Synthesis of Multi-constrained Sparse Rectangular Arrays
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摘要:
针对多约束稀布矩形阵列天线的优化设计问题，该文提出一种新的矩阵映射(NMM)方法。首先，综合考虑阵元的可分布范围与可分布数量，重新定义阵元坐标矩阵的维数以提高阵元分布的自由度。其次，当坐标矩阵定义的阵元数量大于实际阵元数量时，建立选择矩阵以确定各阵元的取舍。再次，针对现有矩阵映射方法无法完全避免不可行解的问题，构建了一种NMM方法，通过两种不同的矩阵映射函数将多约束优化问题转换为无约束优化问题。最后进行仿真对比实验，实验结果证明了算法的有效性。
Abstract:A Novel Matrix Mapping (NMM) method is proposed for the synthesis of sparse rectangular arrays with multiple constraints. Firstly, the sizes of element coordinate matrices are resized to improve the Degree Of Freedom (DOF) of elements by taking account of both placeable number and distributable range of elements. Then, a selection matrix is established to determine which elements should be turned off when the coordinate matrices should be thinned. By establishing two different mapping functions, a NMM method is presented to overcome the drawbacks of existing methods in terms of flexibility and effectiveness. Finally, comparison experiments are conducted to verify the effectiveness of the proposed method. The numerical validation points out that the proposed method outperforms the existing methods in the design of sparse rectangular arrays.
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Key words:
- Antenna arrays /
- Sparse planar arrays /
- Constrained optimization /
- Sidelobe level
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表 1 实验1仿真结果对比(dB)
实验类型 方法 最优值 最差值 均值 方差 A NMM –61.2178 –52.3630 –57.8363 4.0813 MMM –53.5222 –50.4478 –51.9317 0.4940 B NMM –22.7591 –20.4355 –21.4060 0.1993 MMM –19.1338 –17.9751 –18.5972 0.0875 
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表 2 算法运算效率对比
实验1 方法 平均运行时间(s) 平均内存峰值使用量(kB) 平均适应值(dB) 可行解占比(%) A MMM算法 247.614 620 –51.9317 44 本文方法 283.704 620 –57.8363 100 B MMM算法 20472.744 904 –18.5972 60 本文方法 25823.421 984 –21.4060 100
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表 3 实验2仿真结果对比(dB)
实验类型 方法 最优值 最差值 均值 方差 A NMM –60.2701 –50.6686 –56.0144 4.7592 B NMM –22.0422 –20.1613 –20.9181 0.2303
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