Including the Angular Domain in the Analysis of Finite Multi-Packet Peer-to-Peer Networks with Uniformly Distributed Sources

This paper presents a mathematical framework for including the angular domain beside the radial one in the theoretical modeling of wireless networks, in which spatial reuse enables the coexistence of multiple single-hop peer-to-peer communications inside a finite region. The proposed model analyzes a scenario where the transmitting sources are uniformly distributed over a disk and the communications are subjected to path-loss attenuation and multipath-fading, considering the actual location of each destination and its antenna system. Different from most of the previous theories in which the coverage probability of a destination is estimated assuming that the destination itself is positioned at the center of the network, in the proposed analysis, the destination location is generic. This generalization, together with the consideration of the spatial channel model and of the actual receiving pattern, allows one to investigate the influence of the angular domain on the statistic of the interference power and on the coverage probability. The conceived theory, which is further verified by Monte Carlo validations, is finally exploited to derive the network transmission capacity, with the purpose to illustrate the possible advantages that may derive from a reliable modeling of the non-isotropic context, in which each destination has to operate realistically.