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 <i>a</i> = √<i>n</i>, by use of Poisson distribution with density 1. All nodes transmit at a constant power <i>P</i> , and the power decays with attenuation exponent <i>α > 2</i>. The data rate of a transmission is determined by the <i>SINR</i> as <i>B</i>log(1+ SINR), where <i>B</i> is the bandwidth. There are <i>ns</i> randomly and independently chosen multicast sessions. Each multicast session has <i>k</i> randomly chosen terminals. We show that when <i>k</i> ≤ θ₁[(<i>n</i>)/((log<i>n</i>)^{2α+ 6})] and <i>ns</i> ≥ θ₂<i>n</i>^1/2+β, the capacity that each multicast session can achieve, with high probability, is at least <i>c</i>₈[(√<i>n</i>)/(<i>ns</i>√<i>k</i>)], where <i>θ</i>₁, <i>θ</i>₂, and <i>c</i>₈ are some special constants and <i>β > 0</i> is any positive real number. We also show that for <i>k</i> = <i>O</i>( [(<i>n</i>)/(log²<i>n</i>)]) , the per-flow multicast capacity under Gaussian channel is at most <i>O</i>([(√<i>n</i>)/(<i>ns</i> √<i>k</i>)]) when we have at least <i>ns</i> = Ω(log<i>n</i>) random multicast flows. Our result generalizes the unicast capacity for random networks using percolation theory.