In this paper, we focus on the coexistence between a MIMO radar and cellular base stations. We study the interfering channel estimation, where the radar is operated in the "search and track" mode, and the BS receives the interference from the radar. Unlike the conventional methods where the radar and the cellular systems fully cooperate with each other, in this work we consider that they are uncoordinated and the BS needs to acquire the interfering channel state information (ICSI) by exploiting the radar probing waveforms. For completeness, both the line-of-sight (LoS) and Non-LoS (NLoS) channels are considered in the coexistence scenario. By further assuming that the BS has limited a priori knowledge about the radar waveforms, we propose several hypothesis testing methods to identify the working mode of the radar, and then obtain the ICSI through a variety of channel estimation schemes. Based on the statistical theory, we analyze the theoretical performance of both the hypothesis testing and the channel estimation methods. Finally, simulation results verify the effectiveness of our theoretical analysis and demonstrate that the BS can effectively estimate the interfering channel even with limited information from the radar.