基于一致性平均和卡尔曼滤波的分布式天线阵频率和相位同步
Frequency and Phase Synchronization in Distributed Antenna Arrays Based on Consensus Averaging and Kalman Filtering
摘要：
提出了一种分布式天线阵频率和相位联合同步的分散化方法。阵列中的节点与其相邻节点共享其频率和相位，以跨阵列对齐这些参数。我们的信号模型包括本地振荡器的频率漂移和相位抖动，以及在节点处的频率和相位估计误差，并使用实际的统计数据对它们进行建模。提出了一种分散式频率和相位一致性（DFPC）算法，该算法采用平均一致性方法，阵列中的每个节点通过计算其相邻节点的频率和相位的平均值来迭代更新其频率和相位。仿真结果表明，DFPC算法收敛后，可以对齐的频率和相位的所有节点的残余相位误差，这是由振荡器和估计误差。为了减小残余相位误差，提高节点间的同步性，提出了一种基于卡尔曼滤波器的分散式频率相位一致性（KF-DFPC）算法。从理论上推导了KF-DFPC和DFPC算法收敛时的总剩余相位误差。这些算法的同步性能进行了比较，在这个理论上的残余相位误差的光通过改变信号的持续时间，节点的连接，在阵列中的节点的数量，和发送信号的信噪比。仿真结果表明，所提出的KF-DFPC算法比其他算法，包括DFPC收敛在更少的迭代。此外，对于本地信息广播之间的较短间隔，KF-DFPC算法在减小残余总相位误差方面显著优于DFPC算法，而与接收信号的信噪比无关。
英文摘要：
A decentralized approach for joint frequency and phase synchronization in distributed antenna arrays is presented. The nodes in the array share their frequencies and phases with their neighboring nodes to align these parameters across the array. Our signal model includes the frequency drifts and phase jitters of the local oscillators as well as the frequency and phase estimation errors at the nodes and models them 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 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 transmitted signals. Simulation results demonstrate that the proposed KF-DFPC algorithm converges in fewer iterations than other algorithms including DFPC. 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.
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