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

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