On the reliability in d-dimensional broadcast wireless networks

In this paper, we present a new analytic derivation of two reliability indices, packet delivery ratio (PDR) and packet reception ratio (PRR), for d-dimensional (d-D) broadcast wireless networks where nodes are distributed according to a homogeneous Poisson point process. Given a point-to-point node packet reception probability (NRP) as a function of distance, PDR of nodes on d-D area is derived from PDR in a 1-D network by converting d-D Poisson Euclidean distance ordered node distribution to a type of one-dimensional (1-D) Poisson distribution so that the joint probability density function of nodes´ positions in the d-D area is transformed as the joint probability density function on a 1-D line. PRR over a coverage area is derived by integrating the NRPs for different nodes over the coverage area. The approach is applied to a broadcast wireless network with Nakagami fading channel and ALOHA channel with Raleigh fading and intederence. The analytic derivation is verified by NS2 simulations.