Beampattern analysis of cooperative beamforming with carrier frequency offsets in three-dimensional wireless networks

Cooperative beamforming (CB), where spatially distributed nodes synchronize their transmit phases to maximize the power of their combined signal at a desired receiver, can be used as an effective solution for hardware-limited nodes to achieve communication range extension. Thus, CB demonstrates effectiveness in providing higher reliability, lower latency, and extended transmission range for nodes in non-terrestrial networks (NTNs), which inherently face power and hardware limitations. In this paper, we consider the CB technique using UAVs in three-dimensional (3D) networks and analyze the average beampattern of the virtual antenna array constructed by the multiple UAVs. Further, because the mobile nature of the UAVs may cause carrier frequency offsets (CFOs), we analyze the impact of the CFO using the non-parametric kernel method. The simulation and analytical results show that the peak average beampattern degrades by about 3 dB with the CFO standard deviation of 1 kHz, which emphasizes the significance of frequency synchronization.