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This paper presents a simple single-carrier (SC) distributed space-time block coded transmission scheme for asynchronous cooperative communications over frequency-selective channels. The cyclic prefix (CP) at the source node and relay nodes is used to combat inter-symbol interference from multi-path fading and the timing errors from the relay nodes. In this scheme, the relay nodes only implement very simple operations on their received signals to construct distributed space-time block code, and decoding, DFT and IDFT operations are only needed at the destination node. The low complexity SC zero-forcing frequency domain equalization (ZF-FDE) is applied at the destination node to recover the transmitted signals. The analysis and simulation results demonstrate that this simple SC scheme can achieve order-two spatial diversity gain for amplify-and-forward based cooperative communication over frequency-selective channels in the presence of asynchronization between relay nodes.