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Analytical Modeling of Heterogeneous Cellular Networks by Sayandev Mukherjee

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2  Structure of the SINR calculation problem

We begin with the simple SINR calculation problem of Chapter 1 and generalize it to a deployment with more than one tier of BSs. We then examine the features of the problem that permit us to evaluate the CCDF of the SIR in terms of Laplace transforms of fading coefficients on the links to the user location from the BSs in the tiers. Then we abstract the problem formulation slightly in order to define a general probability calculation of a vector of random variables, which we call the canonical problem. We derive general results and conditions under which the canonical probability may be expressed in terms of Laplace transforms of certain random variables. This is one half of the mathematical core of ...

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