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Reliable channel state information at the transmitter (CSIT) can improve the throughput of wireless networks significantly. In a realistic scenario, there is a mismatch between the CSIT and the true channel. The CSIT may be outdated due to channel variations or could be erroneous due to quantization effects. In this paper, robust transmit beamforming (rBF) and the combination of time-reversal space-time block codes (TR-STBCs) with rBF, both optimized for transmission over frequency-selective fading channels with decision-feedback equalization (DFE), are considered. The reliability of the CSIT is taken into account for the design of channel state dependent transmit signal processing algorithms to achieve robustness against imperfect CSIT. Noisy (quantized) CSIT, outdated CSIT, and the combination of both cases are considered. We show that the performance of the rBF scheme is upper and lower bounded by that of transmit BF with perfect CSIT and optimized delay diversity (ODD) without instantaneous CSIT, respectively. The combination of a TR-STBC with rBF yields significant BF gains in addition to the diversity gains of the TR-STBC for reliable CSIT, whereas for unreliable CSIT, the performance is identical to that of the TR-STBC.