Studying the SINR process of the typical user in Poisson networks by\n using its factorial moment measures

Abstract

Based on a stationary Poisson point process, a wireless network model with\nrandom propagation effects (shadowing and/or fading) is considered in order to\nexamine the process formed by the signal-to-interference-plus-noise ratio\n(SINR) values experienced by a typical user with respect to all base stations\nin the down-link channel. This SINR process is completely characterized by\nderiving its factorial moment measures, which involve numerically tractable,\nexplicit integral expressions. This novel framework naturally leads to\nexpressions for the k-coverage probability, including the case of random SINR\nthreshold values considered in multi-tier network models. While the k-coverage\nprobabilities correspond to the marginal distributions of the order statistics\nof the SINR process, a more general relation is presented connecting the\nfactorial moment measures of the SINR process to the joint densities of these\norder statistics. This gives a way for calculating exact values of the coverage\nprobabilities arising in a general scenario of signal combination and\ninterference cancellation between base stations. The presented framework\nconsisting of mathematical representations of SINR characteristics with respect\nto the factorial moment measures holds for the whole domain of SINR and is\namenable to considerable model extension.\n