Scaling laws on multicast capacity of large scale wireless networks

In this paper, we focus on the networking-theoretic multicast capacity for both random extended networks (REN) and random dense networks (RDN) under Gaussian Channel model, when all nodes are individually power-constrained. During the transmission, the power decays along path with the attenuation exponent α > 2. In REN and RDN, n nodes are randomly distributed in the square region with side-length √n and 1, respectively. We randomly choose n _B nodes as the sources of multicast sessions, and for each source v, we pick uniformly at random n _d nodes as the destination nodes. Based on percolation theory, we propose multicast schemes and analyze the achievable throughput by considering all possible values of n _s and n _d · As a special case of our results, we show that for n _s = Θ(n), the per-session multicast capacity of RDN is Θ Equation Persented when n _d = O Equation Persented and is Θ(1/n) when n _d = Ω Equation Persented the per-session multicast capacity of REN is Θ Equation Persented when n _d = O Equation Persented and is Θ Equation Persented when n _d = Ω Equation Persented.