This paper investigates the application of intelligent reflecting surface (IRS) in an underlay cognitive radio network (CRN), where a multi-antenna cognitive base station (CBS) utilizes spectrum assigned to the primary user (PU) to communicate with a secondary user (SU) via IRS in the presence of multiple coordinated eavesdroppers. To achieve the trade-off between the secrecy rate (SR) and energy consumption, we propose a secrecy energy efficiency (SEE) maximization scheme by jointly design the transmit beamforming at CBS and the reflect beamforming at IRS under the SR constraint of SU, the transmit power constraint of CBS, the limited interference temperature of PU and the unit modulus constraint of IRS. The problem is challenging to solve due to the coupled optimization variables and unit modulus constraint, for which an iterative alternating optimization algorithm is proposed. As for optimizing the reflect beamforming, we introduce an auxiliary variable and convert the original non-convex problem into a semi-definite programming with rank-1 constraint, and then propose an iterative penalty function based algorithm to implement the optimal reflect beamforming. As for optimizing the transmit beamforming, we convert the original problem into an equivalent subtractive form, which is further transformed into a convex function by employing the difference of two-convex functions method. Furthermore, we provide a second-order-cone-programming approximation approach to reduce the computational complexity. The effectiveness and superiority of our proposed algorithm are verified in the simulation results.
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