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The average symbol error probability (ASEP) of multiple-input multiple-output (MIMO) systems employing transmit antenna selection (TAS) and orthogonal space-time block code (OSTBC) over correlated Rayleigh fading channels is considered. We first derive the correlation coefficients between two antenna elements as a function of the antenna spacing, the standard deviation of the power azimuth spectrum (PAS) and the mean angle of arrival (AOA) for the truncated Laplacian model, which is appropriate for indoor channels. Then we introduce the correlation matrix, and establish a correlated channel model. Based on the equivalent scalar additive white Gaussian noise (AWGN) channel approach, the exact form expressions of the signal-to-noise ratio (SNR) at the receiving end are derived. The system performance under different conditions was evaluated through numerical simulations. Numerical results show that: the ASEP performance is affected by the spatial correlation, which varies according to the antenna spacing, PAS standard deviation and mean AOA.