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In this paper, we propose an ergodic interference alignment (IA) method for interference elimination in spectrum sharing multiple-input multiple-output (MIMO) radar and multi-user MIMO communication systems. In existing ergodic IA methods, the channel state information (CSI) is generally assumed to be constant, but time-varying channels should be considered in practice. Differently, our proposed ergodic IA allows to time-varying and/or frequency selective channels for spectrum sharing radar-communication systems. The essence is equivalent to design a simple transmit beamforming, which helps to find a pair of desired complementary channels easily without long-time system delay, therefore, the interferences can be effectively cancelled. The proposed method is evaluated by generalized likelihood ratio test (GLRT) and signal to interference plus noise ratio (SINR) for the radar functionality, while the communication functionality is examined by bit error rate (BER) performance. Both theoretical analysis and simulation results validate that the effectiveness of the ergodic IA method for spectrum sharing radar-communication systems. [ABSTRACT FROM AUTHOR]