It has been shown in a previous version of this paper that hierarchical cooperation achieves a linear throughput scaling for unicast traffic, which is due to the advantage of long-range concurrent transmissions and the technique of distributed multiple-input–multiple-output (MIMO). In this paper, we investigate the scaling law for multicast traffic with hierarchical cooperation, where each of the $n$ nodes communicates with $k$ randomly chosen destination nodes. Specifically, we propose a new class of scheduling policies for multicast traffic. By utilizing the hierarchical cooperative MIMO transmission, our new policies can obtain an aggregate throughput of $Omega big (( {{ n}over { k}})^{1-epsilon }big )$ for any $epsilon >0$. This achieves a gain of nearly $sqrt {{ n}over { k}}$ compared to the noncooperative scheme in Li 's work (Proc. ACM MobiCom, 2007, pp. 266–277). Among all four cooperative strategies proposed in our paper, one is superior in terms of the three performance metrics: throughput, delay, and energy consumption. Two factors contribute to the optimal performance: multihop MIMO transmission and converge-based scheduling. Compared to the single-hop MIMO transmission strategy, the multihop strategy achieves a throughput gain of $( {{ n}over { k}})^{{ h-1}over { h(2h-1)}}$ and meanwhile reduces the energy consumption by $k^{{ alpha -2}over { 2}}$ times approximately, where $h>1$ is the number -
f the hierarchical layers, and $alpha >2$ is the path-loss exponent. Moreover, to schedule the traffic with the converge multicast instead of the pure multicast strategy, we can dramatically reduce the delay by a factor of about $( {{ n}over { k}})^{{ h}over { 2}}$. Our optimal cooperative strategy achieves an approximate delay-throughput tradeoff $D(n,k)/T(n,k)=Theta (k)$ when $hrightarrow infty $. This tradeoff ratio is identical to that of noncooperative scheme, while the throughput is greatly improved.
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