# Robust Low-Sidelobe Transmit Beamforming under Peak-to-Average-Power Ratio Constraint
## 5 Conclusions  
This paper presents a robust TBF method with sidelobe-level control for phased-array radar under PAPR and norm constraints. To suppress the strong clutter and rapidly changing interference on the near-ground side for LSS radar, we developed a robust TBF problem to minimize the PSL in the preset region, where the PAPR constraint and the norm constraint are introduced to enhance the radar transmit efficacy and to improve the robustness, respectively. To further improve the robustness, we merged the steering vector mismatch into the proposed problem and translated the corresponding nonconvex problem into an SOCP problem by using a series of convex relaxations. Numerical results proved that the proposed method can effectively suppress the interference on the ground side due to the very low sidelobe level on the near-ground side and is robust to the steering vector mismatch, and the PAPR value has an effect on the sidelobe level. As the PAPR continues to decline, the sidelobe level is further suppressed; however, once the tolerance is greater than 1.3, its effect on the sidelobe level is almost negligible.  
It is worth noting that the results obtained based on a fundamental model without considering mutual coupling are somewhat different from those in the actual situation. We may further consider more physical factors and apply the proposed digital TBF method to other situations. In cutting-edge applications such as automatic driving and UAV-mounted radar, small-scale digital arrays cannot precisely distinguish intensive targets and meet the real-time requirement due to their limited performance in terms of the detection range, angular resolution, and SNR. A large-scale array is then adopted to enhance the radar performance. To reduce the cost and hardware complexity, the employed large-scale array is usually not a full-digital array but has special structures, such as an analog phased array or a hybrid analog-and-digital array. Therefore, the corresponding transmit beamforming is equivalent to a sophisticated nonconvex constrained optimization problem because of the nonconvex constraints generated by the array structure and the beamforming requirement. Furthermore, to improve the array efficiency, antenna selection is now widely used to segment the whole array into several sparse sub-arrays for multifunctional applications, i.e., the coexistence of communication and radar systems. Along with the antenna selection, transmit beamforming should be translated into a sparsity-regularized nonconvex constrained optimization problem. In all of these cases, how to efficiently solve transmit beamforming problems is a key question. To sum up, our future work will explore the further development of the proposed method so that it can be applied to more complicated scenarios.  
Figure 5: The sidelobe level with constant upper limits of the norm and different PAPR tolerances.  
**Author Contributions:** Conceptualization, L.C., R.C. and H.L.; methodology, L.C., R.C. and Z.D.; software, R.C.; validation, L.C. and R.C.; formal analysis, L.C., R.C. and Z.D.; investigation, L.C., R.C., Z.D., Y.Z. and H.L.; resources, L.C., R.C., Z.D. and H.L.; data curation, L.C., R.C. and Z.D.; writing--original draft preparation, L.C., R.C., Z.D. and Y.Z.; writing--review and editing, R.C. and Z.D.; visualization, L.C., R.C., Z.D., Y.Z. and H.L.; supervision, L.C., R.C., Z.D. and H.L.; project administration, L.C., R.C., Z.D., Y.Z. and H.L.; funding acquisition, H.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported in part by the Natural Science Foundation of Jiangsu Province under Grant BK20221486.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.