A non-orthogonal decode-and-forward scheme with relay selection is proposed in order to achieve higher spectral efficiency and more cooperative diversity gain in the two-hop relay networks. In the single relay case, the relay node is available to cooperate non-orthogonally with the source node only if it can decode correctly. When there are multiple nodes in the network, a relay selection method is given to select the best relay which decodes correctly and has the best channel to destination. Asymptotic analysis of outage probability shows that the scheme with relay selection achieves the same diversity-multiplexing tradeoff as the non-orthogonal amplify-and-forward scheme, but it obtains more outage capacity at lower SNR and is easier to implement.
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