稀疏信号处理在雷达检测和成像中的应用研究
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摘要
稀疏信号处理理论，特别是近年压缩感知理论(Compressive Sensing,CS)的建立和快速发展，为利用稀疏信号处理技术解决雷达实际信号处理问题提供了新的方向。稀疏信号处理技术给我们提供了一个利用少量回波数据精确获取雷达目标信息的框架。近年来，压缩感知的理论和算法有很大发展，国内外研究表明，稀疏信号采样和恢复技术在雷达应用上具有很大的潜力。基于CS的雷达系统可以简化雷达硬件设计，提高系统分辨率，缩短数据获取时间，减少数据存储和传输量以及重构缺损信号。本论文列举了CS理论在雷达目标检测以及成像中的若干应用。利用概念分析、理论推导和实测数据验证等手段对雷达稀疏信号处理的一些新方法进行了研究。最后研究了基于CS的雷达观测矩阵设计以及优化算法的实时处理电路设计。本文的具体工作安排如下：
1.针对雷达稀疏信号处理实际应用，结合CS基本理论，对雷达回波信号的稀疏表示、观测矩阵设计、优化问题求解以及对杂波的处理进行了分析。
2.提出天波超视距雷达(OTHR)缺损信号的完整多普勒频谱重构方法。OTHR雷达工作在电磁环境复杂的高频波段，外部噪声的干扰，特别是闪电和流星余迹等瞬态干扰很强，信号容易受到强瞬态干扰的影响。对强瞬态干扰的剔除将导致信号缺损。同时现代OTHR通常要求在多模式、多目标的条件下工作，这也导致对同一目标和场景的回波在时间上不能均匀连续采样，信号出现缺损。根据信号的缺损规律，构建CS信号恢复模型，通过稀疏分解对信号完整的频谱进行了重构。
3.研究了高频(HF)雷达随机跳频信号的距离-多普勒二维高分辨处理。HF雷达所处频段拥挤不堪，很难找到连续的宽频带实现距离高分辨。结合频率监测系统，提出利用随机分布的稀疏频点实现距离-多普勒二维高分辨处理。由于频带缺损，带宽合成的效果不好，目标像出现高的旁瓣和栅瓣。针对这个问题，利用稀疏信号处理技术，构建距离-速度二维冗余时频字典矩阵，通过稀疏优化求解实现目标的二维高分辨。针对运动目标的距离-速度冗余时频字典矩阵相关性过大的问题，提出通过速度预估计的方法缩小字典速度维的尺寸，重新构造规模较小的时频字典，增强了字典的正交性。该方法提高了CS算法的恢复精度和稳健性，同时也大大提升了优化求解的计算效率。
4.提出基于CS的动目标显示(MTI)雷达多普勒解模糊方法。该方法发射抖动脉冲重复频率(PRF)脉冲序列实现雷达回波信号的非均匀采样。利用目标多普勒的稀疏特性以及非均匀采样特性，构造多普勒频率远大于发射PRF的字典矩阵，通过求解优化问题直接恢复出不模糊的目标多普勒。针对强杂波影响信号的恢复精度问题，对多普勒解模糊方法进行了改进。首先发射一组参考等PRF的脉冲序列来得到杂波谱估计，然后把杂波抑制结合到CS优化求解中，在恢复出目标真实多普勒的同时实现了杂波抑制。
5.提出带宽外推(BWE)结合CS的短孔径超分辨逆合成孔径雷达(ISAR)成像方法。短孔径ISAR成像可以减轻高次相位项的影响，简化了复杂运动目标的信号模型。根据CS理论，目标强散射点的恢复概率和精度与信号观测长度成正比，短孔径ISAR成像由于观测时间短，目标像方位分辨率通常较低。基于此问题，在保持信号相干性的前提下采用BWE技术对信号进行外推，增加了观测信号的维度。然后重新构造观测时间更长的CS模型，通过优化求解改善ISAR的方位分辨率。
6.提出基于CS的雷达观测矩阵电路设计方法以及正交匹配追踪(OMP)优化算法的电路实现方法。CS理论能否成功应用在雷达实时信号处理中，随机观测矩阵的设计以及优化问题的高效求解成为关键。随机观测矩阵的设计将涉及雷达参数的改变和控制，文中提出了可编程逻辑门阵列(FPGA)+数字模拟转换器(DAC)实现雷达随机观测的设计方法，同时提出了FPGA+并串转化实现宽带稀疏信号的随机调制方法。对于稀疏信号处理的优化求解问题，基于本实验室开发的高性能FPGA信号处理平台，设计了高度并行和深度流水的计算电路。对比了基于修正Gram-Schmidt法(MGS) QR分解最小二乘和共轭梯度(CG)迭代法最小二乘的实现效率。所设计的电路可以直接应用于雷达实时稀疏信号处理。
The theory of sparse signal processing, especially the establishment and rapiddevelopment of compressive sensing (CS) in recent years, has provided a new direction forthe application of sparse signal processing technology in the solution of practical radar signalprocessing problems. Sparse signal processing technology provides us with a framework toaccurately obtain the target information of the radar with a few echo data. According to theresearch at home and abroad, sparse signal sampling and recovery technique own a greatpotential in radar application. The radar system based on CS can simplify the design of radarhardware, improve the resolution, shorten the time for obtaining data, reduce data memorycapacity and reconstruct partial signals. This dissertation enumerates some applications of CStheory in radar target detection and imaging, makes a research on some new methods of radarsparse signal processing by means of conceptual analysis, theoretical derivation, real dataverification, etc., and finally studies the design of the radar measurement matrix based on CSand the real-time processing circuit design of its optimization algorithm. The main content ofthis dissertation is summarized as follows.
