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Canonical domains for cellular networks: Analysis of the one-dimensional case

From its origins, cellular networks have been in constant evolution. Nowadays, real-world deployments admit very irregular network topologies in order to satisfy nonuniformly distributed service demands, i.e., there are small cells in areas where users are concentrated. This makes the planning, analysis, and optimization of such irregular topologies difficult. Methods based on stochastic geometry have been proposed and successfully used to capture some characters of this heterogeneity; and recently, the analysis based on canonical domains and spatial transformations has also been proposed as a complementary tool to aid in network planning and optimization tasks. The key idea is to simplify the analysis by using a dual/canonical domain that is perfectly symmetric and homogeneous. Unfortunately, yet expected, these synthetic models have fallen into disuse as they cannot capture the heterogeneity of the increasingly complex real-world deployments. However, the introduction of the aforementioned framework creates an opportunity to revisit these reference models and to study them from several new points of view. In addition, the one-dimensional network model fits with several relevant study items, such as Intelligent Transportation Systems and road-side deployments. The contribution of this paper is to present the analysis of the one-dimensional canonical domain (and several applications of it) as an initial effort to pave the way towards further generalizations, such as the challenging two-dimensional case.