Looking at Cellular Networks Through Canonical Domains and Conformal Mapping

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 nonuniform service demand, network deployments are becoming increasingly irregular. This paper introduces a new idea to deal with the nonuniform network topology. Rather than capturing the network character (e.g., load distribution) by means of stochastic methods, the proposed novel approach aims at transferring the analysis from the physical (irregular) domain to a canonical/dual domain that simplifies the work due to its symmetry. To carry out this task, physical and canonical domains are connected using conformal (Schwarz-Christoffel) mapping, a rich and mature theory from complex analysis. Thus, the main contribution of this paper is to introduce the analysis through canonical domains and validate the usability of conformal mapping as a feasible solution approach for this problem.