Beampattern Analysis of Uplink Cooperative Beamforming of UAV Swarm to LEO Satellite

Cooperative beamforming (CB) is a promising approach to improve the communication range of nodes constrained by hardware limitations. It is a technique in which multiple spatially separated nodes synchronize the transmission phase to optimize the power of the collective signal at the target receiver. The integration of Low Earth orbit (LEO) satellite communications with various aerial platforms is expected to redefine global connectivity for sixth-generation (6G) cellular networks. However, the high mobility of LEO satellites induces Doppler shifts, resulting in frequency offsets (FOs) in CB. In this paper, we consider a uplink transmission of multiple UAVs through CB, where the UAVs are widely dispersed in a three-dimensional (3D) space. We show that the received signal at the LEO satellite may suffer from residual frequency offsets (FOs), even when the satellite applies the FO compensation for the Doppler shift based on the relative speed variation between the center of the UAV cluster and itself, because of spatial dispersion of the UAV swarm. Motivated by this issue, this paper examines the impact of such FOs (or residual Doppler) on the CB performance, focusing on the beampattern analysis.