Multicast Capacity of Wireless Ad Hoc Networks Under Gaussian Channel Model

Xiang-Yang Li,Shaojie Tang,Shi Li,Yunhao Liu

doi:10.1109/tnet.2009.2037431

Abstract

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 ns randomly and independently chosen multicast sessions. Each multicast session has k randomly chosen terminals. We show that when k ≤ θ 1 [( n )/((log n ) 2α+ 6 )] and ns ≥ θ 2 n 1/2+β , the capacity that each multicast session can achieve, with high probability, is at least c 8 [(√ n )/( ns √ k )], where θ 1 , θ 2 , and c 8 are some special constants and β > 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 ([(√ n )/( ns √ k )]) when we have at least ns = Ω(log n ) random multicast flows. Our result generalizes the unicast capacity for random networks using percolation theory.

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