1 Multicast Performance with Hierarchical Cooperation Xinbing Wang, Luoyi Fu, Chenhui Hu Dept. of Electronic Engineering Shanghai Jiao Tong University, China Email: {xwang8,fly hch}@sjtu.edu.cn Abstract—It has been shown in [1] that hierarchical coopera- tion achieves a linear throughput scaling for unicast traffic, which is due to the advantage of long range concurrent transmissions and the technique of distributed MIMO. In this paper 1 , 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 poli- cies can obtain an aggregate throughput of Ω( n k ) 1-ϵ for any ϵ> 0. This achieves a gain of nearly n k compared with the non- cooperative scheme in [26]. Among all four cooperative strategies proposed in our paper, one is superior to in terms of the 3 performance metrics: throughput, delay and energy consumption. Two factors contribute to the optimal performance: multi-hop MIMO transmission and converge-based scheduling. Compared with the single-hop MIMO transmission strategy, the multi-hop strategy achieves a throughput gain of ( n k ) h-1 h(2h-1) and meanwhile reduces the energy consumption by k α-2 2 times approximately, where h> 1 is the number of the hierarchical layers, and α> 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 k ) h 2 . Our optimal cooperative strategy achieves an approximate delay- throughput tradeoff D(n, k)/T (n, k) = Θ(k) when h →∞. This tradeoff ratio is identical to that of non-cooperative scheme, while the throughput is greatly improved. I. I NTRODUCTION 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 n nodes in a unit disk area, they show that the per-node throughput capacity scales as Θ 1 √ n log n for random networks, and the per-node transport capacity for arbitrary networks scales as Θ 1 √ n , respectively. The results on network capacity provide us both a theoreti- cal bound and insights in the protocol design and architecture of wireless networks. Thus, great efforts are devoted to un- derstand the scaling laws in wireless ad hoc networks. One important stream of work is improving unicast capacity. With 1 An earlier version of this paper appeared in the Proceedings of IEEE Infocom 2010 [33].. percolation theory, Franceschetti et al. [4] show that a rate Θ 1 √ n is attainable in random ad hoc networks under Gen- eralized Physical Model. However, it is still vanishing when we have infinite number of nodes. To achieve linear capacity scaling, Grossglauser et al. [5] exploit nodes’ mobility to increase network throughput while at a cost of induced delay. Tradeoff between capacity and delay is studied in literatures [10] – [12]. An alternative way is adding infrastructure to the network. It is shown in [13] – [17] that when the number of base stations grows linearly as that of the nodes (implying a huge investment), capacity will scale linearly. Moreover, instead of letting nodes perform traditional operations such as storage, replication and forwarding, [18] and [19] introduce coding into the network. This also brings about the gain on throughput. Recently, Aeron et al. [6] introduce a multiple-input multiple-output (MIMO) collaborative strategy achieving a throughput of Ω(n −1/3 ). Different from the Gupta and Ku- mar’s results, they use a cooperative scheme to obtain capacity gain by turning mutually interfering signals into useful ones. Later, ¨ Ozg¨ ur et al. [1] [2] utilize hierarchical schemes rely- ing on distributed MIMO communications to achieve linear capacity scaling. The optimal number of hierarchical stages is studied in [7], while multi-hop and arbitrary networks are investigated in [8] and [9], respectively. Another line of research deals with more generalized traf- fic patterns. In [20], Toumpis develops asymptotic capacity bounds for non-uniform traffic networks. In [21], broadcast capacity is discussed. Then, a unified perspective on the capacity of networks subject to a general form of information dissemination is proposed in [22]. As a more efficient way for one-to-many data distribution than multiple unicast, multicast is well fit for the applications such as group communications and multi-media services. Thus, it raises great interests to the research community and has been studied by different manners in [23] – [30]. Specifically, in [24], the authors derive the asymptotic upper and lower bounds for multicast capacity by focusing on data copies and area argument in the routing tree established in the paper; In [25], multicast capacity is studied under a more realistic channel model, physical layer model instead of simplified protocol model assumed in many previ- ous literatures; In [26], through mathematical derivations and simulations, the authors demonstrate that multicast achieves a gain compared to unicast when information is disseminated to n destinations in mobile ad hoc networks; In [27], a