Multicast Capacity of Wireless Ad Hoc Networks Under Gaussian Channel Model
Xiang‐Yang Li, Yunhao Liu, Shi Li, Shaojie Tang · IEEE/ACM Transactions on Networking · 2010
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 lengtha= √n, by use of Poisson distribution with density 1. All nodes transmit at a constant powerP, and the power decays with attenuation exponentα > 2. The data rate of a transmission is determined by theSINRasBlog(1+ SINR), whereBis the bandwidth. There arensrandomly and independently chosen multicast sessions. Each multicast session haskrandomly chosen terminals. We show that whenk≤ θ1[(n)/((logn)2α+ 6)] andns≥ θ2n1/2+β, the capacity that each multicast session can achieve, with high probability, is at leastc8[(√n)/(ns√k)], whereθ1,θ2, andc8are some special constants andβ > 0is any positive real number. We also show that fork=O( [(n)/(log2n)]) , the per-flow multicast capacity under Gaussian channel is at mostO([(√n)/(ns√k)]) when we have at leastns= Ω(logn) random multicast flows. Our result generalizes the unicast capacity for random networks using percolation theory.