Scaling laws on multicast capacity of large scale wireless networks
C. Wang, X.‐Y. Li, Changjun Jiang, Shaojie Tang, Y. Liu, Jizhong Zhao · 2009
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 radic(n) and 1, respectively. We randomly choose nsnodes as the sources of multicast sessions, and for each source v, we pick uniformly at random ndnodes as the destination nodes. Based on percolation theory, we propose multicast schemes and analyze the achievable throughput by considering all possible values of nsand nd. As a special case of our results, we show that for ns= Theta(n), the per-session multicast capacity of RDN is Theta((1)/(radic(ndn))) when nd= O((n)/((log n)3)) and is Theta((1)/(n)) when nd= Omega((1)/(log n)); the per-session multicast capacity of REN is Theta((1)/radic(ndn)) when nd= O((n)/((log n)alpha+1)) and is Theta((1)/(nd) ldr (log n)-(alpha)/(2)) when nd= Omega((n)/(log n)).