A model-free framework for coverage evaluation in device-to-device heterogeneous networks

Consider a decentralized device-to-device (D2D) network consisting of K different types of D2D pairs in which the D2D pairs of each specific type form an independent homogeneous Poisson point process (PPP) and the transmitter (TX) of each D2D pair has a unique intended receiver (RX). For this heterogeneous network model, we develop a model-free tractable framework to analyze the coverage probability without any specific model assumptions for channel fading, stochastic transmit power and distance. First we device a novel approach to finding the Laplace transform of the reciprocal of the SIR which is used to characterize the model-free coverage probability of the D2D pair of each type. Our main analytical findings show that the model-free bounds of the coverage probability can be obtained and they reduce to a closed-form result as long as the received signal power has an Erlang distribution. These findings are applied to expound when the randomness of the received signal power benefits/jeopardizes the coverage probability and how to use the distributed stochastic power control to improve the coverage probability of each D2D pair.