Advanced Wireless Networks, 3rd Edition

10Stochastic Geometry

10.1 Background Theory

10.1.1 Point Process

As we will see already in the next chapter, see (11.2.3–11.2.4) or (11.3.3), the key parameter in the analysis of the link’s Shannon capacity in a network is the level of interference produced by other links’ activities on the reference link. Let us assume that the signal power decays with the distance between the transmitter and the receiver according to the power law , where is the spatial location of a reference transmitter, P_t(x) is the transmit power indexed by the transmitter location, ℝ^d is the spatial location of the receiver, h_xy is a random variable accounting for the random channel (power) gain between the two locations x and y, is the Euclidean norm, A is a propagation constant, and η is the path-loss exponent. Now the SINR at a reference receiver in the network can be calculated as

(10.1.1)

where y is the location of the reference receiver, x₀ is the location of the reference transmitter (desired transmitter), ...