Interference in Poisson Networks with Isotropically Distributed Nodes

TL;DR

This paper models interference in finite, non-stationary wireless networks with isotropic node distributions, providing precise characterizations of interference and boundary effects for practical network analysis.

Contribution

It introduces a novel interference model for isotropic, non-stationary Poisson networks, deriving closed-form expressions and bounds for key interference metrics.

Findings

Boundary effects significantly impact network performance.

Closed-form interference expressions are derived for specific path loss exponents.

Neglecting border effects can lead to substantial accuracy loss.

Abstract

Practical wireless networks are finite, and hence non-stationary with nodes typically non-homo-geneously deployed over the area. This leads to a location-dependent performance and to boundary effects which are both often neglected in network modeling. In this work, interference in networks with nodes distributed according to an isotropic but not necessarily stationary Poisson point process (PPP) are studied. The resulting link performance is precisely characterized as a function of (i) an arbitrary receiver location and of (ii) an arbitrary isotropic shape of the spatial distribution. Closed-form expressions for the first moment and the Laplace transform of the interference are derived for the path loss exponents $\alpha=2$ and $\alpha=4$, and simple bounds are derived for other cases. The developed model is applied to practical problems in network analysis: for instance, the accuracy loss due to neglecting border effects is shown to be undesirably high within transition regions of certain deployment scenarios. Using a throughput metric not relying on the stationarity of the spatial node distribution, the spatial throughput locally around a given node is characterized.