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This paper studies theoretically the bit error rate (BER) performance of cooperative transmission using space-time block code (STBC) in a fully distributed manner. Specifically, we first propose a STBC-based cooperative signaling structure to make the cooperation of three single-antenna terminals possible. Then, we derive the closed-form BER expressions for both cooperation and noncooperation schemes under flat Rayleigh fading channel plus additive white Gaussian noise (AWGN). The validity of these expressions is verified by Monte-Carlo simulations. A variety of numerical and simulation results reveal that the cooperative transmission achieves higher diversity gain and better performance than the direct transmission for the same total transmit power.