Decentralized Frequency Alignment for Collaborative Beamforming in Distributed Phased Arrays

A new approach to distributed synchronization (frequency alignment) for the coordination of nodes in open loop coherent distributed antenna arrays to enable distributed beamforming is presented. This approach makes use of the concept of consensus optimization among nodes without requiring centralized control. Decentralized frequency consensus can be achieved through iterative frequency exchange among nodes. We derive a model of the signal received from a coherent distributed array and analyze the effects on beamforming of phase errors induced by oscillator frequency drift. We introduce and discuss the average consensus protocol for frequency transfer in undirected networks where each node transmits and receives frequency information from other nodes. We analyze the following cases: 1) undirected networks with a static topology; 2) undirected networks with a dynamic topology, where connections between nodes are made and lost dynamically; and 3) undirected networks with oscillator frequency drift. We show that all the nodes in a given network achieve average consensus and the number of iterations needed to achieve consensus can be minimized for a given cluster of nodes. We derive the theoretical phase error resulting from both processing noise and measurement noise, and derive an optimal update interval that minimizes the error. Numerical simulations demonstrate that the consensus algorithm enables tolerable errors to obtain high coherent gain of greater than 90% of the ideal gain in an error-free distributed phased array.