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 root n and 1, respectively. We randomly choose n. 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/root n(d) n) when n(d) = O(n/(log n)(3)) and is Theta(1/n) when n(d) = Omega(n/log n); the per-session multicast capacity of RFN is Theta(1/root n(d) n) when n(d) = O(n/(log n)(alpha+1)) and is Theta(1/n(d) . (log n)(-alpha/2)) when n(d) = Omega(n/log n).