Multicast Scaling Laws with Hierarchical Cooperation

A new class of scheduling policies for multicast traffic are proposed in this paper. By utilizing hierarchical cooperative MIMO transmission, our new policies can obtain an aggregate throughput of $\Omega\big((\frac{n}{k})^{1-\epsilon}\big)$ for any $\epsilon>0$. This achieves a gain of nearly $\sqrt{\frac{n}{k}}$ compared with non-cooperative scheme in \cite{paper:MulticastCapacityXYLi}. Between the two cooperative strategies in our paper, the converge-based one is superior to the other on delay, while the throughput and energy consumption performances are nearly the same. Moreover, to schedule the traffic in a converge multicast manner instead of the simple multicast, we can dramatically reduce the delay by a factor nearly $(\frac{n}{k})^\frac{h}{2}$, where $h>1$ is the number of the hierarchical layers. Our optimal cooperative strategy achieves an approximate delay-throughput tradeoff $D(n,k)/T(n,k)=\Theta(k)$ when $h\rightarrow\infty$. This tradeoff ratio is identical to that of non-cooperative scheme, while the throughput performance is greatly improved. Besides, for certain $k$ and $h$, the tradeoff ratio is even better than that of unicast.