The acquisition of channel state information (CSI) is essential in MIMO-OFDM communication systems. Data-aided enhanced receivers, by incorporating domain knowledge, effectively mitigate performance degradation caused by imperfect CSI, particularly in dynamic wireless environments. However, existing methodologies face notable challenges: they either refine channel estimates within MIMO subsystems separately, which proves ineffective due to deviations from assumptions regarding the time-varying nature of channels, or fully exploit the time-frequency characteristics but incur significantly high computational overhead due to dimensional concatenation. To address these issues, this study introduces a novel data-aided method aimed at reducing complexity, particularly suited for fast-fading scenarios in fifth-generation (5G) and beyond networks. We derive a general form of a data-aided linear minimum mean-square error (LMMSE)-based algorithm, optimized for iterative joint channel estimation and signal detection. Additionally, we propose a computationally efficient alternative to this algorithm, which achieves comparable performance with significantly reduced complexity. Empirical evaluations reveal that our proposed algorithms outperform several state-of-the-art approaches across various MIMO-OFDM configurations, pilot sequence lengths, and in the presence of time variability. Comparative analysis with basis expansion model-based iterative receivers highlights the superiority of our algorithms in achieving an effective trade-off between accuracy and computational complexity.