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 = root n, by use of Poisson distribution with density 1. All nodes transmit at a constant power F, and the power decays with attenuation exponent alpha > 2. The data rate of a transmission is determined by the SINR as B log(1 + SINR), where B is the bandwidth. There are as randomly and independently chosen multicast sessions. Each multicast session has k randomly chosen terminals. We show that when k <= theta(1) n/(log n)(2 alpha+6) and n(s) >= theta(2)n(1/2+beta) capacity that each multicast session can achieve, with high probability, is at least c(s) root n/n(s)root k, where theta(1), theta(2), and c(s) are some special constants and beta > 0 is any positive real number. We also show that for k = O(n/log(2) n), the per-flow multicast capacity under Gaussian channel is at most O(root n/n(s)root k) when we have at least n(s) = Omega(log n) random multicast flows. Our result generalizes the unicast capacity for random networks using percolation theory.