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Rapid growth and increasing demands for near-ubiquitous high-quality high-data-rate services present the most challenges for wireless system design. As an effective method to provide such services, space-time (ST) coding is gaining more and more attention. The paper extends ST coding, originally designed for known frequency-nonselective fading channels, to unknown frequency-selective channels. An ST transmit diversity wireless time-division multiple-access system, that is equipped with multiple antennas at both transmit and receive sides, is considered. In this system, a novel scheme is presented to suppress intersymbol interference and to demodulate coherently the information symbols with estimated channel state information. The proposed algorithm is powerful and computationally efficient. In addition to the discussion of system identifiability, both theoretical analysis and numerical simulation are presented to illustrate the performance of the proposed estimator and receiver in multipath fading channels.