Multicast capacity of wireless ad hoc networks

Assume that <i>n</i> wireless nodes are uniformly 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 (or receive) at <i>W</i> bits/second over a common wireless channel. For each node <i>v<inf>i</inf></i>, we randomly and independently pick <i>k</i>-1 points <i>p<inf>i,j</inf></i> (1 ≤ <i>j</i> ≤ <i>k</i>-1) from the square, and then multicast data to the nearest node for each <i>p<inf>i,j</inf></i>. We derive matching asymptotic upper bounds and lower bounds on multicast capacity of random wireless networks. Under protocol interference model, when <i>a</i>²/<i>r</i>² = <i>O</i>(<i>n</i>/log(<i>n</i>)), we show that the total multicast capacity is Θ (√<i>n</i>/log <i>n</i> ċ (<i>W</i>/√<i>k</i>)) when <i>k</i> = <i>O</i>(<i>n</i>/log <i>n</i>); the total multicast capacity is Θ (<i>W</i>) when <i>k</i> = Ω(<i>n</i>/log <i>n</i>). 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. We also extend our capacity bounds to <i>d</i>-dimensional networks.