  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.
