## 3 Proposed Max-SNR-FP Scheme
### Optimize \(\mathbf{v}\) Given \(\mathbf{\Phi}\) and \(\mathbf{\Psi}\)
By comparing the three proposed schemes with the existing scheme in [34], the decreasing order of their achievable rates is: Max-SNR-FP, Max-SNR-MM, the existing scheme, and Max-SNR-EAR. The decreasing order of the computational complexity is: the existing scheme, Max-SNR-FP, Max-SNR-MM, and Max-SNR-EAR. An extension to optimize multi-user hybrid IRS and UAV-aided DM networks will be considered in our future work. \[P_{r} =\text{Tr}\Big{(}\mathbf{\Psi}\Big{(}\rho_{sr}\text{Pr}_{sr}\mathbf{v }\mathbf{v}^{H}\mathbf{H}_{sr}^{H}+\sigma_{r}^{2}\mathbf{I}_{M}\Big{)}\mathbf{ \Psi}^{H}\Big{)}\]0 Achievable rate versus the numbers of IRS phase shift elements. \[P_{r} =\text{Tr}\Big{(}\mathbf{\Psi}\Big{(}\rho_{sr}\text{Pr}_{sr}\mathbf{v }\mathbf{v}^{H}\mathbf{H}_{sr}^{H}+\sigma_{r}^{2}\mathbf{I}_{M}\Big{)}\mathbf{ \Psi}^{H}\Big{)}\]1 Computational complexity versus the numbers of IRS elements. **Author Contributions**: [PERSON] were mainly responsible for the model building and algorithmic design of the system. [PERSON] and [PERSON] were mainly responsible for the directional and IRS-aided directional modulation networks. [PERSON] designed the whole frame and structure of the paper. [PERSON] and [PERSON] were mainly responsible for the UAV and IRS-aided UAV communication networks. [PERSON] improved the readability of the paper with grammatical modification and polishing. All authors have read and agreed to the published version of the manuscript. **Funding**: This work was supported by the National Natural Science Foundation of China (nos. U22A2002, 62071234, and 61972093), the Hainan Province Science and Technology Special Fund (ZDKJ2021022), the Scientific Research Fund Project of Hainan University (grant KYQD(ZR)-21008), the Fujian University Industry University Research Joint Innovation Project (no. 2022H6006), and the Innovative Research Project of Postgraduates in Hainan Province (Qhyb2022-83). **Data Availability Statement**: No data are associated with this article. **Acknowledgments**: We thank the anonymous reviewers for their helpful comments. **Conflicts of Interest**: The authors declare that they have no conflict of interest. ## Abbreviations

The following abbreviations are used in this manuscript: \begin{tabular}{l l} IRS & Intelligent reflecting surface \\ UAV & Unmanned aerial vehicle \\ DM & Directional modulation \\ SNR & Signal-to-noise ratio \\ FP & Fractional programming \\ Max-SNR-FP & Maximum SNR-FP \\ EAR & Equal amplitude reflecting \\ Max-SNR-EAR & Maximum SNR-EAR \\ MM & Majorization-minimization \\ Max-SNR-MM & Maximum SNR-MM \\ PSM & Phase shift matrix \\ LoP & Line-of-propagation \\ SCA & Successive convex approximation \\ SR & Secrecy rate \\ AN & Artificial noise \\ PSM & Phase shift matrix \\ MISO & Multiple-input single-output \\ PL & Path loss \\ SLNR & Signal-to-leakage-noise ratio \\ BS & Base station \\ FLOPs & Float-point operations \\ \end{tabular} 

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