Scaling Laws of Capacity for Large Scale Wireless Networks

In this paper, we focus on the networking-theoretic multicast capacity bounds for both random extended networks (REN) and random dense networks (RDN) under Gaussian Channel model, when all wireless nodes have the same constant transmission power P . During the transmission, the power decays along path with attenuation exponent α > 2. In REN and RDN, n nodes are randomly distributed in the square region with sidelength √ n and 1, respectively. We randomly choose ns nodes as the sources of multicast sessions, and for each source v, we pick uniformly at random nd nodes as the destination nodes of v. Based on percolation theory, we propose multicast schemes and analyze the achievable throughput taking account of all ns and nd. As the specific case of our results, we show that for ns = Θ(n), the per-session multicast capacity of RDN is Θ( 1 √ndn ) when nd = O( n (log n)3 ) and is Θ( 1 n ) when nd = Ω( n log n ); the per-session multicast capacity of REN is Θ( 1 √ ndn ) when nd = O( n (log n)α+1 ) and is Θ( 1 nd · (log n) 2 ) when nd = Ω( n log n ).