In this paper, we propose a jointly designed diagonal precoder and minimum mean-square error receiver with ordered successive interference cancellation (MMSE-OSIC) for the double space-time transmit diversity (DSTTD) system with low feedback and low-complexity. The proposed transceiver utilizes the structure of the equivalent channel of DSTTD, showing lower computational complexity and better error rate performance than the conventional antenna shuffling schemes with the channel state information at the transmitter.