Performance characteristics of collaborative beamforming for wireless sensor networks with Gaussian distributed sensor nodes

Collaborative beamforming has been recently introduced in the context of wireless sensor networks (WSNs) to increase the transmission range of individual sensor nodes. In this paper, it is proposed to model the spatial distribution of sensor nodes in a cluster using Gaussian probability density function (pdf). Gaussian pdf is more appropriate for many WSN applications than the previously considered uniform pdf which is more suitable when sensor nodes are deployed one at a time. The average beampattern and its characteristics, the distribution function of the beampattern level in the sidelobe region, and the upper bound on the outage probability of sidelobes are derived using the theory of random arrays.