共形阵列天线能够与载体共形，可以较好地保持载体气动性能，增加结构强度， 并且易于实现大角度扫描，因此，被广泛应用于各类飞行器的雷达系统中。共形阵列 天线的性能优劣会影响雷达系统的灵敏度和分辨率，因此需要更多的阵元数量以增加 天线的口径面积，但过多的阵元数量增加了雷达系统的复杂度和成本。故对共形阵列 天线进行稀疏优化设计具有重要的研究价值。
本论文针对这一应用需求，采用迭代加权 l1 范数算法，从阵列的阵元数量、最高 副瓣电平、多波束扫描和交叉极化电平抑制等四个方面对共形阵列天线进行稀疏综合 设计。论文从平面阵列入手研究阵列稀疏算法，并将算法应用于圆环阵列、柱面共形 阵列和球面共形阵列的稀疏综合设计。论文的主要内容包括:
1. 利用基于凸优化理论的范数最小化方法，将 l0 范数最小化问题转换为更高维 度的 l1 范数最小化问题，对直线阵列和平面阵列天线进行稀疏综合，同时优化其最高 副瓣电平，并通过全波仿真软件对直线阵的稀疏综合效果进行仿真验证。仿真结果验 证了阵列稀疏算法的有效性，稀疏直线阵列的阵元数相比满阵减少了 65%，且最高副 瓣电平低于-20dB。
2. 在迭代加权 l1 范数稀疏算法的基础上，将阵元最小间距控制加入阵列稀疏优 化过程中，对圆环阵列进行稀疏综合，设计了一款 24 元稀疏圆环阵列，阵元数量相 比满阵减少了 25%。设计了一款微带天线，并以其为阵元对圆环阵列进行全波仿真， 最后对圆环阵列进行实物加工和测试。
3. 基于迭代加权l1范数稀疏算法，对柱面共形阵列进行多波束方向图稀疏综合， 设计了一款 78 元稀疏柱面共形阵列。算法对阵列的 9 个扫描波束进行低副瓣方向图 稀疏综合，稀疏后的阵元数量相比满阵减少了 49%，并且阵列方向图最高副瓣电平均 低于-18dB。最后在全波仿真软件中对稀疏柱面共形阵列进行仿真验证，仿真结果与 算法综合得到的阵列方向图具有较好的一致性，验证了该算法在柱面共形阵列稀疏综 合中的有效性。
4. 利用极化合成原理，同时结合迭代加权 l1 范数稀疏算法，对以双极化天线为 单元的球面共形阵列进行稀疏综合优化。设计了一款 42 元稀疏球面共形阵列，优化 后的阵元数量相比满阵减少了 50%。阵列实现了 3 个角度的波束扫描，同时最高副瓣 电平和最高交叉极化电平低于-20dB。对稀疏球面阵列进行全波仿真，仿真结果显示 稀疏阵列在不同扫描方向图的两个正交切面内的最高副瓣电平低于-17dB，在主瓣范 围内最高交叉极化电平低于-20dB，表明本文算法能够有效适用于球面共形阵列的稀 疏综合设计。

The conformal array antenna can conform to the carrier, which can better maintain the aerodynamic performance of the carrier, increase the structural strength, and easily realize wide-angle scanning. Therefore, conformal array antennas are widely used in radar systems of various aircraft. The performance of the conformal array antenna will affect the sensitivity and resolution of the radar system, and the array system requires more array elements to increase the aperture area of the antenna. But too many array elements increase the complexity and cost of the radar system. Therefore, the sparse optimal design of conformal array antenna has important research value.
In this paper, the research on the sparse array antenna synthesis selects the iterative weighted l1-norm algorithm. The sparse design of the conformal array antenna is studied from four aspects: the number of array elements, the highest sidelobe level, multi-beam scanning and cross-polarization level. The research studies the array sparse algorithm starting from the planar array, and applies the algorithm to the sparse comprehensive design of circular array, cylindrical conformal array and spherical conformal array. The main contents of the paper include:
1. Using the norm minimization method based on convex optimization theory, the l0-norm minimization problem is transformed into a higher-dimensional l1-norm minimization problem. This work performs a sparse synthesis of linear and planar array antennas while optimizing their highest sidelobe levels, and then verifies the sparse synthesis effect of linear array in full-wave simulation software. The simulation results verify the effectiveness of the array sparse algorithm. Compared with the full array, the number of array elements in the sparse linear array is reduced by 65%, and the highest sidelobe level is lower than -20dB.
2. Based on the iterative weighted l1-norm sparse algorithm and combining the minimum spacing control of the array elements, a 24-element sparse cylindrical array is designed. The number of array elements is compared with the full array has been reduced by 25%. Then A microstrip antenna is designed, and it is used as an array element to carry out full-wave simulation of the circular array. Finally, the sparse cylindrical array is fabricated and measured.

3. Based on the iterative weighted l1-norm sparse algorithm, the multi-beam pattern sparse synthesis optimization design is carried out for the cylindrical conformal array. A 78-element sparse cylindrical conformal array is designed. The algorithm performs sparse synthesis of low sidelobe patterns on the 9 scanning beams of the array, and the number of sparse array elements is reduced by 49% compared with the full array. The sparse array realizes the scanning of 9 beam directions, and the highest sidelobe level of the pattern is lower than - 18dB. Finally, the sparse cylindrical conformal array is simulated and verified in the full- wave simulation software. The simulation results are in good agreement with the array pattern synthesized by the algorithm, which verifies effectiveness for the algorithm of the sparse cylindrical conformal array synthesis.
4. Using the principle of polarization synthesis, combined with the iterative weighted l1- norm sparse algorithm, the sparse synthesis optimization of the spherical conformal array is carried out. A 42-element sparse spherical conformal array is designed, which uses dual- polarized antennas as elements. The number of sparse array elements is reduced by 50% compared with the full array. The sparse array realizes beam scanning in 3 angles, while the highest sidelobe level and the highest cross-polarization level are lower than -20dB. Then, the sparse spherical array is simulated and verified in the full-wave simulation software. The simulation results show that the highest sidelobe level of the sparse array in the two orthogonal sections of different scanning patterns is lower than -17dB. The highest cross- polarization level in the main lobe range is lower than -20dB. Which shows that the algorithm in this paper can be applied to the sparse synthesis design of spherical conformal arrays.