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This work addresses joint transceiver optimization for multiple-input, multiple-output (MIMO) systems. In practical systems the complete knowledge of channel state information (CSI) is hardly available at transmitter. To tackle this problem, we resort to the codebook approach to precoding design, where the receiver selects a precoding matrix from a finite set of pre-defined precoding matrices based on the instantaneous channel condition and delivers the index of the chosen precoding matrix to the transmitter via a bandwidth-constraint feedback channel. We show that, when the symbol constellation is improper, the joint codebook based precoding and equalization can be designed accordingly to achieve improved performance compared to the conventional system.