In this paper, we consider the effect of carrier offsets in arbitrarily correlated flat-fading multiple-input multipleoutput (MIMO) Rayleigh channels. We propose a doubledifferential coding for square orthogonal space-time block code (OSTBC) with non-unitary constellations over flat-fading MIMO channels with carrier offsets. In order to improve the performance of the proposed double-differential orthogonal space-time block code (DDOSTBC) over arbitrarily correlated Rayleigh channel we introduce

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... a full memoryless precoder matrix in the transmitter. For the proposed precoded DDOSTBC, a pair-wise error performance (PEP) analysis is conducted. Then we propose a precoder design based on the PEP upper bound. The proposed DDOSTBC differs from the previously proposed DDOSTBC by: 1) The previously proposed DDOSTBC is aplicable to only a specific class of OSTBC which follows diagonal group property, whereas, the proposed DDOSTBC is applicable to any square OSTBC. 2) The previously proposed DDOSTBC can work with M -PSK constelation only, whereas, the proposed DDOSTBC is applicable to M -QAM, M -PAM, or M -PSK constellations. The proposed DDOSTBC provides higher performance gain as compared to the same rate previously proposed DDOSTBC. In addition, the proposed precoded DDOSTBC is able to perform better than the unprecoded DDOSTBC over arbitrarily correlated Rayleigh channels.