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In this paper, we propose a low-complexity decision-directed channel-estimation scheme, which offers improved performance for space-frequency-block-coded orthogonal frequency-division multiplexing (SFBC-OFDM) systems under doubly selective (i.e., frequency selective and fast fading) channels. First, we propose a square-root-free inverse-QR-decomposition-based groupwise recursive (SIQR-GR) channel-estimation algorithm employing sequences of scaled Givens rotations. The proposed SIQR-GR scheme recursively processes data decisions corresponding to the SFBC groups within each OFDM block to improve system performance under doubly selective channels. Furthermore, the avoidance of square roots and the utilization of scaled Givens rotations ensure that the proposed SIQR-GR scheme is computationally efficient. Second, we derive semi-analytical expressions for the normalized mean square error (NMSE) performance of SIQR-GR and verify the accuracy of the NMSE analysis via numerical simulations. Finally, we provide performance and complexity comparisons between SIQR-GR and previously proposed schemes. These comparisons show an excellent performance-complexity tradeoff achieved by SIQR-GR over the previous solutions under various channel conditions. [ABSTRACT FROM AUTHOR]