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Previous work on cooperative communications has concentrated primarily on the diversity benefits of such techniques. This paper, instead, considers the multiplexing benefits of cooperative communications. First, a new interpretation on the fundamental tradeoff between the transmission rate and outage probability in multiple-antenna relay networks is given. It follows that multiplexing gains can be obtained at any finite signal-to-noise ratio (SNR), in full-duplex multiple-antenna relay networks. Thus, relaying can offer not only stronger link reliability, but also higher spectral efficiency. Specifically, the decode-and-forward protocol is applied and networks that have one source, one destination, and multiple relays are considered. A receive power gain at the relays, which captures the network large-scale fading characteristics, is also considered. It is shown that this power gain can significantly affect the system diversity-multiplexing tradeoff for any finite SNR value. Several relaying protocols are proposed and are shown to offer nearly the same outage probability as if the transmit antennas at the source and the relay(s) were colocated, given certain SNR and receive power gains at the relays. Thus, a higher multiplexing gain than that of the direct link can be obtained if the destination has more antennas than the source. Much of the analysis in the paper is valid for arbitrary channel fading statistics. These results point to a view of relay networks as a means for providing higher spectral efficiency, rather than only link reliability.