稀布天线阵列的优化布阵技术研究
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摘要
在许多工程应用中，要求天线阵列有窄的扫描波束，并不要求有相应的增益，这类应用正好可以采用天线单元在阵列孔径上稀疏布置的方法来实现，它能构造出一个降低了增益的强方向性阵列，以较少的天线单元达到分辨率等技术指标，从而降低天线系统的成本。由于阵列中天线单元的稀疏布置，使得扫描波束变窄，空间分辨率提高，天线单元间的互耦减弱，这些优点使得稀布天线阵列成为非周期阵列中颇具实用性的一类阵列天线。目前，稀布天线阵列在抗环境干扰的卫星接收天线，高频地面相控阵雷达天线和射电天文中的干涉阵列等领域中正得到越来越广泛的应用。
天线的最大相对旁瓣电平是评价天线性能的一个重要参数，对稀布天线阵列而言，如何设计一组阵元间距和阵元激励，使稀布天线阵列的最大相对旁瓣电平在整个可见区最小是稀布天线阵列综合问题中研究了半个多世纪的一类重要课题。近年来，天线单元稀疏布置的天线阵列(稀布天线阵列)被分为两大类：稀疏阵列和稀布阵列。稀疏阵列来源于均匀阵列，它是将一定数目的天线单元从均匀间隔阵列中稀疏而形成的，其阵元间距是原均匀阵列的阵元间距的整数倍；稀布阵列的天线单元在天线孔径上随机分布，其阵元间距是相互不可整除的。相对而言，稀布阵列优化布阵无需象稀疏阵列那样约束天线单元在等间隔的规则栅格上，所以优化布阵的自由度更大，有利于更大限度地降低天线阵列的最大相对旁瓣电平，进一步提高稀布天线阵列的旁瓣性能。
本文在给定阵列的几何形状的前提下，针对如何通过适当地选取稀布天线阵列的阵元间距来最大限度地降低阵列的最大相对旁瓣电平这一基本综合问题展开研究。由于稀布天线阵列的最大相对旁瓣电平是阵元位置的非线性函数，没有现存的解析方法来确定最大相对旁瓣电平，也就是说，即使已知所有阵元的位置，也没有可凭借的解析方法来求得最大相对旁瓣电平出现的位置，所以本文的研究对象是一个非线性最优化问题。文中针对稀疏天线阵列综合提出了分区穷举法，并分析了它的性能及适用的场合；针对稀布天线阵列综合可能涉及的不同约束，提出了一种基于现代计算智能方法——遗传算法的改进算法，并应用于稀布直线阵列的多约束优化布阵；最后将这种综合方法从一维线性稀布阵列的优化布阵推广到了二维稀布平面阵列的优化布阵。
本文的贡献和创新之处包括：
1．建立了稀疏阵列和稀布阵列优化布阵的最优化数学模型，讨论了最优阵元配置的求解问题。
2．中小型稀疏阵列的穷举综合法中，枚举阵列结构的计算量是值得研究的一个问题，文中分析比较了两种枚举直线阵列结构的算法：递归算法和二进制序列穷举法。
3．提出了稀疏直线阵列优化布阵的分区穷举方法，修正了在阵列孔径的均匀分区上分配阵元数目的理论公式。
4．讨论了非对称的阵列结构对稀疏阵列旁瓣电平优化的影响；即结构上的对称性是可利用的优化自由度，由方向性天线单元综合的非对称稀疏天线阵列扫描时峰值旁瓣性能的恶化比对称结构的稀疏阵列更小。
5．改进了实数遗传算法的交叉和变异策略，结合高效的FFT算法计算稀疏阵列的方向图函数，使优化稀疏阵列激励幅度的算法的稳健性和收敛性得到改善。
6．提出一种修正的实数遗传算法，解决了稀布直线天线阵列的多约束(约束孔径、阵元数和最小阵元间距)优化布阵，该算法利用阵元间距约束，减小遗传算法的搜索空间，有效地减小了计算量，提高了算法的收敛性能。
7．在最小阵元间距由欧氏距离简化为切比雪夫间距的情况下，将修正实数遗传算法综合多约束稀布线阵的方法拓展到了矩形边界稀布平面阵列的多约束优化布阵。
For many radar and communications applications of scanning array antennas, extreme narrow main beamwidth is desired, whereas high gain is not so extremely required, the sparse antenna arrays, whose element spacing is kept relatively larger thanλ/2 over an antenna aperture, can cover these applications. The sparse antenna arrays have advantages in high-resolution thinned configurations, and fewer elements for comparable beamwidth. The cost of the sparse antenna arrays is much lower to meet the design goal of high-resolution than that of periodic arrays. Due to the array thinning, beamwidth narrowing and element-interaction reduction, the sparse antenna arrays with the strong directivity have a great deal applications in aperiodic arrays. In recent years, the sparse antenna arrays are widly applied in satellite communications, high frequency groundwork phased array radar and interferometer of radio astronomy.
