In this paper, a high-rate space-time block-coded (STBC) mobile communication system using imperfect channel-state-information (CSI) is presented, which is working over the time-selective flat-fading wireless channels. In the work, a flat-fading channel is modelled as a first-order Markov-process, taking into account Doppler shifts and carrier frequency offsets. The STBC data-rate 5/4 with two-transmitter antennas is attained by maximizing the coding gain and by minimizing the transmitted signal peak-to-minimum-power-ratio, while using the selective power scaling in combination with quadrature-phase-shift-keying digital modulation technique. The time-selective nature of underlying channel leads to reduction in the diversity gain, though optimum power scaling factor is incorporated. However, imperfect CSI usually arises due to the availability of noisy channel estimates at the receiver, which causes system performance degradation. Simulation results are presented to illustrate that the effective throughput in terms of frame-error-rate or symbol-error-rate of the presented data-rate $${5 \mathord{\left/ {\vphantom {5 4}} \right. \kern-0pt} 4}$$ STBC system is adversely affected because of the noisy channel estimates. But, an efficient channel estimator helps in combating the time-selectivity of channel, and in turn results in effective throughput improvement under the high signal-to-noise-ratio (SNR) conditions only. Subsequently, the data-rate $${9 \mathord{\left/ {\vphantom {9 8}} \right. \kern-0pt} 8}$$ STBC system with four-transmitter antennas is explored using similar strategy working over the time-nonselective (time-varying) flat-fading channels, which performs well under the high SNR and low channel estimation noise/error conditions.