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Coverage and Meta Distribution Analysis in Ultra-Dense Cellular Networks with Directional Antennas

This paper proposes a one-tier ultra-dense cellular network framework based on the characteristics of directional beamforming to explore the downlink signal-to-interference ratio (SIR) performance. The features of the proposed cellular network include: small base stations (SBSs) are equipped with directional antennas; the beam boresight directions of antennas are adaptively adjusted with the locations of users on the two-dimensional horizontal plane while the boresight directions are perfectly aligned with their associated users. In addition, an angle fading model, which follows from the exponential distribution, is developed to simulate the signals attenuation of interference links. The angle fading of the interference signals depends on the angle offset between the locations of users and the beam boresight directions of their interfering SBSs. With the assistance of stochastic geometry, the analytical expressions of coverage probability and average ergodic rate are derived by combining with the probability density function of angle offset variable. Then, the meta distribution of SIR is obtained to capture the performance changes of individual links for users. The numerical results indicate that the performance advantages of the proposed directional network obviously exceed that of the conventional isotropic antennas case. Monte-Carlo simulations validate the correctness of numerical results.