### A sufficient condition for tail asymptotics of SIR distribution in downlink cellular networks

**2016-02-02**

1602.00844 | cs.IT

We consider the spatial stochastic model of single-tier downlink cellular
networks, where the wireless base stations are deployed according to a general
stationary point process on the Euclidean plane with general i.i.d. propagation
effects. Recently, Ganti & Haenggi (2016) consider the same general cellular
network model and, as one of many significant results, derive the tail
asymptotics of the signal-to-interference ratio (SIR) distribution. However,
they do not mention any conditions under which the result holds. In this paper,
we compensate their result for the lack of the condition and expose a
sufficient condition for the asymptotic result to be valid. We further
illustrate some examples satisfying such a sufficient condition and indicate
the corresponding asymptotic results for the example models. We give also a
simple counterexample violating the sufficient condition.

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