Packet Delivery Ratio in k-Dimensional Broadcast Ad Hoc Networks

In this letter, we present a new analytic derivation of a reliability metric, Packet Delivery Ratio (PDR), in broadcast mobile ad hoc networks (MANETs) where nodes are distributed according to a homogeneous k-dimensional (k-D) Poisson point process. Given a point-to-point node packet reception probability (NRP) as a function of distance, PDR of nodes on k-D area is derived by converting k-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 k-D area is transformed as the joint probability density function on a 1-D line. Then, PDR on a 1-D line is derived from the product of the un-ordered nodes reception probabilities. The PDR approach is applied to a broadcast MANET with Nakagami fading channel with path loss. The analytic derivation is verified by NS2 simulations.