Simple Approximations of the SIR Meta Distribution in General Cellular Networks

Sanket Sanjay Kalamkar (1) , Martin Haenggi (2)

1 DYOGENE - Dynamics of Geometric Networks
2 UND - University of Notre Dame [Indiana]

Compared to the standard success (coverage) probability , the meta distribution of the signal-to-interference ratio (SIR) provides much more fine-grained information about the network performance. We consider general heterogeneous cellular networks (HCNs) with base station tiers modeled by arbitrary stationary and ergodic non-Poisson point processes. The exact analysis of non-Poisson network models is notoriously difficult, even in terms of the standard success probability, let alone the meta distribution. Hence we propose a simple approach to approximate the SIR meta distribution for non-Poisson networks based on the ASAPPP ("approximate SIR analysis based on the Poisson point process") method. We prove that the asymptotic horizontal gap $G_0$ between its standard success probability and that for the Poisson point process exactly characterizes the gap between the $b$th moment of the conditional success probability, as the SIR threshold goes to 0. The gap $G_0$ allows two simple approximations of the meta distribution for general HCNs: 1) the per-tier approximation by applying the shift $G_0$ to each tier and 2) the effective gain approximation by directly shifting the meta distribution for the homogeneous independent Poisson network. Given the generality of the model considered and the fine-grained nature of the meta distribution, these approximations work surprisingly well.

Mots clés: Stochastic geometry; Interference; Heterogeneous cellular networks; Meta distribution; Poisson point process; Signal-to-interference ratio

Domaines: Informatique [cs]; Théorie de l'information [cs.IT]; Réseaux et télécommunications [cs.NI]

Sanket Sanjay Kalamkar, Martin Haenggi. Simple Approximations of the SIR Meta Distribution in General Cellular Networks. IEEE Transactions on Communications, 2019, 67 (6), pp.4393-4406. ⟨10.1109/TCOMM.2019.2900676⟩. ⟨hal-02417353⟩