This paper studies a cognitive radio (CR) network which consists of a full-duplex (FD) multi-user (MU) multiple-input multiple-output (MIMO) secondary user (SU) networks operating within the coverage of multiple primary users (PUs). It is assumed that the channel state information (CSI) matrices associated with SU systems are perfectly known whereas the CSI ones from SUs to PUs are imperfectly estimated. The problem of interest is to design robust precoding matrices at the SUs to maximize the

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... sum rate subject to the SU transmit power constraints and harmful interference restrictions at PUs. Due to non-concavity of the objective function and intractability of robust PU interference constraints, the design problem is non-convex and challenging to directly solve. We exploit the difference of two concave functions to recast the sum rate objective function as a lower bounded concave one. In addition, a linear matrix inequality (LMI) transformation is used to handle the semi-infinite robust interference constraints. Then, the sequential convex programming method is carried out to iteratively solve a convex optimization problem in each iteration. The simulation results are provided to investigate the CR sum-rate (spectral efficiency) performance and the robustness against the CSI uncertainty.