  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.
