A Two-Tone Frequency Hopping Waveform for Decentralized Consensus-Based Joint Frequency and Phase Alignment in Distributed Antenna Arrays

Wireless alignment of the frequencies and phases of the antenna elements in a distributed antenna array is necessary to ensure high-gain distributed beamforming, as well as to achieve improved system gain, adaptability, and robustness to failures. However, the increase in the density of wireless systems every year is creating less spectrum availability and more interference for the operation of other wireless technologies. Specifically, such interference can degrade the ability to coordinate the nodes in a distributed array, which must align their electrical states to the wavelength level using wireless connectivity. In this work, we propose to use a spectrally-sparse and frequency-diverse two-tone waveform that hops between different subbands over the broadcast to mitigate the impact of interference on the array synchronization. A decentralized electrical state (frequency and phase) synchronization scheme is proposed, in which the two-tone waveform is iteratively broadcasted between the neighboring nodes by modulating the signal onto different carrier frequencies over the iterations, and where the frequency and phase of the local oscillator of each node are encoded in the difference between the frequencies and phases of the individual tones. Nodes implement an iterative average consensus algorithm, in which they first recover the states of the neighboring nodes from their observed signals, compute an average of the locally observed values, and then update the difference in frequencies and phases of their two tones to match the average value. This process is repeated iteratively at each node, resulting in synchronizing the array to a small residual phase error within a few iterations. Simulation results are included where the performance of the proposed scheme is analyzed by varying the connectivity of the array, the update interval, and the bandwidth of the two-tone waveform.