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We propose a novel semi-blind tensor-based MIMO channel estimation scheme that employs orthogonal space-time block codes and per-antenna power loading at the transmitter. Our scheme eliminates the unknown transmit codewords and constructs a tensor model that contains the channel coefficients by performing post-processing at the receiver. Then, the channel matrix has been found through appropriate tensor decompositions of the post-processed data. Since the inherent structure of the data model has been exploited, we obtain a more accurate channel estimate compared to previously devised matrix-based approaches. Further, introduced ambiguities have been resolved via additional pilot symbols in a semi-blind manner. Simulation results demonstrate performance improvements of our proposed tensor-based approach with respect to some current state-of-the-art semi-blind channel estimation schemes.