鲁棒波束形成技术的Krylov子空间理论与算法研究

Adaptive beamforming has become a fundamental technique for numerous array signal processing applications and received considerable attention during the past several decades. It is assumed that the signal model is exactly known in conventional beamforming algorithms. However, there exist various mismatches in real arrays, which can severely deteriorate the performance of practical systems. Therefore, a key technique in adaptive beamforming is to enhance the robustness of the beamformer against model mismatches. The existing literature and our previous work have demonstrated that the Krylov subspace method is one of the most effective robust beamforming techniques due to its low computational complexity, high robust performance and small sample size. In this project, we will study the robust beamforming algorithms in Krylov subspace through theoretical analysis, algorithms design and experiments. First, we will study the mathematical principle of the robustness of beamforming algorithms in Krylov subspace. Second, we will construct a unified theoretical framework for robust beamforming from the viewpoint of regularization. Finally, we will design and implement a new kind of beamforming algorithm in Krylov subspace that has the properties of low computational complexity, high robustness, strong tracking ability and good numerical stability. The successful implementation of this project will enhance the overall performance of the beamforming technology in radar, communication and navigation applications.

自适应波束形成是阵列信号处理的核心内容和研究热点。传统波束形成算法假定信号模型精确已知，然而实际阵列中存在许多不确定因素会导致信号模型失配，进而恶化系统性能。因此，提高波束形成算法对模型误差的鲁棒性是实际应用中必须攻克的一项关键技术。现有文献和我们前期的研究工作表明，Krylov子空间方法不仅计算量低、鲁棒性好，而且样本数少，是最具实用价值的鲁棒波束形成算法之一。本项目结合理论分析和算法设计，对基于Krylov子空间的鲁棒波束形成技术展开深入研究。首先研究Krylov子空间波束形成算法的鲁棒性原理，推导并分析滤波因子和投影矩阵对模型误差的抑制机理。然后以正则化理论为基础，建立鲁棒波束形成技术的统一理论框架。最后依据Krylov子空间投影和子空间快速更新，设计复杂度低、鲁棒性好、跟踪性强和稳定性高的波束形成算法。本项目的成功研究将全面提升波束形成技术在雷达、通信和导航等系统中的综合性能。

自适应波束形成是阵列信号处理的核心内容和研究热点。传统波束形成算法假定信号模型精确已知，然而实际阵列中存在许多不确定因素会导致信号模型失配，进而恶化系统性能。因此提高波束形成算法对模型误差的鲁棒性是实际应用中必须攻克的一项关键技术。.Krylov子空间方法不仅计算量低、鲁棒性好，而且样本数少，是最具实用价值的鲁棒波束形成算法之一。本项目结合理论分析与算法设计，对基于Krylov子空间的鲁棒波束形成技术展开深入研究。首先研究Krylov子空间波束形成算法的鲁棒性原理，以正则化理论为基础建立鲁棒波束形成技术的统一理论框架。然后利用子空间投影和快速更新设计复杂度低、鲁棒性好、跟踪性强和稳定性高的波束形成算法。最后研制了一款七单元卫星导航抗干扰天线原理样机，实验结果证实了算法的有效性和先进性。.项目取得重要结果及其意义如下：.1，给出研究鲁棒波束形成方法的正则化理论框架，并基于此设计了三对角加载鲁棒波束形成算法，具备计算量小、鲁棒性高、便于在FPGA芯片中实现的优点。.2，提出一种快速、稳定的子空间跟踪算法，并将该算法应用于波达角估计，改善了实时角度估计算法对抗冲击噪声的能力。.3，结合旁瓣对消器和Krylov子空间投影，提出一种基于Ritz值的快速信源个数检测算法，具备计算量小、检测概率高的特点，为快速目标检测提供了重要的技术途径。.4，应用鲁棒波束形成的思想方法设计阵列方向图，证明在一定条件下，不考虑阵元误差的直接综合方法具有对抗阵元误差的能力，为直接阵列综合方提供了理论依据。.5，研制七单元卫星导航抗干扰天线原理样机，实验结果表明所设计的算法能够对抗干信比为100dB的单个干扰信号和干信比为80dB的五个干扰信号。