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 alpha > 2. In REN, n nodes are randomly distributed in the square region of side length root 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 nd destinations. By effectively combining two types of routing and scheduling strategies, we analyze the asymptotic achievable throughput for all n(s) = omega(1) and n(d). As a special case of our results, we show that for n(s) = Theta(n), the per-session multicast capacity for REN is of order Theta(1/root n(d)n) when n(d) = O(n/(log n)(alpha+1)) and is of order Theta(1/n(d) . (log n)(-alpha/2)) when n(d) = Omega(n/log n).