Simple Approximations of the SIR Meta Distribution in General Cellular Networks

Abstract

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 G0 between its standard success probability and that for the Poisson point process exactly characterizes the gap between the bth moment of the conditional success probability, as the SIR threshold goes to 0. The gap G0 allows two simple approximations of the meta distribution for general HCNs: 1) the per-tier approximation by applying the shift G0 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 finegrained nature of the meta distribution, these approximations work surprisingly well.Index Terms-Interference, heterogeneous cellular networks, meta distribution, Poisson point process, signal-to-interference ratio, stochastic geometry S. S. Kalamkar is with INRIA, Paris, France. M. Haenggi is with the

On the meta distribution in spatially correlated non-Poisson cellular networks

“…As discussed in [8], the direct computation of the meta distribution in (8) is not straightforward. A general approach to overcome this issue is to capitalize on the Gil-Pelaez inversion theorem [15], which allows one to formulate the meta distribution as a function of the moments of the (conditional) coverage probability in (9).…”

“…In the present paper, motivated by these considerations and by [9], we generalize the IDT approach for computing the meta distribution in non-Poisson cellular networks. We consider a recent and improved definition of the coverage probability, which allows one to account for the signal quality during the cell association and data transmission phases [10], [11].…”

SIR Analysis in 3D UAV Networks: A Stochastic Geometry Approach

“…The homogeneous infinite Poisson point process (HPPP) is a very popular choice for the distribution of the spatial locations of terrestrial transceivings due to its simplicity and tractability [3] - [5], whereas recently has been adopted for the spatial modeling of UAV networks [6] - [8]. In particular, in [6], a coverage and rate analysis is conducted by assuming that UAVs are deployed in a plane above the ground forming a PPP.…”

Coverage and Energy Efficiency Analysis for Two-Tier Heterogeneous Cellular Networks Based on Matérn Hard-Core Process

“…Recently, it has been observed that the coverage of cellular networks based on non-PPP models can be approximated by adjusting the SIR threshold of the corresponding network based on a PPP model with the same density. The adjusting coefficient is called SIR gain and the method is called ASAPPP [13][14][15][16][17][18][19][20]. Using this method, the SIR gain for the MHCP modelled network can be expressed as…”

“…[17] derives the coverage probability of the two-tier HCN modelled by PPP and PCP, but the derivation process is too complicated and the results can only be obtained by numerical computation. [18] and [19] analyze the distribution of the conditional success probability for HCN based on PPP and non-PPP, respectively. According to the principle of nearest BS access, [20] investigate the approximate SIR distribution of K-tier HCNs with the use of ASAPPP method.…”