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Spectrum sharing and full duplexing are two promising technologies for alleviating the severe spectrum crunch that has threatened to blight the progress of future wireless communication systems. In this paper, we consider a two tier coexistence framework involving a collocated multiple-input-multiple-output (MIMO) radar system (RS) and a full-duplex MIMO cellular system (CS). Considering imperfect channel state information and hardware impairments at the CS, we focus on a spectrum sharing environment to improve the quality of service (QoS) for cellular users by designing i) precoders at CS via the minimization of sum mean-squared-errors, subject to the constraints of transmit powers of the CS and probability of detection (PoD) of the RS, and ii) precoders at the RS to mitigate the interference from RS towards CS. While the monotonically increasing relationship between PoD and its non-centrality parameter is …