阵列方向图综合与自适应波束形成技术研究
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摘要
阵列方向图综合与自适应波束形成在雷达、声纳、无线通信和天文学等领域都有着广泛的应用。在这些领域中，通过方向图综合与自适应波束形成，对特定角度或角度区域接收或发射信号，而对其它区域尽量少的接收或发射信号，甚至对某些角度完全抑制。然而现有方法在处理一些特殊阵列，或在一些特殊情况下，面临着一些挑战。本论文在总结并发展了一些常规阵列方向图综合方法后，重点针对共形阵列和大型阵列，提出了一些新的方法，以克服传统方法在这些应用中的不足；并针对自适应波束形成在某些特定情况下的稳健性进行了研究，并提出了新的方法。本文主要内容如下：
本文首先总结了凸优化算法在针状波束方向图与赋形方向图综合中的应用。提出了一种非均匀阵列快速赋形方向图综合方法，并应用到了阵元失效的方向图校正中。用凸优化算法提出了一种和差波束方向图综合算法，该算法能同时优化阵元位置、和方向图激励与差方向图激励，以减少阵元个数，降低系统复杂度。介绍了粒子群优化算法，并提出了一种基于该方法的模糊离散粒子群算法。介绍了基于矩阵束方法的阵列综合方法，并将该方法推广到了二维阵列综合中。
然后重点研究了共形阵列方向图综合算法。研究了给定阵列，优化阵元激励以达到目标方向图的情况。提出了一种基于有源方向图分解的方法，该方法能减少方向图采样点数，减少数据存储量，减少运算量，产生精确的主瓣指向和零陷。同时，还提出了一种带阵元位置优化的共形阵列方向图综合方法。该方法通过几个采样位置的独立方向图插值得到任意天线位置的方向图，并通过稳健的方向图综合方法来解决插值误差和阵元间互耦的影响。通过全波仿真证明了方法的有效性。
本文还对大型阵列方向图快速综合算法进行了研究。受非均匀快速傅里叶变换启发，提出了一种非均匀阵列针状波束方向图快速综合方法。该方法基于快速傅里叶变换，因此与现有方法相比，该方法能综合更大的阵列且能更快的得到更好的结果。同时针对平顶方向图综合问题，提出了一种能综合得到任意形状平顶区域的方法，这在卫星通信中有重要的用途。该方法能在给定的均匀平面阵列中选择需要的阵元，并控制激励动态范围。
最后本文研究了自适应波束形成的稳健算法。针对大的阵列校正误差，提出了一种抗该类误差的稳健算法。该算法同时估计干扰协方差矩阵和目标信号的阵列流形。即使在很大的阵列校正误差存在的情况下，该方法依然能得到较好的结果，并好于现有方法。本文还将波束形成问题转化为一个加权方向图综合问题。通过对该加权方向图主瓣宽度及旁瓣电平的设计，可以提高波束形成器在某些情况下的稳健性。该方法能优先的抑制位于旁瓣区域的干扰，并对模型误差具有一定的稳健性。
Array pattern synthesis and adaptive beamforming have found a wide range ofapplications in radar, sonar, wireless communication and astronomy, et.al. By thepattern synthesis or adaptive beamforming techniques, the systems in these applicationscan transmit/receive the signal to/from a specified direction or a range of directions, andtransmit/receive as little signal as possible to/from other directions, or completelysuppress the signal to/from some directions. However, in some kind of arrays or in somespecially situations, the exsiting methods will suffer from some kind of problems. Thisdissertation summarizes the applications of some existing pattern synthesis methods andproposes some modified methods, and then focuses on the pattern synthesis ofconformal arrays and large arrays. New pattern synthesis methods for conformal arraysand large arrays are proposed to address the shortcomings of the conventional methods.To improve the robustness of the adaptive beamforming against model errors, severalnew robust beamformer are presented. The main contributions are illustrated as follows:
Firstly, the dissertation summarizes the applications of the convex optimization onpattern synthesis of pencil beam or shaped beam patterns, and a shaped beam patternsynthesis method with nonuniform arrays is proposed and is applied to array failurecorrection. A pattern synthesis method based on convex optimization is proposed tosynthesize the sum and difference patterns. This method can optimize the elementpositions and excitations for sum and difference patterns simultaneously. Therefore, thesystem complexity can be reduced. The dissertation introduced the particle swarmoptimization method, and proposed a new fuzzy discrete particle swarm optimizationmethod. What’s more, the matrix pencil method based pattern synthesis method isintroduced and extended to2D arrays.