The peak side lobe level (PSLL) is a key parameter of an antenna arrays, one of the interesting sparse array synthesis problems is to find an optimum set of element spacings and excitations that would minimize the highest side lobe level (viz.PSLL) in the entire visible region. This is a hard synthesis problem of sparse arrays which has been studied for almost sixty years. These years, the nonuniform antenna arrays have been classified into two categories: sparse arrays with randomly spaced elements and thinned arrays, which are derived by selectively zeroing some elements of an initial equally spaced array. Sparse arrays with incommensurable element spacings have more degree of freedom to lower the peak side lobe level for the simple reason that elements of sparse array do not need to be restricted by the regular linear lattice.
In this dissertation, the basic synthesis problem of sparse antenna arrays was studied, that is, how to find the element positions to minimize the PSLL of a sparse antenna array when the array configuration is fixed apriori. The difficult of this problem may be attributed the fact that the side lobe level depends on the element spacings in a highly nonlinear manner, and that, in general, there is no known analytical method to determine the highest side lobe level, or the angular direction where the highest side lobe may occur, even with all element positons given. So the optimization of the element positions of the sparse antenna arrays is a nonlinear optimization. Divisional exhaustive method is applied to optimize the thinning of linear thinned arrays; its performance trials reveal the applicability when it is applied to element spacing synthesis. And various constrains may occurs in the synthesis of sparse arrays, a novel intellectualized method, viz. a modified real genetic algorithms (MGA), is developed to attack the synthesis problem of linear sparse arrays with multiple design constrains. At last, the novel algorithm of MGA was extended to the optimization of the 2-demension sparse antenna arrays.
The main contributions of this dissertation include two aspects. One is the study on exhaustive method for the element position design of thinned arrays; the other is the application of genetic algorithms for the optimization of sparse arrays.
Several valuable and important results which bring forth new ideas are achieved and listed as the following:
1. The mathematical model for the optimization of thinned arrays and sparse arrays was built, and the optimal solutions of sparse antenna arrays were discussed.
2. In the process of exhaustive synthesis of minitype thinned arrays, enumerating the configuration of linear thinned arrays is main task of design. Two enumerate algorithms of exhaustive study on configuration of linear thinned arrays are proposed, they are recursion algorithm and binary sequence enumerate algorithm. Some comparison studies on their performance are made in order to reveal the feasibility relations with the thinned ratio and aperture of the array antennas.
3. A new method of exhaustive method with divisional pre-processing is proposed, in which the formula of element distribution is modified, and then it is compared with other design methods of thinned arrays.
4. The asymmetric configuration is an available degree of freedom to control the characters of thinned arrays. Simulation results show that the optimized asymmetric linear arrays using genetic algorithm which lack the design constraint of bilateral symmetry can not only obtain lower sidelobes, but also weaken the deterioration of scanning beam if the thinned arrays are made up of directional elements.
5. The crossover and mutation strategy of genetic algorithm (GA) with real chromosome are improved, and they can be utilized to improve the side lobe performance of a thinned array by designing the element currents.
6. A modified real genetic algorithm (MGA) for the synthesis of sparse linear arrays is developed. It has been utilized to optimize the element positions to reduce the PSLL of the array. And here the multiple optimization constraints include the number of element, the aperture and the minimum element spacing. The MGA utilized the coding resetting of gene variables to avoid infeasible solution during the optimization process. Also, the proposed approach has reduced the size of the searching area of the GA by means of indirect description of individual.
