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In cellular networks, users are grouped into different cells and served bydifferent access points (base stations) that provide wireless access toservices and applications. In general, the service demand is veryheterogeneous, non-uniformly distributed, and dynamic. Consequently, radioaccess networks create very irregular topologies with more access points whereservice demand is concentrated. While this dynamism requires networks with theability to adapt to time-varying conditions, the non-uniformity of the servicedemand makes the planning, analysis, and optimization difficult. In order tohelp with these tasks, a framework based on canonical domains and spatialmappings (e.g., conformal mapping) have recently been proposed. The idea is tocarry out part of the planning in a canonical (perfectly symmetric) domain thatis connected to the physical one (real-scenario) by means of a spatialtransformation designed to map the access points consistently with the servicedemand. This paper continues the research in that direction by introducingadditional tools and possibilities to that framework, namely the use ofcentroidal Voronoi algorithms and non-conformal composite mappings. Moreover,power optimization is also introduced to the framework. The results show theusability and effectiveness of the proposed method and its promising researchperspectives.

Spatial Mappings for Planning and Optimization of Cellular Networks