A closed-form expression for coverage probability of random cellular network in composite Rayleigh-Lognormal fading channels

Poisson point process (PPP) network model in which base stations (BSs) and users have Poisson distributions has been recently used to replace grid model for analyzing the performance of cellular networks. The closed-form for the coverage probability of a typical user that connects to the closest base station (BS), however, is only found in case of high transmission signal-to-noise (SNR) and only in Rayleigh fading. This paper derives a closed-form expression for the network coverage probability in composite Rayleigh-Lognormal for both low and high SNR. The analytical results show that the coverage probability is proportional to path loss exponent coefficient, and inversely proportional to exponential function of 1 over SNR. The analytical results are also verified by Monte Carlo simulations.