General capacity scaling of wireless networks

Abstract

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> ∈ [1, n], n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ∈ (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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> ∈ [1, n]. (3)We allow the number of sessions changing in the range n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ∈ (1, n], rather than assume that n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = Θ(n) as in the literature.We derive the general lower bounds on the capacity for the arbitrary case of (λ, n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> , n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ). Particularly, we show that for the special cases (λ = 1, n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> ∈ [1, n], n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = n) and (λ = n, n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> ∈ [1, n], n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = n), our schemes achieve the highest multicast throughputs proposed in the existing works.