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In this paper, the design of a simple orthogonal distributed space-time block code for a noncoherent amplify-and-forward (AF) half-duplex cooperative relay system is proposed by utilizing a pair of coprime phase-shift keying (PSK) constellations and the Alamouti coding scheme. It is shown that one significant advantage of such design is that, in a noise-free case, for any given nonzero received signals, the channel coefficients and the transmitted signals can be blindly and uniquely determined with a simple closed-form solution. The other significant advantage is that, in a noise case, the least square error (LSE) receiver also has a simple closed-form solution to jointly estimate the channel and the transmitted signals. Simulation results show that our proposed scheme obtains a significant gain of signal-to-noise ratio over the training scheme.