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In this paper, a decision directed square-root free inverse QR-decomposition based groupwise recursive (SIQR-GR) channel estimation scheme is proposed for space-frequency block coded orthogonal frequency division multiplexing (SFBC-OFDM) systems. The proposed SIQR-GR channel estimation algorithm employs sequences of scaled Givens rotations to recursively processes data decisions corresponding to the SFBC groups within each OFDM block. As a result of the groupwise recursive processing, the proposed SIQR-GR scheme yields improved system performance under doubly-selective (i.e., frequency- selective and fast fading) channels. To evaluate the performance advantages of SIQR-GR we compare the normalized mean square error (NMSE) and symbol error rate (SER) performances of SIQR-GR to those corresponding to previously proposed channel estimation schemes. Furthermore, we also present computational complexity comparisons between SIQR-GR and the previously proposed schemes. These comparisons show an excellent performance-complexity tradeoff achieved by SIQR-GR over the previously proposed solutions.