Iterative fast Fourier transform algorithm based on mutual coupling compensation strategy and its application
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摘要: 介绍了一种基于互耦补偿矩阵(MCCM)的迭代快速傅里叶变换(IFFT)技术，并将其应用于宽角度扫描相控阵的低旁瓣综合中。首先，在所提出的综合方法中，将互耦补偿矩阵引入到IFFT技术中以考虑阵元间的互耦效应，使考虑互耦的阵列远场重新满足方向图乘积原理。然后，提出了一款基片集成波导背腔结构的宽波束天线单元，该天线能够同时激励起TE110与TE210两种模式从而展宽其工作频带且具有宽波束性能，并且基于此单元分别建立了阵元数为35，75，100的宽角度扫描相控阵天线。最后，利用所提出的IFFT技术对这三个相控阵进行低旁瓣综合。与基于有源单元方向图遗传算法的对比结果表明，在−60°到60°的扫描范围内均能实现低旁瓣电平，并且IFFT优化算法具有更快的速度。Abstract: In this paper, an improved iterative fast Fourier transform (IFFT) based on the mutual coupling compensation matrix (MCCM) is introduced and applied to the low-sidelobe synthesis of wide-angle scanning phased arrays. Firstly, the MCCM is integrated into the IFFT to take into account the mutual coupling effects between the array elements. In this situation, the far field of an array which takes the mutual coupling into calculation can satisfy the principle of pattern multiplication. Secondly, a wide-beam element antenna backed by a substrate integrated waveguide (SIW) cavity is proposed. The proposed wide-beam antenna can simultaneously excite the TE110 and TE210 modes to expand its operation bandwidth. Based on this element, three wide-angle scanning phased array antennas with 35, 75 and 100 elements are formed and calculated. Finally, the proposed IFFT algorithm is used in the low-sidelobe synthesis of the three phased arrays. Compared with the results of the genetic algorithm based on the active element patterns, this algorithm can realize low-sidelobe performance within the scanning range from −60° to 60° at faster speed.
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图 1 子阵提取AEP示意图
Figure 1. Schematic diagram of subarray Active Element Pattern (AEP) extraction
图 3 基于互耦补偿矩阵的IFFT技术优化阵列流程图
Figure 3. Flow chart of IFFT algorithm based on the mutual coupling compensation matrix (MCCM)
图 5 天线单元的反射系数与xOz平面内的辐射方向图
Figure 5. Reflection coefficients and radiation pattern in xOz plane
表 1 Uniform/GA/IFFT优化结果对比
Table 1. Comparison of Uniform/GA/IFFT optimization results
scan angle/（°） PSLL/dB HPBW/（°） gain/dBi population iter_max gen_max num_try required time/s 0（GA） −30.08 4.8 32.37 200 300 288.15 0（IFFT） −30.71 5.0 32.50 100 200 13.65 0（Uniform） −13.38 3.6 33.30 none none none 30（GA） −30.33 5.3 32.22 200 300 293.93 30（IFFT） −30.15 5.8 32.26 100 200 19.72 30（Uniform） −12.61 4.2 32.99 none none none 60（GA） −30.07 9.4 29.88 200 300 282.18 60（IFFT） −30.10 10.3 28.95 100 200 22.90 60（Uniform） −11.43 7.3 30.64 none none none 
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表 2 Uniform/GA/IFFT优化结果对比
Table 2. Comparison of Uniform/GA / IFFT optimization results
scan angle/（°） PSLL/dB HPBW/（°） gain/dBi population iter_max gen_max num_try required time/s 0（GA） −30.30 2.1 35.85 200 300 625 0（IFFT） −30.68 2.4 37.06 100 500 22.42 0（Uniform） −13.3 1.7 36.61 none none none 30（GA） −30.06 2.5 35.59 200 300 600 30（IFFT） −30.15 2.9 35.24 100 500 32.64 30（Uniform） −12.9 2.0 36.29 none none none 60（GA） −30.02 4.5 33.35 200 300 600 60（IFFT） −30.08 5.3 31.91 100 500 39.86 60（Uniform） −12.29 3.4 34.04 none none none
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表 3 Uniform/GA/IFFT优化结果对比
Table 3. Comparison of Uniform/GA / IFFT optimization results
scan angle/（°） PSLL/dB HPBW/（°） gain/dBi population iter_max gen_max num_try required time/s 0（GA） −30.12 1.5 37.11 200 300 945 0（IFFT） −30.74 1.8 38.46 100 1 000 34.40 0（Uniform） −13.33 1.3 37.86 none none none 30（GA） −30.04 1.9 36.76 200 300 882 30（IFFT） −30.13 2.1 36.56 100 1 000 53 30（Uniform） −13.01 1.6 37.54 none none none 60（GA） −30.00 3.2 34.65 200 300 888 60（IFFT） −30.11 3.9 33.23 100 1 000 59 60（Uniform） −12.51 3.0 35.31 none none none
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