  In this paper, intelligent reflecting surface (IRS) is introduced to enhance
the network performance of cognitive radio (CR) systems. Specifically, we
investigate robust beamforming design based on both bounded channel state
information (CSI) error model and statistical CSI error model for primary user
(PU)-related channels in IRS-aided CR systems. We jointly optimize the transmit
precoding (TPC) at the secondary user (SU) transmitter (ST) and phase shifts at
the IRS to minimize the ST' s total transmit power subject to the quality of
service of SUs, the limited interference imposed on the PU and unit-modulus of
the reflective beamforming. The successive convex approximation (SCA) method,
Schur's complement, General sign-definiteness principle, inverse Chi-square
distribution and penalty convex-concave procedure are invoked for dealing with
these intricate constraints. The non-convex optimization problems are
transformed into several convex subproblems and efficient algorithms are
proposed. Simulation results verify the efficiency of the proposed algorithms
and reveal the impacts of CSI uncertainties on ST's minimum transmit power and
feasibility rate of the optimization problems. Simulation results also show
that the number of transmit antennas at the ST and the number of phase shifts
at the IRS should be carefully chosen to balance the channel realization
feasibility rate and the total transmit power.
