Fundamentals of Modeling Finite Wireless Networks Using Binomial Point Process

Modeling the locations of nodes as a uniform binomial point process, we present a generic mathematical framework to characterize the performance of an arbitrarily located reference receiver in a finite wireless network. Different from most of the prior works where the serving transmitter (TX) is located at the fixed distance from the reference receiver, we consider two general TX-selection policies: 1) uniform TX-selection: the serving node is chosen uniformly at random from amongst all transmitting nodes and 2) k-closest TX-selection: the serving node is the kth closest node (out of all transmitting nodes) to the reference receiver. The key intermediate step in our analysis is the derivation of a new set of distance distributions that lead not only to the tractable analysis of coverage probability but also enable the analysis of wide range of classical and currently trending problems in wireless networks. Using this new set of distance distributions, we further investigate the diversity loss due to SIR correlation in a finite network. We then obtain the optimal number of links that can be simultaneously activated to maximize network spectral efficiency. Finally, we evaluate optimal caching probability to maximize the total hit probability in cache-enabled finite networks.