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Space-time codes are the joint design of channel coding, modulation, transmit and receive diversity to provide the best tradeoff between data rate, diversity advantage, and code complexity. Specific codes improve the transmission performance in wireless fading channel by providing both the diversity advantage and the coding advantage, where channel state information (CSI) is available at the receiver. But in practice, it is very difficult to estimate the CSI accurately because of the characteristic of wireless fading channel: multi-path fading and time-variance. Hence, a theoretical study of the symbol error rate (SEK) for orthogonal space-time block codes (OSTBC) is presented in this paper, in the absence of perfect CSI. It is proved that the squaring method used to simplify the decoding of OSTBC in [Li Xiangming et al., 2001] could also be used when there is no perfect CSI at receiver. Using this squaring method, a closed-form expression of both SNR and SER for OSTBC can also be derived under these conditions. Simulation results show that performance in the presence of the channel estimation errors is less than that with ideal condition, and that more estimation errors, means more performance loss. It is also proved through the simulations that the BER bound increases slowly when the variance of channel estimation errors is less than some little value, e.g. 0.2. So in practice, it is important to keep the variance of estimation errors less than this value.