Rate Meta-distribution in mmW D2D Networks with Beam Misalignment

This paper studies the coverage performance of device-to-device (D2D) communication under the millimeter wave (mmW) spectrum. The transmitter and receiver sides of users are equipped with directional antennas and adopt beamforming (BF). By considering a truncated Gaussian misalignment assumption, we derive computationally tractable expressions of the conditional rate coverage probability's moments as a function of the number of antenna elements. The Beta approximation of the rate meta-distribution is obtained based on the first and the second moment. The numerical simulations confirm our analytical results. They show that the coverage performance can deteriorate significantly due to misalignment. Furthermore, an optimal number of antenna elements must be chosen to get the best coverage. In addition, there exists an optimal number of antennas which maximizes the number of users who satisfy the reliability constraints. This optimal value is a function of the reliability threshold.