Analysis of Collaborative Beamforming for Wireless Sensor Networks with Phase Offset

Abstract

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, the phase ambiguity caused by carrier phase jitter or offset between the transmitter and receiver nodes always exists in a practical system. Although the effects of imperfect phase have been studied for Uniform node distribution and Tikhonov phase noise model, the performance analysis of collaborative beamforming with arbitrary node distributions and any phase offset which may have various probability density functions (PDFs) depending on phase-locked loop circuits 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 non-parametric kernel method is used to build the PDFs of node and phase offset, the proposed non-parametric approach can provide accurate performance analysis for various node and phase noise distributions which may or may not be represented by explicit PDF functions. Computer simulation is conducted to verify validity of the proposed method.