Effect of shadowing on outage probability in fluid cellular radio networks

We propose an adaptive model for the study of cellular networks called the fluid model, useful to each specific network environment characterized by the radio propagation (distance path-loss and shadowing) and by the network configuration. The key idea of the fluid model is to consider the discrete base stations (BS) entities as a continuum of transmitters which are spatially distributed in the network. This allows us to obtain simple analytical expressions of the main characteristics of the network. We focus on the downlink other-cell interference factor, f, which is defined here as the ratio of outer cell received power to the inner cell received power. Taking into account the shadowing, f is expressed as a lognormal random variable. Closed-form formulas of the interference factor's mean mf and standard deviation σ f are provided in this paper. From f, we are able to derive the global outage probability and the spatial outage probability, which depends on the location of a mobile station (MS) initiating a new call. Comparisons to Monte Carlo simulations are proposed, performed in a traditional hexagonal network. Although this factor has been firstly defined for CDMA networks, the analysis presented hereafter is still valid for other systems using frequency reuse 1, like OFDMA (WiMAX), TDMA (GSM with frequency hopping), or even ad hoc networks.