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Due to higher peak-to-average power ratio and higher power backing-off in OFDM relaying systems, a cyclic prefixed single-carrier cooperative diversity system is considered in this paper. Under the transmission power constraint, the joint optimal power allocation to the source and relay node is investigated. For a two-hop decode-and-forward relaying protocol, the optimal power allocation is first obtained in the considered system, and then the opportunistic destination terminal selection is applied to improve the achievable average spectral efficiency (ASE). Based on the proposed QR decomposition (QRD)-based receiver in the destination terminal, closed-form expressions for the maximum achievable ASE are derived. Simulation results verify the derived closed-form analytical expressions.