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In this paper, the performance of multi-level quadrature amplitude modulation (M-QAM) systems is studied analytically when Alamouti space-time transmit diversity (STTD) coding is used for transmission over Rayleigh fading channels. The effect of self-interference (interference from another simultaneously transmitted symbol in the STTD scheme for the same user) due to imperfect channel estimation is investigated. Based on the characteristic function method, a closed-form expression of the bit error rate (BER) is derived. Numerical results for 16/64-QAM show that, with the Alamouti STTD technique, the BER performance of the QAM system can be improved significantly. The effect of receive antenna diversity is also investigated. It is shown that high-order QAM constellations can be employed even in low signal to noise ratio (SNR) with the transmit diversity technique in conjunction with receive antenna diversity.