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A new blind channel estimation approach for orthogonally coded multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems is proposed. The main idea of our technique is, using specific properties of the orthogonal space-time block codes (OSTBCs), to estimate the finite impulse response (FIR) channel parameters in the time domain instead of doing this in the frequency domain independently for each subcarrier. This results in a substantially improved parsimony of the channel parametric model as compared to the direct per subcarrier channel estimation methods and allows coherent processing across the subcarriers. It is shown that using the semidefinite relaxation (SDR) technique, our channel estimation problem can be approximated as a convex semidefinite programming (SDP) problem and, hence, can be solved efficiently using modern convex optimization methods. Our simulations validate the performance and/or computational complexity advantages of the proposed method as compared to some current state-of-the-art blind MIMO-OFDM channel estimation methods.