The achievement of optimum performance of a co-existing radar and communication (CRC) system is a challenging task when the channel state information (CSI) for the interference channels is imperfect, particularly when the power of the CRC system is restricted. To address this issue, this article proposes a robust CRC system design that considers CSI uncertainty. Specifically, the objective is to design a robust beamforming scheme to maximize the radar performance subject to the user signal-to-interference-plus-noise ratio （SINR）and the transmit power of the CRC system. Due to the infinite number of constraints that result from the CSI uncertainty of the interference channels, a loosely bound robust approach is developed, which employs the shrinkage method to convert the infinite number of constraints into a finite number of constraints. However, the performance of the loosely bound robust approach is not satisfactory. Therefore, this paper further proposes a sub-optimal robust approach that employs the S-procedure to transform the infinite number of inequality constraints into equivalent finite linear matrix inequalities (LMIs). The simulation results indicate that the design of the robust CRC system can significantly improve the system performance compared to the traditional design approach.