The dissertation, on the basis of the practical applications of radar sparse signalprocessing and combining the basic theory of CS, analyzes sparse expression of radar echosignals, measurement matrix design, optimization problem solution and clutter processing.
Over-the-horizon radar(OTHR) operating in the high frequency (HF) band can providelong-range detection of targets in large surveillance areas. However, OTHR signal is usuallycontaminated by transient interference, such as lightning, meteor trail echoes and man-madeimpulse interference. To filter out these interferences is available, while it destroys theintegrity of signal in time domain. What’s more, modern OTHR system is usually required tobe multi-mode and able to detect multi-targets simultaneously under different backgrounds.To satisfy these requirements, incontinuous sampling mode is usually applied resulting inparts of signal missing. In this paper, a novel algorithm is proposed to reconstruct theintegrate spectrum of OTHR with partial signal. The spectrum reconstruction problem isshifted into a problem of a norm1constrained optimal problem. By solving this problem withgreedy algorithm efficiently, the integrate frequency spectrum of OTHR signal isreconstructed optimally.
The dissertation studies the range-Doppler two-dimensional (2D) high resolutionconstruction of HF radar randomly hopped frequency signals. In a congest frequency band,it’s hard for a HF radar to find continuous broadband to realize high range resolution. Thus, the dissertation proposes to use randomly-distributed sparse frequencies to realizerange-Doppler2D high resolution processing. Because of the absence of some frequencies,high sidelobes and grating lobes will arise in the target’s range profile. To solve this problem,a range-velocity redundant time-frequency dictionary matrix is built to realize thetwo-dimensional high resolution target construction through optimization solution. For theproblem of the great coherence of the dictionary matrix of the moving target, the dissertationalso suggests to reduce the size of the dictionary by speed estimation, so as to improve itsorthogonality of the dictionary’s items. This method is able to enhance the recovery accuracyand stability of CS algorithm, and meanwhile improve the calculation efficiency ofoptimization solution.
A novel velocity ambiguity resolving method is proposed for moving target indication(MTI) radar, in which CS is applied to recover the unambiguous Doppler spectrum of targetsfrom the randomly pulse repetition frequency (PRF)-jittering pulses. Aiming at the issue thatstrong clutter affects the recovery accuracy of signals, the Doppler ambiguity resolvingmethod is improved. Firstly a group of reference pulse is transmitted to obtain clutterspectrum estimation. Then weighting in CS recovery is utilized to suppress the clutter byusing the estimated clutter spectrum.
In this dissertation, we present an algorithm for inversed synthetic aperture radar (ISAR)imaging with super resolution by combining CS and bandwidth extrapolation (BWE)technique. For ISAR imaging, the backscattering field of target is usually contributed by afew strong scattering centers, whose number is much less than that of image pixels. Thus, CSis intuitively suitable for constructing super resolution ISAR image. According to CS theory,the number of extracted dominating scatters relies on the signal length, which indicates that ifonly limited data is available, it is difficult to generate dense ISAR image robustly by CS, andsome signal components tend to lose. To soften this constraint, BWE is combined with CSimaging to increase the degree of signal freedom while preserving its coherence. A refinedCS-based formation for ISAR image-resolution enhancement is then developed. Both real andsimulated data experiments are performed to evaluate the proposed approach, and an exampleof using this technique demonstrates the enhanced image resolution in application ofmaneuvering target imaging.
