Effect of Frequency Offset on Collaborative Beamforming of UAV Swarm in Space-Air-Ground Integrated Networks

The space-air-ground integrated networks (SAGNs) are promising components of the next generation communication system, and unmanned aerial vehicle (UAV) swarms are the primary infrastructures of the SAGNs aerial layer, used for relaying information. Furthermore, UAV swarms form virtual antenna arrays (VAAs) and implement collaborative beamforming (CB), which can improve the deep-space communication distance and expand the ground coverage. However, in practical engineering, due to the doppler effect and local oscillator random frequency drift, there is a frequency offset between UAVs, even after frequency synchronization, resulting in CB performance degradation. Therefore, in the presence of frequency offset, this paper investigates and presents the derivation of the average far-field beampattern, 3-dB beamwidth, and complementary cumulative distribution function (CCDF) for UAV swarm executing CB in SAGNs. The results show that the average far-field beam-pattern, peak power, 3-dB beamwidth, and CCDF, deteriorate as frequency offset intensifies. Furthermore, as the UAV swarm scale increases, the peak power attenuation is aggravated, and the decrease in CCDF is steeper. With the increase in the UAV swarm distribution range, the 3-dB beamwidth expansion is alleviated.