Capacity of large scale wireless networks under Gaussian channel model

Abstract

In this paper, we study the multicast capacity of a large scale random wireless network. We simply consider the extended multihop network, where a number of wireless nodes v_i(1 ≤ i ≤ n) are randomly located in a square region with side-length a = √n, by use of Poisson distribution with density 1. All nodes transmit at constant power P, and the power decays along path, with attenuation exponent α > 2. The data rate of a transmission is determined by the SINR as B log(1 + SINR). There are n_s randomly and independently chosen multicast sessions. Each multicast has k randomly chosen terminals. We show that, when k ≤ θ₁ n/(log n)^2α+6, and n_s ≥ θ₂n^1/2+β, the capacity that each multicast session can achieve, with high probability, is at least c₈√n/n_s√k, where θ₁, θ₂, and c₈ are some special constants and β > 0 is any positive real number. Our result generalizes the unicast capacity [3] for random networks using percolation theory.