7. The MGA is extended for the element position optimization of rectangular sparse plane arrays with multiple optimization constraints. If the space between the elements was simplified from the actual distance (in Euclidean space) to Chebychev distance, the nonlinear constraint of the element spacing can be simplified, and then the MGA can search a smaller solution space and improve the computing efficiency.
天线的最大相对旁瓣电平是评价天线性能的一个重要参数，对稀布天线阵列而言，如何设计一组阵元间距和阵元激励，使稀布天线阵列的最大相对旁瓣电平在整个可见区最小是稀布天线阵列综合问题中研究了半个多世纪的一类重要课题。近年来，天线单元稀疏布置的天线阵列(稀布天线阵列)被分为两大类：稀疏阵列和稀布阵列。稀疏阵列来源于均匀阵列，它是将一定数目的天线单元从均匀间隔阵列中稀疏而形成的，其阵元间距是原均匀阵列的阵元间距的整数倍；稀布阵列的天线单元在天线孔径上随机分布，其阵元间距是相互不可整除的。相对而言，稀布阵列优化布阵无需象稀疏阵列那样约束天线单元在等间隔的规则栅格上，所以优化布阵的自由度更大，有利于更大限度地降低天线阵列的最大相对旁瓣电平，进一步提高稀布天线阵列的旁瓣性能。
本文在给定阵列的几何形状的前提下，针对如何通过适当地选取稀布天线阵列的阵元间距来最大限度地降低阵列的最大相对旁瓣电平这一基本综合问题展开研究。由于稀布天线阵列的最大相对旁瓣电平是阵元位置的非线性函数，没有现存的解析方法来确定最大相对旁瓣电平，也就是说，即使已知所有阵元的位置，也没有可凭借的解析方法来求得最大相对旁瓣电平出现的位置，所以本文的研究对象是一个非线性最优化问题。文中针对稀疏天线阵列综合提出了分区穷举法，并分析了它的性能及适用的场合；针对稀布天线阵列综合可能涉及的不同约束，提出了一种基于现代计算智能方法——遗传算法的改进算法，并应用于稀布直线阵列的多约束优化布阵；最后将这种综合方法从一维线性稀布阵列的优化布阵推广到了二维稀布平面阵列的优化布阵。
本文的贡献和创新之处包括：
1．建立了稀疏阵列和稀布阵列优化布阵的最优化数学模型，讨论了最优阵元配置的求解问题。
2．中小型稀疏阵列的穷举综合法中，枚举阵列结构的计算量是值得研究的一个问题，文中分析比较了两种枚举直线阵列结构的算法：递归算法和二进制序列穷举法。
3．提出了稀疏直线阵列优化布阵的分区穷举方法，修正了在阵列孔径的均匀分区上分配阵元数目的理论公式。
4．讨论了非对称的阵列结构对稀疏阵列旁瓣电平优化的影响；即结构上的对称性是可利用的优化自由度，由方向性天线单元综合的非对称稀疏天线阵列扫描时峰值旁瓣性能的恶化比对称结构的稀疏阵列更小。
5．改进了实数遗传算法的交叉和变异策略，结合高效的FFT算法计算稀疏阵列的方向图函数，使优化稀疏阵列激励幅度的算法的稳健性和收敛性得到改善。
6．提出一种修正的实数遗传算法，解决了稀布直线天线阵列的多约束(约束孔径、阵元数和最小阵元间距)优化布阵，该算法利用阵元间距约束，减小遗传算法的搜索空间，有效地减小了计算量，提高了算法的收敛性能。
7．在最小阵元间距由欧氏距离简化为切比雪夫间距的情况下，将修正实数遗传算法综合多约束稀布线阵的方法拓展到了矩形边界稀布平面阵列的多约束优化布阵。
For many radar and communications applications of scanning array antennas, extreme narrow main beamwidth is desired, whereas high gain is not so extremely required, the sparse antenna arrays, whose element spacing is kept relatively larger thanλ/2 over an antenna aperture, can cover these applications. The sparse antenna arrays have advantages in high-resolution thinned configurations, and fewer elements for comparable beamwidth. The cost of the sparse antenna arrays is much lower to meet the design goal of high-resolution than that of periodic arrays. Due to the array thinning, beamwidth narrowing and element-interaction reduction, the sparse antenna arrays with the strong directivity have a great deal applications in aperiodic arrays. In recent years, the sparse antenna arrays are widly applied in satellite communications, high frequency groundwork phased array radar and interferometer of radio astronomy.
