## 1 Introduction  
In recent years, as a promising transmission method, the new generation wireless systems can rely on IRS and UAV to enhance their spectral and energy efficiency since IRS is examined as a cost-effective deployment approach [1; 2; 3]. Specifically, by varying the amplitude and phase for the incident signal, an IRS leverages its low-cost reconfigurable passive elements to reflect signals to distant users effectively [4; 5]. The system relying on IRS can enhance the link quality and enlarge the coverage significantly when IRS is able to adjust amplitude-reflection coefficients and phase-shift variables appropriately [6; 7; 8]. The authors in [7] studied secure IRS-UAV systems by integrating IRS with UAV in wireless networks, which are susceptible to eavesdropping related to air-ground line-of-sight channels. To facilitate security, IRS can be leveraged due to its capability of reconfiguring the propagation environment, and thus IRS helps to reduce the impacts of eavesdroppers. The secure transmission of an IRS-assisted UAV network is analyzed under the impact of an eavesdropper. The transmit beamforming, the trajectory of UAV and the phase shift of IRS can be optimized to further obtain maximal rates [7]. Besides, IRS has two prominent features--passive reflection with low power consumption and the operation of full-duplex (FD) mode without self-interference--and these benefits are crucial in comparison with conventional approaches--for example, relaying networks [9]. To further increase energy and spectrum efficiency, the power-domain NOMA technology has been studied as a potential technique for IoT applications [10; 11]. The NOMA architecture can be described as follows. In the transmit side of a NOMA system, different amounts of power at the transmitter or the base station (BS) are assigned to multiple users when superimposing signal processing, while those users share the same orthogonal resources such as frequency, time and spreading code. At the receiver side associated with a downlink, demultiplexing the transmitted signals is conducted by employing successive interference cancellation (SIC) [12]. To decode the needed signals, the user treats all the weaker user signals as interference; then, its own signal can be decoded in the last step [13; 14; 15]. In contrast to the downlink, the common receiver or the BS achieves a signal in an uplink, allowing multiple users to consume the common communication. This means that all users send a superposed signal comprising the signals of these users toward the BS. For signal detection, the BS needs the assistance of SIC to decode the signals of the transmitting users [12]. In this way, a higher number of users can be served in the context of NOMA, which exhibits a significant improvement compared with the conventional orthogonal multiple access (OMA)-aided transmission approach [11]. The combination of IRS and NOMA could be a prominent technique to leverage energy-efficient and low-cost deployment [16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. The authors in [16] designed an IRS-NOMA system by considering both continuous phase shifting and discrete phase shifting corresponding to the ideal IRS and the non-ideal IRS circumstance. To demonstrate performance, closed-form expressions are derived to examine the average required transmit power, the outage probability and the diversity order by benefiting from the Laguerre series and the isotropic random vector. In demonstrated analytical results, the BS antenna number and the IRS element number are consistently affected by varying the transmit power. In [17], IRS-aided simultaneous wireless information and power transfer (SWIPT) NOMA networks are studied. In particular, a problem of minimizing the transmit power at the BS can be solved by jointly optimizing the BS transmit beamforming vector, power splitting (PS) ratio, SIC decoding order and IRS phase shift. This optimization is guaranteed to satisfy the energy harvested threshold of each user and the quality-of-service (QoS) constraint.