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In this paper we develop a new analytical methodology for the evaluation of the outage probability of cooperative decode-and-forward (DF) automatic-repeat-request (ARQ) relaying under packet-rate fading (fast fading or block fading) channels, where the channels remain fixed within each ARQ transmission round, but change independently from one round to another. We consider a single relay forwarding Alamouti-based retransmission signals in the cooperative ARQ scheme. In particular, (i) we derive a closed-form asymptotically tight (as SNR → ∞) approximation of the outage probability; (ii) we show that the diversity order of the DF cooperative ARQ relay scheme is equal to 2L-1, where L is the maximum number of ARQ (re)transmissions; and (iii) we develop the optimum power allocation for the DF cooperative ARQ relay scheme. The closed-form expression clearly shows that the achieved diversity is partially due to the DF cooperative relaying and partially due to the fast fading nature of the channels (temporal diversity). With respect to power allocation, it turns out that the proposed optimum allocation scheme depends only on the link quality of the channels related to the relay, and compared to the equal power allocation scheme it leads to SNR performance gains of more than 1 dB. Numerical and simulation studies illustrate the theoretical developments.