A Tractable Closed-Form Approximation of the Ergodic Rate in Poisson Cellular Networks

TL;DR

This paper introduces a precise approximation for the MGF of aggregate interference in Poisson cellular networks, enabling closed-form ergodic capacity expressions that facilitate network densification analysis and optimization.

Contribution

It provides a novel, accurate closed-form approximation for the interference MGF, simplifying stochastic geometry analysis of dense cellular networks.

Findings

The approximation closely matches Monte Carlo simulations.

Closed-form ergodic capacity expressions depend on user and base station densities.

Results offer practical insights for network densification strategies.

Abstract

The employment of stochastic geometry for the analysis and design of ultra dense networks (UDNs) has provided significant insights into network densification. In addition to the characterization of the network performance and behavior, these tools can also be exploited toward solving complex optimization problems that could maximize the capacity benefits arising in UDNs. However, this is preconditioned on the existence of tractable closed form expressions for the considered figures of merit. In this course, the present paper introduces an accurate approximation for the moment generating function (MGF) of the aggregate other-cell interference created by base stations whose positions follow a Poisson point process of given spatial density. Given the pivotal role of the MGF of the aggregate interference in stochastic geometry and the tractability of the derived MGF, the latter can be employed to substantially simplify ensuing stochastic geometry analyses. Subsequently, the present paper employs the introduced MGF to provide closed form expressions for the downlink ergodic capacity for the interference limited case, and validates the accuracy of these expressions by the use of extensive Monte Carlo simulations. The derived expressions depend on the density of users and base stations, setting out a densification road map for network operators and designers of significant value.