This paper discusses how to optimize the weighting of individual subarrays to derive the low sidelobe level (SLL) based on quadratic programming (QP) and how to derive QP parameters to ensure that the objective function is composed of the quadratic function form, with the actual number identical to the standard objective function of QP. Next, in order to analyze the SLL, a 24 × 24 phased array antenna was compared with 96 transmit–receive modules (TRMs) attached only to the subarray stage and a phased array antenna with 576 TRMs attached to all radiating elements without a subarray. Optimized weighting was applied to the array antennas with a subarray, and Taylor weighting was applied to the array antennas without a subarray. The number of TRMs used in the phased array antenna with the optimized weighting was reduced by 83.3% compared to the phased array antenna in which TRMs were attached to all radiating elements. The SLL and the half-power beamwidths (HPBWs) of the two antennas were practically identical in a narrow beam-scanning environment. Finally, an array pattern (AP) in which mutual coupling between the radiating elements was considered was calculated to verify the optimized weighting. Moreover, the optimized weighting was applied to CST Microwave Studio (an EM full-wave simulation) to compare the results from the AP calculation and a simulation. It was confirmed that the two results above are largely indistinguishable. The analysis found that the HPBW is 3.6${}^{\circ }$× 3.6${}^{\circ }$ and the SLL is −26.18 dB from AP calculations in the boresight direction. When each 5${}^{\circ }$ beam was scanned at the azimuth and elevation, the corresponding HPBW values were 3.7${}^{\circ }$× 3.7${}^{\circ }$ and 3.7${}^{\circ }$× 3.7${}^{\circ }$ and the SLLs were −22.70 dB and −24.44 dB according to the AP calculations.

中文翻译：

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毫米波相控阵天线子阵的形状和加权优化

本文讨论了如何基于二次规划（QP）优化单个子阵列的权重来推导低旁瓣电平（SLL），以及如何推导QP参数以确保目标函数由二次函数形式组成，与实际数字与 QP 的标准目标函数相同。接下来，为了分析 SLL，将 24 × 24 相控阵天线与仅连接到子阵列级的 96 个发射 - 接收模块 (TRM) 和带有 576 个 TRM 的相控阵天线连接到所有辐射元件而没有子阵列。优化加权应用于有子阵列的阵列天线，泰勒加权应用于没有子阵列的阵列天线。优化加权的相控阵天线中使用的 TRM 数量减少了 83 个。与将 TRM 连接到所有辐射元件的相控阵天线相比，降低了 3%。在窄波束扫描环境中，两个天线的 SLL 和半功率波束宽度 (HPBW) 几乎相同。最后，计算考虑了辐射元件之间相互耦合的阵列方向图 (AP) 以验证优化的加权。此外，优化的加权应用于 CST Microwave Studio（EM 全波模拟）以比较 AP 计算和模拟的结果。经证实，上述两个结果在很大程度上无法区分。分析发现HPBW为3.6 最后，计算考虑了辐射元件之间相互耦合的阵列方向图 (AP) 以验证优化的加权。此外，优化的加权应用于 CST Microwave Studio（EM 全波模拟）以比较 AP 计算和模拟的结果。经证实，上述两个结果在很大程度上无法区分。分析发现HPBW为3.6 最后，计算考虑了辐射元件之间相互耦合的阵列方向图 (AP) 以验证优化的加权。此外，优化的加权应用于 CST Microwave Studio（EM 全波模拟）以比较 AP 计算和模拟的结果。经证实，上述两个结果在很大程度上无法区分。分析发现HPBW为3.6${}^{\circ }$× 3.6${}^{\circ }$视轴方向的 AP 计算得出的 SLL 为 −26.18 dB。当每 5${}^{\circ }$ 在方位角和仰角扫描光束，对应的 HPBW 值为 3.7${}^{\circ }$× 3.7${}^{\circ }$ 和 3.7${}^{\circ }$× 3.7${}^{\circ }$ 根据 AP 计算，SLL 分别为 -22.70 dB 和 -24.44 dB。