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 the book. The other half is the study of stochastic models that yield tractable analytic expressions for the Laplace transforms in the canonical probability calculation, and we discuss that topic in Chapter 3.

Statement of the SINR calculation problem

Let us return to the problem of computing the distribution of the SINR at an arbitrarily located user somewhere in a network with one or more tiers of BSs. We begin by defining the candidate serving BSs, the criteria for their selection, the criterion for choosing the BS that will serve the user, and some notation to represent received power from the candidate serving BSs and from all interferers.

Candidate serving BSs and the serving BS

Consider a snapshot of the wireless network at a particular moment in time.