Multicast capacity of wireless ad hoc networks under Gaussian channel model

  • Authors:
  • Xiang-Yang Li;Yunhao Liu;Shi Li;ShaoJie Tang

  • Affiliations:
  • Department of Computer Science, Illinois Institute of Technology, Chicago, IL and Institute of Computer Application Technology, Hangzhou Dianzi University, Zhejiang, China;Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong;Department of Computer Science, Princeton University, Princeton, NJ;Department of Computer Science, Illinois Institute of Technology, Chicago, IL

  • Venue:
  • IEEE/ACM Transactions on Networking (TON)
  • Year:
  • 2010

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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 ≤ θ1 n/(log n)2α+6 and ns ≥ θ2n1/2+β, the capacity that each multicast session can achieve, with high probability, is at least c8 √n/ns√k, where θ1, θ2, and c8 are some special constants and β O is any positive real number. We also show that for k = O(n/log2n), 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.