Robust Beampattern Synthesis for UAV-Swarm-Based Distributed Beamforming

W. Jeremy Morrison, Todd E. Humphreys, and Dao A. Ton-Nu

Abstract:	Distributed and collaborative beamforming (DCBF) combines the inputs or outputs of antennas that are not physically connected and do not share a common clock. In DCBF, the coherent combination of antenna signals hinges on fractional wavelength positioning knowledge of participating antennas and precise timing synchronization of participating radios. When beamforming with antennas located on dynamic vehicles, the antennas’ locations will not be perfectly known and will experience perturbations, motivating a characterization of the resulting beampattern’s statistical properties. This statistical analysis has been lacking from prior work. In this paper, prior work’s derivations for the expected value and variance of the array factor equation are expanded to include arbitrary Gaussian covariances for each antenna’s position. A UAV-based DCBF simulation model is introduced as an example of dynamic distributed arrays and used for numeric statistical beampattern analysis. The difficulties of beampattern synthesis are discussed and an algorithm for beampattern synthesis is presented using particle swarm optimization. It is shown that beamforming is impossible if the standard deviation of antenna positions exceeds 0.4 wavelengths due to randomly induced phase shifts. If standard deviations are non-identical in the three dimensions, beampattern control will be greater along dimensions with more precise positioning knowledge. The number of participating antennas also impacts the beampattern’s stability, with the pattern becoming more stable as antennas are added to the array. It is also shown that using carrier-phase differential GNSS (CDGNSS) to determine the relative positions of antennas enables DCBF for C-band frequencies and below. A timing synchronization method is introduced that leverages the fractional-wavelength CDGNSS positioning estimates. This method’s coupling of positioning and timing errors is discussed. Lastly, a mitigation technique for vehicle positional perturbations is presented and implemented in simulation, demonstrating successful stabilization of the array’s beampattern despite such perturbations.
Published in:	Proceedings of the 37th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2024) September 16 - 20, 2024 Hilton Baltimore Inner Harbor Baltimore, Maryland
Pages:	2754 - 2765
Cite this article:	Morrison, W. Jeremy, Humphreys, Todd E., Ton-Nu, Dao A., "Robust Beampattern Synthesis for UAV-Swarm-Based Distributed Beamforming," Proceedings of the 37th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2024), Baltimore, Maryland, September 2024, pp. 2754-2765. https://doi.org/10.33012/2024.19729
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