Coverage Analysis of Distributed Beamforming With Random Phase Offsets Using Ginibre Point Process

In this paper, we study a wireless network where multiple distributed transmitters control the phases of their signals so that they can be constructively combined at a client receiver. Unlike centralized beamforming with co-located and phase-synchronized antennas, geographically separated transmitters experience phase offsets caused by the individual local oscillators. In practical scenarios, the transmitters should not be placed too close to each other in order to alleviate mutual coupling effects and extend the coverage region. In this regard, we model the spatial distribution of the transmitters as a β -Ginibre point process that models the repulsive feature. We investigate two types of transmission strategies: (i) Transmitter selection in which the client selects the transmitter providing the highest received power at the client, and (ii) Coherent beamforming in which multiple transmitters send their signals simultaneously to the client in the presence of phase offsets among the transmitters. We introduce the exact expression of the coverage probability of the transmitter selection method. Also, we derive an approximation of the coverage probability of the coherent beamforming scheme by leveraging two scaling factors that respectively capture the impacts of the phase offsets and the degree of repulsion on the coverage probability. From numerical simulations, we validate the accuracy of our analysis.