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In this paper, we propose a mutual interference alignment (IA) method for interference elimination in co-existing multiple-input multiple-output (MIMO) radar and multi-user MIMO communication systems, namely, radar-communication systems. Traditional IA methods proposed for communication systems cannot be directly adopted in the radar-communications due to failure to fulfill the requirements of radar target detection. In contrast, our proposed mutual IA method can efficiently improve the signal-to-noise ratio (SNR) needed by radar functionalities without reducing the degrees-of-freedom (DoFs) of communication system, which implies no degradation for the communication performance. The algorithm idea is first to align all interferences at every receiver to one signal space, then the interferences can be easily canceled by receive filter. It is examined by the Neyman-Pearson (NP) test for radar functionality, while the communication performance is evaluated by DoFs and bit error rate (BER) analysis. Both theory analysis and numerical results are provided to validate the effectiveness of the proposed mutual IA method for co-existing radar and communication systems. [ABSTRACT FROM AUTHOR]