General capacity scaling of wireless networks

We study the general scaling laws of the capacity for random wireless networks under the generalized physical model. The generality of this work is embodied in three dimensions denoted by (λ ∈ [1, n], n_d ∈ [1, n], n_s ∈ (1, n]). It means that: (1) We study the random network of a general node density λ ∈ [1, n], rather than only study either random dense network (RDN, λ = n) or random extended network (REN, λ = 1) as in the literature. (2) We focus on the multicast capacity to unify unicast and broadcast capacities by setting the number of destinations for each session as a general value n_d ∈ [1, n]. (3)We allow the number of sessions changing in the range n_s ∈ (1, n], rather than assume that n_s = Θ(n) as in the literature.We derive the general lower bounds on the capacity for the arbitrary case of (λ, n_d, n_s). Particularly, we show that for the special cases (λ = 1, n_d ∈ [1, n], n_s= n) and (λ = n, n_d ∈ [1, n], n_s = n), our schemes achieve the highest multicast throughputs proposed in the existing works.