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In this paper, we analyze the performance of orthogonal space-time block codes (OSTBC) with M-PSK and M-QAM modulations over shadowed Rician fading channels. The shadowed Rician channel is a generalization of the Rician model, which is generally used to model mobile satellite channels. We derive the moment generating function (MGF) of instantaneous signal-to-noise ratio (SNR) after space-time block decoding (signal combining) over such channels. Using a well-known MGF-based analysis approach, we obtain some expressions for the average symbol error rate (SER) and bit error rate (BER) of OSTBC over shadowed Rician fading channels.