Performance Analysis of Distributed Beamforming With Random Phase Offsets

In this paper, we investigate a wireless network where multiple distributed transmitters adjust the phases of their signals so that they can be constructively added at an intended receiver (client). Unlike conventional beamforming with co-located and phase-synchronized antennas, geographically separated transmitters may have phase offsets induced by individual local carrier oscillators, that pose a challenge for coherent distributed beamforming. This is especially true for transmitters that are far apart, when distributed clock synchronization protocols may be more difficult to implement. There may also be a desired spatial repulsion among the positions of the transmitters in order to mitigate mutual coupling effects and extend the coverage region. In this regard, we analyze the performance of distributed beamforming with phase offsets by modeling the spatial distribution of the transmitters as a $\beta$-Ginibre point process that models the repulsive behavior. We consider two transmission strategies: (i) Transmitter selection in which the client chooses the transmitter providing the highest received power at the client, and (ii) Coherent beamforming in which multiple transmitters simultaneously send their signals to the client. From numerical simulations, we examine the impact of the phase offsets on the performance and confirm the accuracy of our analysis. It is shown that even with significant phase offset errors, employing coherent beamforming can be an effective strategy.