Scaling Laws of Multicast Capacity for Power-Constrained Wireless Networks under Gaussian Channel Model

We study the asymptotic networking-theoretic multicast capacity bounds for random extended networks (REN) under Gaussian channel model, in which all wireless nodes are individually power-constrained. During the transmission, the power decays along path with attenuation exponent α >; 2. In REN, n nodes are randomly distributed in the square region of side length √n. There are n_s randomly and independently chosen multicast sessions. Each multicast session has n_d + 1 randomly chosen terminals, including one source and n_d destinations. By effectively combining two types of routing and scheduling strategies, we analyze the asymptotic achievable throughput for all n_s = ω(1) and nd. As a special case of our results, we show that for n_s = Θ(n), the per-session multicast capacity for REN is of order Θ(1/√n_dn) when nd = O(n/(log n)^a+1) and is of order Θ(1/n_d · (log n)^-n/2) when n_d = Ω(n/log n).