Multicast Capacity of Wireless Ad Hoc Networks Under Gaussian Channel Model

We study the multicast capacity of large-scale random extended multihop wireless networks, where a number of wireless nodes are randomly located in a square region with side length a = √n, by use of Poisson distribution with density 1. All nodes transmit at a constant power P , and the power decays with attenuation exponent α > 2. The data rate of a transmission is determined by the SINR as Blog(1+ SINR), where B is the bandwidth. There are ns randomly and independently chosen multicast sessions. Each multicast session has k randomly chosen terminals. We show that when k ≤ θ₁[(n)/((logn)^{2α+ 6})] and ns ≥ θ₂n^1/2+β, the capacity that each multicast session can achieve, with high probability, is at least c₈[(√n)/(ns√k)], where θ₁, θ₂, and c₈ are some special constants and β > 0 is any positive real number. We also show that for k = O( [(n)/(log²n)]) , the per-flow multicast capacity under Gaussian channel is at most O([(√n)/(ns √k)]) when we have at least ns = Ω(logn) random multicast flows. Our result generalizes the unicast capacity for random networks using percolation theory.