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 B log (1+SINR), where B is the bandwidth. There are n_s randomly and independently chosen multicast sessions. Each multicast session has k randomly chosen terminals. We show that when k≤θ₁n/(log n)^2α+6 and n _s≥θ₂^1/2+β, the capacity that each multicast session can achieve, with high probability, is at least c ₈√n/log n_s√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/log ²n) , the per-flow multicast capacity under Gaussian channel is at most O(√n/n_s) when we have at least n_s=Ω (log n) random multicast flows. Our result generalizes the unicast capacity for random networks using percolation theory.