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

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 = O (min(nr²=a² log n)) channels of equal bandwidth W/C available. We consider a random (C, g) 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 v_i, we randomly pick k - 1 nodes from the other n - 1 nodes as the receivers of the multicast session rooted at node v_i. We derive matching asymptotic upper bounds and lower bounds on multicast capacity. We show that the per-flow multicast capacity is Θ(W√P_rnd/n log n·1/√k) when k = O(P _rnd·n/log n), where P_rnd 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.