Meta Distribution of SIR in Ultra-Dense Networks with Bipartite Euclidean Matchings
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Ultra-dense networks maximise spatial spectral efficiency through spatial reuse. The way in which their dense limit is approached is difficult to understand mathematically, because the Euclidean combinatorial theory, despite being simple to state, is often difficult to work with, and often involves a stochastic model. Small changes in the way these models are defined can make significant differences to the qualitative properties of their predictions, such as concerning the meta distribution of the SIR, the data capacity, or their efficiency. In this paper we focus on triangular correlations and variable link distances in Euclidean space, addressing critical assumptions which are introduced in more elementary models. We study a bipartite Euclidean matching in order to study how incorporating geometric frustration leads to variation in the statistics of the meta distribution of the signal-to-interference ratio compared to these simplified models, comparing with the bipolar or downlink cellular networks studied by Haenggi and others.
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