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.

I. Introduction

Capacity of wireless ad hoc networks is constrained by interference between concurrent transmissions. Observing this, Gupta and Kumar adopt Protocol and Physical Model to define a successful transmission, and study the capacity scaling, i.e., the asymptotically achievable throughput of the network in their seminal work [3]. Assume there are nodes in a unit disk area, they show that the per-node throughput capacity scales as for random networks, and the per-node transport capacity for arbitrary networks scales as , respectively.