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This paper proposes a new transmitter precoding approach for co-existence between multiple-input multiple-output (MIMO) radar and multi-user MIMO communication systems employing phase shift keying (PSK) modulation. To enable the satisfactions of radar communication functionalities, the common practice is to suppress the mutual interferences, while our proposed scheme is to use the known interferences existing already in radar and communications systems and make the most of them: selectively reverse the destructive interferences to the negative direction while retaining the interferences which are beneficial to the desired signal. The resulting interferences are always kept constructive and can contribute to the power of the useful signal. Numerical results validate that the effective signal to noise ratio (SNR) can be enhanced by 7 dB with no additional power-peruser investment. [ABSTRACT FROM AUTHOR]