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Cooperative transmission using space time codes can be used to reduce transmission energy consumption for long range communication in wireless sensor networks (WSN). However, differing from traditional (multi-input-multi-output) MIMO systems, distributed cooperative communication systems in WSN usually lack of perfect synchronization. For the cooperative systems using Alamouti code, the effect of synchronization error on the receive bit error rate (BER) performance over Rayleigh fading channel is investigated in this paper. Taking also path loss effect and the propagation delay into account, the optimal transmit power allocation and the optimal reception areas are presented. The analytical and simulation results show that, for a small range of synchronization error and using the optimal transmit power allocation, the degradation of receive BER performance is negligible for some reception area.