Multicast Capacity of Wireless Ad Hoc Networks

Assume that n wireless nodes are uniformly randomly deployed in a square region with side-length a and all nodes have the uniform transmission range r and uniform interference range R > r. We further assume that each wireless node can transmit (or receive) at W bits/second over a common wireless channel. For each node vi , we randomly and independently pick k-1 points pi,j (1 les j les k-1) from the square, and then multicast data to the nearest node for each pi,j. We derive matching asymptotic upper bounds and lower bounds on multicast capacity of random wireless networks. Under protocol interference model, when a ²/r ²=O(n/log(n)), we show that the total multicast capacity is Theta(radic{n/log n}middot(W/radick)) when k=O(n/log n); the total multicast capacity is Theta(W) when k=Omega(n/log n). We also study the capacity of group-multicast for wireless networks where for each source node, we randomly select k-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. We also extend our capacity bounds to d -dimensional networks.