Secondly, the pattern synthesis of conformal arrays is considered. The first topic ofthis part is to optimize the array excitations of a given array to obtain a desired pattern. Iproposed a novel active element pattern decomposition based method of conformalarray synthesis. This method requires less pattern samples, less memory, lesscomputational cost and can steer the mainlobe or nulls to precise directions. Then, anoptimization method on conformal array element positions is proposed. In this method,the pattern of an element located at an arbitrary position on the platform is obtained by interpolating the element patterns at several sampled locations, and the mutual couplingbetween elements is considered by robust pattern synthesis method. The full wavesimulation results validate these two proposed methods.
Thirdly, this dissertation deals with the fast pattern synthesis method for largearrays. Inspired by the nonuniform fast Fourier transform, I proposed a novel fast pencilbeam pattern synthesis method for large unequally spaced antenna arrays. This methodis based on fast Fourier transform, so larger arrays can be handled and can obtain betterresults when compared with other methods. The dissertation also considered the flat-topfootprint pattern synthesis in this part. The dissertation proposed a synthesis method thatcan obtain arbitrary footprint pattern which is important in satellite applications. Theproposed method chooses the antennas in the given uniform array and the dynamicrange ratio can be controlled.
Finally, the dissertation works on the robust adaptive beamforming methods. Thedisseratation proposed an adaptive beamforming method that is robust against largearray calibration errors. This method reconstructs the interference covariance matrix andestimates the steering vector associated with the desired signal. Compared withstate-of-the-art methods, the proposed method can obtain better results even when largecalibration error exists. What’s more, the dissertation transform the adaptivebeamforming problem into a weighted array pattern synthesis problem. The robustnessof the adaptive beamformer is improved by adding restriction on the mainlobe widthand sidelobe levels. The proposed method can suppress the interferences with highpriority, and it is robust against model errors.
本文首先总结了凸优化算法在针状波束方向图与赋形方向图综合中的应用。提出了一种非均匀阵列快速赋形方向图综合方法，并应用到了阵元失效的方向图校正中。用凸优化算法提出了一种和差波束方向图综合算法，该算法能同时优化阵元位置、和方向图激励与差方向图激励，以减少阵元个数，降低系统复杂度。介绍了粒子群优化算法，并提出了一种基于该方法的模糊离散粒子群算法。介绍了基于矩阵束方法的阵列综合方法，并将该方法推广到了二维阵列综合中。
然后重点研究了共形阵列方向图综合算法。研究了给定阵列，优化阵元激励以达到目标方向图的情况。提出了一种基于有源方向图分解的方法，该方法能减少方向图采样点数，减少数据存储量，减少运算量，产生精确的主瓣指向和零陷。同时，还提出了一种带阵元位置优化的共形阵列方向图综合方法。该方法通过几个采样位置的独立方向图插值得到任意天线位置的方向图，并通过稳健的方向图综合方法来解决插值误差和阵元间互耦的影响。通过全波仿真证明了方法的有效性。
本文还对大型阵列方向图快速综合算法进行了研究。受非均匀快速傅里叶变换启发，提出了一种非均匀阵列针状波束方向图快速综合方法。该方法基于快速傅里叶变换，因此与现有方法相比，该方法能综合更大的阵列且能更快的得到更好的结果。同时针对平顶方向图综合问题，提出了一种能综合得到任意形状平顶区域的方法，这在卫星通信中有重要的用途。该方法能在给定的均匀平面阵列中选择需要的阵元，并控制激励动态范围。
最后本文研究了自适应波束形成的稳健算法。针对大的阵列校正误差，提出了一种抗该类误差的稳健算法。该算法同时估计干扰协方差矩阵和目标信号的阵列流形。即使在很大的阵列校正误差存在的情况下，该方法依然能得到较好的结果，并好于现有方法。本文还将波束形成问题转化为一个加权方向图综合问题。通过对该加权方向图主瓣宽度及旁瓣电平的设计，可以提高波束形成器在某些情况下的稳健性。该方法能优先的抑制位于旁瓣区域的干扰，并对模型误差具有一定的稳健性。
Array pattern synthesis and adaptive beamforming have found a wide range ofapplications in radar, sonar, wireless communication and astronomy, et.al. By thepattern synthesis or adaptive beamforming techniques, the systems in these applicationscan transmit/receive the signal to/from a specified direction or a range of directions, andtransmit/receive as little signal as possible to/from other directions, or completelysuppress the signal to/from some directions. However, in some kind of arrays or in somespecially situations, the exsiting methods will suffer from some kind of problems. Thisdissertation summarizes the applications of some existing pattern synthesis methods andproposes some modified methods, and then focuses on the pattern synthesis ofconformal arrays and large arrays. New pattern synthesis methods for conformal arraysand large arrays are proposed to address the shortcomings of the conventional methods.To improve the robustness of the adaptive beamforming against model errors, severalnew robust beamformer are presented. The main contributions are illustrated as follows:
