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This paper develops a stochastic geometry-based approach for the modeling and analysis of finite millimeter wave (mmWave) wireless networks where a random number of transmitters and receivers are randomly located inside a finite region. We consider a selection strategy to serve a reference receiver by the transmitter providing the maximum average received power among all transmitters. In our system model, we employ the unique features of mmWave communications such as directional transmit and receive beamforming and different channels for line-of-sight (LOS) and non-line-of-sight (NLOS) links. Accordingly, deploying a blockage process suitable for mmWave networks, we study the coverage probability and the ergodic rate for the reference receiver that can be located everywhere inside the network region. As key steps for the analyses, the distribution of the distance from the reference receiver to its serving LOS or NLOS transmitter and LOS and NLOS association probabilities are derived. We also derive the Laplace transform of the interferences from LOS and NLOS transmitters. Finally, we propose upper and lower bounds on the coverage probability that can be evaluated easier than the exact results, and investigate the impact of different parameters including the receiver location, the beamwidth, and the blockage process exponent on the system performance.

Stochastic Geometry Modeling and Analysis of Finite Millimeter Wave Wireless Networks