Scaling laws on multicast capacity of large scale wireless networks

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 n
_s
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)/(radic(n
_d
n))) when n
_d
= O((n)/((log n)
³
)) and is Theta((1)/(n)) when n
_d
= Omega((1)/(log n)); the per-session multicast capacity of REN is Theta((1)/radic(n
_d
n)) when n
_d
= O((n)/((log n)
^alpha+1
)) and is Theta((1)/(n
_d
) ldr (log n)
^-(alpha)/(2)
) when n
_d
= Omega((n)/(log n)).