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 alpha > 2. In REN and RDN, n nodes are randomly distributed in the square region with side-length radic(n) and 1, respectively. We randomly choose n_s 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 = Theta(n), the per-session multicast capacity of RDN is Theta((1)/(radic(n_dn))) when n_d = O((n)/((log n)³)) and is Theta((1)/(n)) when n_d = Omega((1)/(log n)); the per-session multicast capacity of REN is Theta((1)/radic(n_dn)) when n_d = O((n)/((log n)^alpha+1)) and is Theta((1)/(n_d) ldr (log n)^-(alpha)/(2)) when n_d = Omega((n)/(log n)).