The Effect of Local Scattering on the Gain and Beamwidth of a Collaborative Beampattern for Wireless Sensor Networks

Collaborative beamforming is an approach where sensor nodes in a wireless sensor network, deployed randomly in an area of interest, transmit a common message by forming a beampattern towards a destination. Previous statistical analysis of the averaged power beampattern considered multipath-free conditions. Herein, we express the averaged power beampattern when the signal is observed at the destination in the presence of local scattering. Assuming the spreading angles are uniformly distributed around the destination direction, we derive closed-form expressions for the maximum gain and numerically examine the beamwidth as a function of the number of nodes, the cluster size, and the scattering parameters, for node positions with a uniform distribution or a Gaussian distribution.