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.
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