Multicast capacity for multi-hop multi-channel multi-radio wireless networks

Abstract

Assume that n wireless nodes are randomly deployed in a square region with side-length a and all nodes have the uniform transmission range r and uniform interference range R = Θ(r). Each node is equipped with Φ interfaces. There are C = ∅(min(nr2=a2 log n)) channels of equal bandwidth W/C available. We consider a random (Cg) channel assignment where each node may switch between a preassigned random subset of g channels (with g ≥ ∅Φ). In this paper, we study the multicast capacity of such a random wireless network, where for each node vi, we randomly pick k - 1 nodes from the other n - 1 nodes as the receivers of the multicast session rooted at node vi. We derive matching asymptotic upper bounds and lower bounds on multicast capacity. We show that the per-flow multicast capacity is Θ(W√Prnd/n log n ⋅ 1/√k) when k = ∅(Prnd⋅n/log n), where Prnd denotes the probability that two nodes share at least one channel. Our bounds unify the previous capacity bounds on unicast (when k = 2) by Bhandari and Vaidya [3] for multi-channel multi-radio networks.