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We consider a full duplex (FD) multiple-input multiple-output (MIMO) underlay cognitive radio cellular network, in which an FD secondary base-station (BS) serves multiple half-duplex uplink (UL) and downlink secondary users (SUs) at the same time and frequency. We assume that the channel state information (CSI) available at the transmitters is imperfect, and the errors of the CSI are assumed to be norm bounded. Under the impact of channel uncertainty, we address the sum mean-squared-errors minimization problem subject to individual power constraints at the UL SUs, a total power-constraint at the secondary BS, and the interference constraints on the primary users by the secondary network. By transforming the problem into an equivalent semidefinite programming (SDP), we propose an iterative alternating algorithm to compute the transceiver matrices jointly. Moreover, to reduce the high computational complexity of the SDP method, we develop a cutting-set method, which solves the problem by alternating between an optimization step (transceiver design) and a pessimization step (worst-case channel analysis). Numerical results are presented to show the effectiveness and robustness of the proposed algorithms.
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