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. The challenge in using collaborative beamforming in WSNs is the uncertainty regarding the sensor node locations. However, the actual sensor node spatial distribution can be modeled by a properly selected probability density function (pdf). In this paper, we model the spatial distribution of sensor nodes in a cluster of WSN using Gaussian pdf. Gaussian pdf is more suitable in many WSN applications than, for example, uniform pdf which is commonly used for flat ad hoc networks. The average beampattern and its characteristics, the distribution of the beampattern level in the sidelobe region, and the distribution of the maximum sidelobe peak are derived using the theory of random arrays. We show that both the uniform and Gaussian sensor node deployments behave qualitatively in a similar way with respect to the beamwidths and sidelobe levels, while the Gaussian deployment gives wider mainlobe and has lower chance of large sidelobes.