Simple Approximations of the SIR Meta Distribution in General Cellular Networks

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.Comment: This paper has been accepted in the IEEE Transactions on Communications. 14 pages, 13 figure

Simple Approximations of the SIR Meta Distribution in General Cellular Networks

International audienceCompared 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

Analysis of heterogeneous wireless networks using Poisson hard-core hole process

The Poisson point process (PPP) has been widely employed to model wireless networks and analyze their performance. The PPP has the property that nodes are conditionally independent from each other. As such, it may not be a suitable model for many networks, where there exists repulsion among the nodes. In order to address this limitation, we adopt a Poisson hardcore process (PHCP), in which no two nodes can be closer than a repulsion radius from one another. We consider two-tier heterogeneous networks, where the spatial distributions of transmitters in the first-tier and the second-tier networks follow a PHCP and a PPP, respectively. To alleviate inter-tier interference, we consider a guard zone for the first-tier network and presume that the second-tier transmitters located in the zone are deactivated. Under this setup, the activated second-tier transmitters form a Poisson hard-core hole process. We first derive exact computable expressions of the coverage probability and introduce a method to efficiently evaluate the expressions. Then, we provide approximations of the coverage probability, which have lower computational complexities. In addition, as a special case, we investigate the coverage probability of single-tier networks by modeling the locations of transmitters as a PHCP.MOE (Min. of Education, S’pore)Accepted versio