Multicast capacity for large scale wireless ad hoc networks

In this paper, we study the capacity of a large-scale random wireless network for multicast.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> ><i>r</i>. We further assume that each wireless node can transmit/receive at <i>W</i> bits/second over a <i>common</i> wireless channel. For each node <i>v_i</i>, we <i>randomly</i> 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>. The aggregated multicast capacity is defined as the total data rate of all multicast sessions in the network. In this paper we derive matching asymptotic upper bounds and lower bounds on multicast capacity of random wireless networks. We show that the total multicast capacity is Θ(√<i>n</i> over log <i>n</i> dot <i>W</i> over √ <i>k</i>) when <i>k</i> = Ω(<i>n</i> over log <i>n</i>); the total multicast capacity is Θ(<i>W</i>) when <i>k</i> =Θ(<i>n</i> over log <i>n</i>). Our bounds unify the previous capacity bounds on unicast (when <i>k</i>=2) by Gupta and Kumar [7]and the capacity bounds on broadcast (when <i>k</i>=<i>n</i>) in [11,20]. We also study the capacity of group-multicast for wireless networks where for each source node, we randomly select <i>k</i>-1 groups of nodes as receivers and the nodes in each group are within a constant hops from the group leader. The same asymptotic upper bounds and lower bounds still hold. For arbitrary networks, we provide a constructive lower bound Ω(√<i>n</i> over √<i>k</i> dot <i>W</i>) for aggregated multicast capacity when we can carefully place nodes and schedule node transmissions.