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

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