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To obtain full benefits of the Alamouti space-time code design on a time-varying acoustic channel, the channel variation is decoupled into two parts: the gain, which is assumed to be constant over an Alamouti pair (two consecutive OFDM blocks), and the phase, which is not restricted in this manner, but allowed to vary from one block to another in a piecewise linear fashion. Under this model, the receiver assumes a simplified structure in which conventional Alamouti data detection and channel estimation are aided by Doppler tracking. System performance is demonstrated using experimental data transmitted over a 1 km shallow water channel in the 8-18 kHz acoustic band, using QPSK modulation and a varying number of carriers (up to 1024). The proposed design shows a gain of up to 2 dB as compared to the reference single-transmitter case.