Characteristics of collaborative beamforming for wireless sensor networks in phase noise environments

Collaborative beamforming has been widely used in wireless sensor networks to improve the directivity of signals in long-distance transmission. The performance of collaborative beamforming has been well analyzed for the case without phase offset in the literature. However, there always exists the phase ambiguity caused by carrier phase jitter between the transmitter and receiver nodes in a practical system. Although the effects of imperfect phase have been studied for Uniform node distribution and Tikhonov phase noise distribution, the performance analysis of collaborative beamforming with arbitrary node distributions and any phase offset is still an open issue. This paper proposes a unified method to evaluate the performance of collaborative beamforming in the case of phase noise. Since the non-parametric kernel method is used to build the probability density functions of node and phase offset distributions, the proposed non-parametric approach can provide accurate performance analysis for various node and phase noise distributions. The simulation results verify the proposed method.