## 4 Proposed Efficient Design for Transmit Waveform and UAV Altitude
Specifically, the width and power of the right side-lobe region were slightly broader and higher, respectively, than those of the left side-lobe region in order to transfer more power to the second EHD at \(80^{\circ}\) compared with the first EHD at \(-80^{\circ}\). Notably, it was verified that the proposed efficient design achieved similar performance to the optimal design. Further, the beam patterns of both designs closely matched those obtained with the radar-only design, except for the side-lobe regions. Also, Figure 7a-c depict the performance evaluations for Scenario 3, where \([\phi_{1},\phi_{2}]=[-80^{\circ},80^{\circ}]\). Figure 7a,b verifies that the proposed efficient design significantly outperformed the methods with \(H_{\text{min}}\) and \(H_{\text{max}}\), achieving near-optimal performance in terms of both the objective function value and the trade-off region, respectively. As expected, the beam pattern MSE decreased as the harvested power MSE increased, and vice versa. Compared with those in Scenario 1, where \([\phi_{1},\phi_{2}]=[-20^{\circ},20^{\circ}]\), and Scenario 2, where \([\phi_{1},\phi_{2}]=[-60^{\circ},60^{\circ}]\), both the objective function value and the trade-off region in Scenario 3, where \([\phi_{1},\phi_{2}]=[-80^{\circ},80^{\circ}]\), showed different performance. Additionally, Figure 7c presents a comparison of the execution time of each method. As expected, the execution time of the optimal design was about \(1400\) s, while that of the proposed design was within \([160,770]\). Therefore, it was shown that the proposed efficient design substantially reduced the execution time compared with the optimal design. The numerical results verify that the proposed efficient design, which has low complexity and jointly optimizes the transmit waveform and UAV altitude, yields considerable performance improvements in terms of both the beam pattern for radar sensing and the harvested power of the EHDs, as well as the execution time due to the lower computational complexity. Additionally, the performance of UAV-enabled ISWPT systems depends on the network environment, such as the angular directions of the targets, as well as the location and desired amount of harvested power of the EHDs. ## 6 Conclusions

In this study, we developed a method for jointly designing the waveform and UAV altitude to accurately sense multiple targets while efficiently transferring power to multiple devices simultaneously in UAV-enabled ISWPT systems. By analyzing a challenging non-convex optimization problem, we characterized the fundamental trade-off between the desired beam pattern for radar sensing and the desired harvested power of the devices for WPT operation. The method for determining the optimal waveform and altitude was developed based on the PSO algorithm, resulting in the maximum value of the desired harvested power of the EHDs. We further developed an efficient, low-complexity method for jointly designing the transmit waveform and altitude by devising a novel transmit waveform and optimizing its parameters. According to the numerical results, it was confirmed that the proposed method offers benefits not only in terms of radar sensing and WPT performance improvements but also in reducing computational complexity. The extension of the proposed design to semi-physical simulations for practical implementation remains one of our ongoing research topics. **Funding:** This work was supported by the IITP(Institute of Information & Coummunications Technology Planning & Evaluation)-ICAN(ICT Challenge and Advanced Network of HRD) grant funded by the Korea government (Ministry of Science and ICT) (IITP-2024-RS-2022-00156409). **Data Availability Statement:** The data are contained within the article. **Conflicts of Interest:** The author declares no conflicts of interest. Figure 7: Performance comparison of various methods in Scenario 3, where \([\phi_{1},\phi_{2}]=[-80^{\circ},80^{\circ}]\). ## References

* [PERSON] et al.