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Closed-Form Performance Bounds for Stochastic Geometry-Based Cellular Networks

In this paper, we study the performance of partial-fading and Rayleigh fading wireless networks using stochastic geometry. The aim is to provide closed-form bounds for the signal-to-interference-plus-noise ratio (SINR) distribution, average Shannon rate, and outage rate. We first characterize the SINR distribution of partial-fading channels through the Laplace transform of the inverted SINR. Since most communication systems are interference limited, we also consider the case of negligible noise power, and derive the upper and lower bounds for the signal-to-interference ratio distribution under both partial fading and fading cases. These bounds are of closed forms and thus more convenient for theoretical analysis. Based on these derivations, we obtain closed-form bounds for the average Shannon and outage rates. These results are useful for investigating the fifth-generation communication systems, for example massive multi-antenna networks as described in our illustrative example.