On the Joint Impact of Beamwidth and Orientation Error on Throughput in Directional Wireless Poisson Networks

Abstract

We introduce a model for capturing the effects of beam misdirection on coverage and throughput in a directional wireless network using stochastic geometry. In networks employing ideal sector antennas without sidelobes, we find that concavity of the orientation error distribution is sufficient to prove monotonicity and quasi-concavity (both with respect to antenna beamwidth) of spatial throughput and transmission capacity, respectively. Additionally, we identify network conditions that produce opposite extremal choices in beamwidth (absolutely directed versus omni-directional) that maximize the two related throughput metrics. We conclude our paper with a numerical exploration of the relationship between mean orientation error, throughput-maximizing beamwidths, and maximum throughput, across radiation patterns of varied complexity.