The dissertation also studies the design method of radar measurement matrix circuitbased on CS and the circuit realizing method of Orthogonal Matching Pursuit (OMP)optimization algorithm. The design of the random measurement matrix and the highlyefficient solution of the optimization problem are crucial for the successful application of CStheory in real-time radar signal processing. The design of the random measurement matrix involves the change and control of radar parameters, in this dissertation, the design method ofusing Field Programmable Gate Array (FPGA) and digital to analog converter to realize radarrandom measurement and the method of using FPGA and parallel-to-serial converter torealize the random modulation of broadband sparse signals are proposed. To solve theoptimization problem of sparse signal processing, a high-paralleled and deep-pipelinedcalculation circuit is designed on the basis of the high-performance FPGA platform developedby the lab. It compares the efficiency of the least squares problem based on ModifiedGram-Schmidt(MGS) QR decomposition and Conjugate Gradient(CG) iterative method. Thecircuit designed in the dissertation can be directly applied in real-time radar sparse signalprocessing.
1.针对雷达稀疏信号处理实际应用，结合CS基本理论，对雷达回波信号的稀疏表示、观测矩阵设计、优化问题求解以及对杂波的处理进行了分析。
2.提出天波超视距雷达(OTHR)缺损信号的完整多普勒频谱重构方法。OTHR雷达工作在电磁环境复杂的高频波段，外部噪声的干扰，特别是闪电和流星余迹等瞬态干扰很强，信号容易受到强瞬态干扰的影响。对强瞬态干扰的剔除将导致信号缺损。同时现代OTHR通常要求在多模式、多目标的条件下工作，这也导致对同一目标和场景的回波在时间上不能均匀连续采样，信号出现缺损。根据信号的缺损规律，构建CS信号恢复模型，通过稀疏分解对信号完整的频谱进行了重构。
3.研究了高频(HF)雷达随机跳频信号的距离-多普勒二维高分辨处理。HF雷达所处频段拥挤不堪，很难找到连续的宽频带实现距离高分辨。结合频率监测系统，提出利用随机分布的稀疏频点实现距离-多普勒二维高分辨处理。由于频带缺损，带宽合成的效果不好，目标像出现高的旁瓣和栅瓣。针对这个问题，利用稀疏信号处理技术，构建距离-速度二维冗余时频字典矩阵，通过稀疏优化求解实现目标的二维高分辨。针对运动目标的距离-速度冗余时频字典矩阵相关性过大的问题，提出通过速度预估计的方法缩小字典速度维的尺寸，重新构造规模较小的时频字典，增强了字典的正交性。该方法提高了CS算法的恢复精度和稳健性，同时也大大提升了优化求解的计算效率。
4.提出基于CS的动目标显示(MTI)雷达多普勒解模糊方法。该方法发射抖动脉冲重复频率(PRF)脉冲序列实现雷达回波信号的非均匀采样。利用目标多普勒的稀疏特性以及非均匀采样特性，构造多普勒频率远大于发射PRF的字典矩阵，通过求解优化问题直接恢复出不模糊的目标多普勒。针对强杂波影响信号的恢复精度问题，对多普勒解模糊方法进行了改进。首先发射一组参考等PRF的脉冲序列来得到杂波谱估计，然后把杂波抑制结合到CS优化求解中，在恢复出目标真实多普勒的同时实现了杂波抑制。
5.提出带宽外推(BWE)结合CS的短孔径超分辨逆合成孔径雷达(ISAR)成像方法。短孔径ISAR成像可以减轻高次相位项的影响，简化了复杂运动目标的信号模型。根据CS理论，目标强散射点的恢复概率和精度与信号观测长度成正比，短孔径ISAR成像由于观测时间短，目标像方位分辨率通常较低。基于此问题，在保持信号相干性的前提下采用BWE技术对信号进行外推，增加了观测信号的维度。然后重新构造观测时间更长的CS模型，通过优化求解改善ISAR的方位分辨率。
6.提出基于CS的雷达观测矩阵电路设计方法以及正交匹配追踪(OMP)优化算法的电路实现方法。CS理论能否成功应用在雷达实时信号处理中，随机观测矩阵的设计以及优化问题的高效求解成为关键。随机观测矩阵的设计将涉及雷达参数的改变和控制，文中提出了可编程逻辑门阵列(FPGA)+数字模拟转换器(DAC)实现雷达随机观测的设计方法，同时提出了FPGA+并串转化实现宽带稀疏信号的随机调制方法。对于稀疏信号处理的优化求解问题，基于本实验室开发的高性能FPGA信号处理平台，设计了高度并行和深度流水的计算电路。对比了基于修正Gram-Schmidt法(MGS) QR分解最小二乘和共轭梯度(CG)迭代法最小二乘的实现效率。所设计的电路可以直接应用于雷达实时稀疏信号处理。
The theory of sparse signal processing, especially the establishment and rapiddevelopment of compressive sensing (CS) in recent years, has provided a new direction forthe application of sparse signal processing technology in the solution of practical radar signalprocessing problems. Sparse signal processing technology provides us with a framework toaccurately obtain the target information of the radar with a few echo data. According to theresearch at home and abroad, sparse signal sampling and recovery technique own a greatpotential in radar application. The radar system based on CS can simplify the design of radarhardware, improve the resolution, shorten the time for obtaining data, reduce data memorycapacity and reconstruct partial signals. This dissertation enumerates some applications of CStheory in radar target detection and imaging, makes a research on some new methods of radarsparse signal processing by means of conceptual analysis, theoretical derivation, real dataverification, etc., and finally studies the design of the radar measurement matrix based on CSand the real-time processing circuit design of its optimization algorithm. The main content ofthis dissertation is summarized as follows.
