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 n _d. 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 n _dn=O(n/(logn) ^α+1) and is of order Θ(1\n _dṅ(log n)- ^α/2) when n ^d=Ω(n\log n).