Multicast Capacity Scaling of Wireless Networks with Multicast Outage

Multicast transmission has several distinctive traits as opposed to more commonly studied unicast networks. Specially, these include (i) identical packets must be delivered successfully to several nodes, (ii) outage could simultaneously happen at different receivers, and (iii) the multicast rate is dominated by the receiver with the weakest link in order to minimize outage and retransmission. To capture these key traits, we utilize a Poisson cluster process consisting of a distinct Poisson point process (PPP) for the transmitters and receivers, and then define the multicast transmission capacity (MTC) as the maximum achievable multicast rate times the number of multicast clusters per unit volume, accounting for outages and retransmissions. Our main result shows that if $\tau$ transmission attempts are allowed in a multicast cluster, the MTC is $\Theta\left(\rho k^{x}\log(k)\right)$ where $\rho$ and $x$ are functions of $\tau$ depending on the network size and density, and $k$ is the average number of the intended receivers in a cluster. We also show that an appropriate number of retransmissions can significantly enhance the MTC.