  Cognitive radio (CR) is an effective solution to improve the spectral
efficiency (SE) of wireless communications by allowing the secondary users
(SUs) to share spectrum with primary users (PUs). Meanwhile, intelligent
reflecting surface (IRS) has been recently proposed as a promising approach to
enhance SE and energy efficiency (EE) of wireless communication systems through
intelligently reconfiguring the channel environment. In this paper, we consider
an IRS-assisted downlink CR system, in which a secondary access point (SAP)
communicates with multiple SUs without affecting multiple PUs in the primary
network and all nodes are equipped with multiple antennas. Our design objective
is to maximize the achievable weighted sum rate (WSR) of SUs subject to the
total transmit power constraint at the SAP and the interference constraints at
PUs, by jointly optimizing the transmit precoding at the SAP and the reflecting
coefficients at the IRS. To deal with the complex objective function, the
problem is reformulated by employing the well-known weighted minimum
mean-square error (WMMSE) method and an alternating optimization (AO)-based
algorithm is proposed. Furthermore, a special scenario with only one PU is
considered and AO algorithm is adopted again. It is worth mentioning that the
proposed algorithm has a much lower computational complexity than the above
algorithm without the performance loss. Finally, some numerical simulations
have been provided to demonstrate that the proposed algorithm outperforms other
benchmark schemes.