The peak side lobe level (PSLL) is a key parameter of an antenna arrays, one of the interesting sparse array synthesis problems is to find an optimum set of element spacings and excitations that would minimize the highest side lobe level (viz.PSLL) in the entire visible region. This is a hard synthesis problem of sparse arrays which has been studied for almost sixty years. These years, the nonuniform antenna arrays have been classified into two categories: sparse arrays with randomly spaced elements and thinned arrays, which are derived by selectively zeroing some elements of an initial equally spaced array. Sparse arrays with incommensurable element spacings have more degree of freedom to lower the peak side lobe level for the simple reason that elements of sparse array do not need to be restricted by the regular linear lattice.
In this dissertation, the basic synthesis problem of sparse antenna arrays was studied, that is, how to find the element positions to minimize the PSLL of a sparse antenna array when the array configuration is fixed apriori. The difficult of this problem may be attributed the fact that the side lobe level depends on the element spacings in a highly nonlinear manner, and that, in general, there is no known analytical method to determine the highest side lobe level, or the angular direction where the highest side lobe may occur, even with all element positons given. So the optimization of the element positions of the sparse antenna arrays is a nonlinear optimization. Divisional exhaustive method is applied to optimize the thinning of linear thinned arrays; its performance trials reveal the applicability when it is applied to element spacing synthesis. And various constrains may occurs in the synthesis of sparse arrays, a novel intellectualized method, viz. a modified real genetic algorithms (MGA), is developed to attack the synthesis problem of linear sparse arrays with multiple design constrains. At last, the novel algorithm of MGA was extended to the optimization of the 2-demension sparse antenna arrays.
The main contributions of this dissertation include two aspects. One is the study on exhaustive method for the element position design of thinned arrays; the other is the application of genetic algorithms for the optimization of sparse arrays.
Several valuable and important results which bring forth new ideas are achieved and listed as the following:
1. The mathematical model for the optimization of thinned arrays and sparse arrays was built, and the optimal solutions of sparse antenna arrays were discussed.
2. In the process of exhaustive synthesis of minitype thinned arrays, enumerating the configuration of linear thinned arrays is main task of design. Two enumerate algorithms of exhaustive study on configuration of linear thinned arrays are proposed, they are recursion algorithm and binary sequence enumerate algorithm. Some comparison studies on their performance are made in order to reveal the feasibility relations with the thinned ratio and aperture of the array antennas.
3. A new method of exhaustive method with divisional pre-processing is proposed, in which the formula of element distribution is modified, and then it is compared with other design methods of thinned arrays.
4. The asymmetric configuration is an available degree of freedom to control the characters of thinned arrays. Simulation results show that the optimized asymmetric linear arrays using genetic algorithm which lack the design constraint of bilateral symmetry can not only obtain lower sidelobes, but also weaken the deterioration of scanning beam if the thinned arrays are made up of directional elements.
5. The crossover and mutation strategy of genetic algorithm (GA) with real chromosome are improved, and they can be utilized to improve the side lobe performance of a thinned array by designing the element currents.
6. A modified real genetic algorithm (MGA) for the synthesis of sparse linear arrays is developed. It has been utilized to optimize the element positions to reduce the PSLL of the array. And here the multiple optimization constraints include the number of element, the aperture and the minimum element spacing. The MGA utilized the coding resetting of gene variables to avoid infeasible solution during the optimization process. Also, the proposed approach has reduced the size of the searching area of the GA by means of indirect description of individual.
7. The MGA is extended for the element position optimization of rectangular sparse plane arrays with multiple optimization constraints. If the space between the elements was simplified from the actual distance (in Euclidean space) to Chebychev distance, the nonlinear constraint of the element spacing can be simplified, and then the MGA can search a smaller solution space and improve the computing efficiency.
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