Firstly, the dissertation summarizes the applications of the convex optimization onpattern synthesis of pencil beam or shaped beam patterns, and a shaped beam patternsynthesis method with nonuniform arrays is proposed and is applied to array failurecorrection. A pattern synthesis method based on convex optimization is proposed tosynthesize the sum and difference patterns. This method can optimize the elementpositions and excitations for sum and difference patterns simultaneously. Therefore, thesystem complexity can be reduced. The dissertation introduced the particle swarmoptimization method, and proposed a new fuzzy discrete particle swarm optimizationmethod. What’s more, the matrix pencil method based pattern synthesis method isintroduced and extended to2D arrays.
Secondly, the pattern synthesis of conformal arrays is considered. The first topic ofthis part is to optimize the array excitations of a given array to obtain a desired pattern. Iproposed a novel active element pattern decomposition based method of conformalarray synthesis. This method requires less pattern samples, less memory, lesscomputational cost and can steer the mainlobe or nulls to precise directions. Then, anoptimization method on conformal array element positions is proposed. In this method,the pattern of an element located at an arbitrary position on the platform is obtained by interpolating the element patterns at several sampled locations, and the mutual couplingbetween elements is considered by robust pattern synthesis method. The full wavesimulation results validate these two proposed methods.
Thirdly, this dissertation deals with the fast pattern synthesis method for largearrays. Inspired by the nonuniform fast Fourier transform, I proposed a novel fast pencilbeam pattern synthesis method for large unequally spaced antenna arrays. This methodis based on fast Fourier transform, so larger arrays can be handled and can obtain betterresults when compared with other methods. The dissertation also considered the flat-topfootprint pattern synthesis in this part. The dissertation proposed a synthesis method thatcan obtain arbitrary footprint pattern which is important in satellite applications. Theproposed method chooses the antennas in the given uniform array and the dynamicrange ratio can be controlled.
Finally, the dissertation works on the robust adaptive beamforming methods. Thedisseratation proposed an adaptive beamforming method that is robust against largearray calibration errors. This method reconstructs the interference covariance matrix andestimates the steering vector associated with the desired signal. Compared withstate-of-the-art methods, the proposed method can obtain better results even when largecalibration error exists. What’s more, the dissertation transform the adaptivebeamforming problem into a weighted array pattern synthesis problem. The robustnessof the adaptive beamformer is improved by adding restriction on the mainlobe widthand sidelobe levels. The proposed method can suppress the interferences with highpriority, and it is robust against model errors.
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