Relay networks having $n$ source-to-destination pairs and $m$ half-duplex relays, all operating in the same frequency band in the presence of block fading, are analyzed. This setup has attracted significant attention and several relaying protocols have been reported in the literature. However, most of the proposed solutions require either centrally coordinated scheduling or detailed channel state information (CSI) at the transmitter side. Here, an opportunistic relaying scheme is proposed, which alleviates these limitations. The scheme entails a two-hop communication protocol, in which sources communicate with destinations only through half-duplex relays. The key idea is to schedule at each hop only a subset of nodes that can benefit from \emph{multiuser diversity}. To select the source and destination nodes for each hop, it requires only CSI at receivers (relays for the first hop, and destination nodes for the second hop) and an integer-value CSI feedback to the transmitters. For the case when $n$ is large and $m$ is fixed, it is shown that the proposed scheme achieves a system throughput of $m/2$ bits/s/Hz. In contrast, the information-theoretic upper bound of $(m/2)\log \log n$ bits/s/Hz is achievable only with more demanding CSI assumptions and cooperation between the relays. Furthermore, it is shown that, under the condition that the product of block duration and system bandwidth scales faster than $\log n$, the achievable throughput of the proposed scheme scales as $\Theta ({\log n})$. Notably, this is proven to be the optimal throughput scaling even if centralized scheduling is allowed, thus proving the optimality of the proposed scheme in the scaling law sense.
T HE DEMAND for ever larger and more efficient wireless communication networks necessitates new network architectures, such as ad hoc networks and relay networks. As such, there has been significant activity in the past decade toward understanding the fundamental system throughput limits of such architectures and developing communication schemes that seek to approach these limits.
Among other notable recent results on the throughput scaling of wireless networks, Gowaikar et al. [1] proposed a new wireless ad hoc network model, whereby the strengths of the connections between nodes are drawn independently from a common distribution, and analyzed the system throughput under various fading distributions. Such a model is appropriate for environments with rich scattering but small physical size, so that the connections are governed by random fading instead of deterministic path loss attenuations. When the random channel strengths follow a Rayleigh fading model, the system throughput scales as log n. This result is achievable through a multihop scheme that requires central coordination of the routing of nodes. Moreover, full knowledge of the channel state information (CSI) of the entire network is needed to enable the central coordination.
Along with the work on multihop schemes, such as [1] and [2], there is another line of work characterizing the system throughput for wireless networks operating with two-hop relaying. The listen-and-transmit protocol, studied by Dana and Hassibi [3] from the power-efficiency perspective, turns out to have interesting properties from the system throughput standpoint as well. This is in fact a two-hop amplify-andforward scheme, where relays are allowed to adjust the phase and amplitude of the received signals. A throughput of Θ(n) bits/s/Hz is achieved by allowing n source-to-destination (S-D) pairs to communicate, while m = Θ(n 2 ) nodes in the network act as relays. It is assumed that each relay node has full knowledge of its local channels (backward channels from all source nodes, and forward channels to all destination nodes), so that the relays can perform distributed beamforming. Morgenshtern and Bölcskei worked in [4] with a similar distributed beamforming setup, and their results reveal tradeoffs between the level of available channel state information and the system throughput. In particular, utilizing a scheme with relays partitioned into groups, and where relays in each group have CSI knowledge of only one backward and one forward channel, the number of relays required to support a Θ (n) throughput is m = Θ(n 3 ). In other words, with lower level CSI, the number of required relays increases from Θ(n 2 ) to Θ(n 3 ). An equivalent point of view is to state the throughput in terms of the total number of transmitting nodes in the system, p = n + m. Then the system throughput is Θ p1/3 , when the relays in each group know the channel for only one source-destination pair. When relays know the channels for all source and destination nodes, the throughput scales as Θ p 1/2 .
Although these works have made great strides toward understanding wireless ad hoc network capacity, implementations of the schemes require either central coordination among nodes [1], [2] or some level of CSI (channel amplitude and/or phase) at the transmitter side [3], [4]. The centralized coordination between wireless relays does not come for free, since the overhead to set up the cooperation may drastically reduce the useful throughput [5]. 1 Likewise, in a large system, obtaining this level of CSI, especially at the transmitter side, may not be feasible. This paper addresses the need to alleviate these limitations by proposing an opportunistic relaying scheme that works in a completely decentralized fashion and imposes less stringent CSI requirements.
The main contributions of this work can be summarized as follows.
• A two-hop opportunistic relaying scheme for operating over fading channels is proposed and analyzed. The scheme’s salient features are:
-It operates in a decentralized fashion. No cooperation among nodes is assumed or required. -Only modest CSI requirements are imposed. At each hop, each receiver is assumed to have knowledge of its local incoming channel realizations, while transmitters have access to only index-valued CSI via low-rate feedback from the receivers.
• The throughput of the proposed scheme is characterized by: -It is shown that, in the regime of a large number of nodes n and fixed number of relays m, the proposed scheme achieves a system throughput of m/2 bits/s/Hz. This can be contrasted with the information-theoretic upper bound (m/2) log log n on the scaling of the throughput, achievable only with full cooperation among the relays and full CSI (backward and forward) at the relays. These results reveal an interesting feature of multiuser diversity: whereas full cooperation between relays can readily form parallel channels, and multiuser diversity can boost the throu
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