Large Deviation Principles For Empirical Measures Of Signal To Interference Noise Ratio (SINR) Graph
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Date
2022-11
Authors
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Publisher
University Of Ghana
Abstract
We obtain a Large Deviation Principle (LDP) and Asymptotic Equipartition
Property (AEP) for Critical, Super-critical and Sub-critical telecommunication
network modelled as SINR random network. Given devices space D, an intensity
measure _m 2 R+ is a transitional kernel Q from the space D to positive real
numbers R+ and a path loss function. The study defines a Marked Poisson Point
Process (MPPP). For a given MPPP and technical constant __; _ : (0;1) !
(0;1); the study defines a Marked SINR Network as a Telecommunication
Network and associate it with two empirical measures; the empirical marked
measure and the empirical connectivity measure on two different scales as _2a_
and _, on a topological space, where _ is the intensity measure of the PPP which
defines a SINR random network. For the class of telecommunication networks,
the study proves a joint LDP for the empirical measures of the telecommunication
network. Using this joint LDP, the study proves Asymptotic Equipartition
Property (AEP) for the stochastic telecommunication network modelled as the
marked SINR network. In addition, the study proves a Local Large Deviation
Principle (LLDP) and a classical McMillian Theorem for the stochastic SINR
network process. Further, for a typical empirical paired measure, we deduce from
local large deviation principle a bound on the cardinality of the space of marked
SINR network. Note that, the LDP for the empirical measures of this stochastic
SINR network modelled as Telecommunication network was derived on space of
measures equipped with the _ topology, and the LLDP were deduced in the
space of the SINR model process without any topological restriction. All our rate
function are expressed as relative entropies of the marked SINR on the device
space D.
Description
PhD. Statistics
Keywords
Signal To Interference Noise Ratio (SINR) Graph, Empirical Measures