIF) algorithms, in light of this theoretical residual phase error by varying the duration of the signals, connectivity of the nodes, the number of nodes in the array, and signal to noise ratio of the received signals. Simulation results demonstrate that under certain conditions the proposed KF-DFPC algorithm outperforms and converges in fewer iterations than all the algorithms. Furthermore, for shorter intervals between local information broadcasts, the KF-DFPC algorithm significantly outperforms the DFPC algorithm in reducing the residual total phase error, irrespective of the signal to noise ratio of the received signals.