Coverage Analysis for Millimeter Wave Cellular Networks With Imperfect Beam Alignment

Millimeter wave (mmWave) communications is a promising approach to satisfy the increasing high data rate requirement of next generation mobile communications. This paper studies the downlink coverage performance of mmWave cellular networks with imperfect beam alignment. An enhanced antenna model is adopted to model the directional antenna beamforming pattern, in which the mainlobe beamwidth and directivity gain can be expressed as functions of the number of elements in the antenna array. After deriving the probability density function of the distance between mobile station and its serving base station (BS), the directivity gain with imperfect beam alignment is obtained as a discrete random variable. Then, a computationally tractable expression is obtained for the coverage probability of mmWave cellular networks. This generalized expression can be applied in different blockage regimes, e.g., general blockage regime, full-blockage regime, and nonblockage regime with or without beam alignment errors. Numerical results show that small beam alignment errors will not deteriorate the coverage performance significantly, and the antenna array with the less number of elements provides higher robustness against the beam alignment errors. Moreover, when the beam alignment error is small enough, the coverage performance can be improved by increasing the BS intensity and the number of elements in the antenna array.