Looking at Cellular Networks Through Canonical Domains and Conformal Mapping

TL;DR

This paper proposes a novel approach using conformal mapping to transform irregular cellular network topologies into uniform canonical domains, simplifying load analysis and improving network planning efficiency.

Contribution

It introduces and validates the use of conformal (Schwarz-Christoffel) mapping for analyzing non-uniform cellular network topologies, bridging complex analysis with network planning.

Findings

Conformal mapping effectively transforms irregular network domains into uniform ones.

The approach simplifies load coupling analysis in cellular networks.

Validation shows improved understanding of non-uniform network behavior.

Abstract

In order to cope with the rapidly increasing service demand in cellular networks, more cells are needed with better resource usage efficiency. This poses challenges for the network planning since service demand in practical networks is not geographically uniform and, to cope with the non-uniform service demand, network deployments are becoming increasingly irregular. This paper introduces a new idea to deal with the non-uniform network topology. Rather than capturing the network character (e.g. load distribution) by means of stochastic methods, the proposed novel approach aims at transforming the analysis from the physical (irregular) domain to a canonical/dual (uniform) domain that simplifies the work due to its symmetry. To carry out this task, physical and canonical domains are connected using the conformal (Schwarz-Christoffel) mapping, that makes the rich and mature theory of Complex Analysis available. The main contribution of this paper is to introduce and validate the usability of conformal mapping in the load coupling analysis of cellular networks.