Impact of the geometry, path-loss exponent and random shadowing on the mean interference factor in wireless cellular networks

The interference factor, defined for a given location in the network as the ratio of the sum of the path-gains form interfering base-stations (BS) to the path-gain from the serving BS is an important ingredient in the analysis of wireless cellular networks. It depends on the geometric placement of the BS in the network and the propagation gains between these stations and the given location. In this paper we study the mean interference factor taking into account the impact of these two elements. Regarding the geometry, we consider both the perfect hexagonal grid of BS and completely random Poisson pattern of BS. Regarding the signal propagation model, we consider not only a deterministic, signal-power-loss function that depends only on the distance between a transmitter and a receiver, and is mainly characterized by the so called path-loss exponent, but also random shadowing that characterizes in a statistical manner the way various obstacles on a given path modify this deterministic function. We present a detailed analysis of the impact of the path loss exponent, variance of the shadowing and the size of the network on the mean interference factor in the case of hexagonal and Poisson network architectures. We observe, as commonly expected, that small and moderate shadowing has a negative impact on regular networks as it increases the mean interference factor. However, as pointed out in the seminal paper [16], this impact can be largely reduced if the serving BS is chosen as the one which offers the smallest path-loss. Revisiting the model studied in this latter paper, we obtain a perhaps more surprising result saying that in large irregular (Poisson) networks the shadowing does not impact at all the interference factor, whose mean can be evaluated explicitly in a simple expression depending only on the path-loss exponent. Moreover, in small and moderate size networks, a very strong variability of the shadowing can be even beneficial in both hexagonal and Poisson networks.