The dissertation, on the basis of the practical applications of radar sparse signalprocessing and combining the basic theory of CS, analyzes sparse expression of radar echosignals, measurement matrix design, optimization problem solution and clutter processing.
Over-the-horizon radar(OTHR) operating in the high frequency (HF) band can providelong-range detection of targets in large surveillance areas. However, OTHR signal is usuallycontaminated by transient interference, such as lightning, meteor trail echoes and man-madeimpulse interference. To filter out these interferences is available, while it destroys theintegrity of signal in time domain. What’s more, modern OTHR system is usually required tobe multi-mode and able to detect multi-targets simultaneously under different backgrounds.To satisfy these requirements, incontinuous sampling mode is usually applied resulting inparts of signal missing. In this paper, a novel algorithm is proposed to reconstruct theintegrate spectrum of OTHR with partial signal. The spectrum reconstruction problem isshifted into a problem of a norm1constrained optimal problem. By solving this problem withgreedy algorithm efficiently, the integrate frequency spectrum of OTHR signal isreconstructed optimally.
The dissertation studies the range-Doppler two-dimensional (2D) high resolutionconstruction of HF radar randomly hopped frequency signals. In a congest frequency band,it’s hard for a HF radar to find continuous broadband to realize high range resolution. Thus, the dissertation proposes to use randomly-distributed sparse frequencies to realizerange-Doppler2D high resolution processing. Because of the absence of some frequencies,high sidelobes and grating lobes will arise in the target’s range profile. To solve this problem,a range-velocity redundant time-frequency dictionary matrix is built to realize thetwo-dimensional high resolution target construction through optimization solution. For theproblem of the great coherence of the dictionary matrix of the moving target, the dissertationalso suggests to reduce the size of the dictionary by speed estimation, so as to improve itsorthogonality of the dictionary’s items. This method is able to enhance the recovery accuracyand stability of CS algorithm, and meanwhile improve the calculation efficiency ofoptimization solution.
A novel velocity ambiguity resolving method is proposed for moving target indication(MTI) radar, in which CS is applied to recover the unambiguous Doppler spectrum of targetsfrom the randomly pulse repetition frequency (PRF)-jittering pulses. Aiming at the issue thatstrong clutter affects the recovery accuracy of signals, the Doppler ambiguity resolvingmethod is improved. Firstly a group of reference pulse is transmitted to obtain clutterspectrum estimation. Then weighting in CS recovery is utilized to suppress the clutter byusing the estimated clutter spectrum.
In this dissertation, we present an algorithm for inversed synthetic aperture radar (ISAR)imaging with super resolution by combining CS and bandwidth extrapolation (BWE)technique. For ISAR imaging, the backscattering field of target is usually contributed by afew strong scattering centers, whose number is much less than that of image pixels. Thus, CSis intuitively suitable for constructing super resolution ISAR image. According to CS theory,the number of extracted dominating scatters relies on the signal length, which indicates that ifonly limited data is available, it is difficult to generate dense ISAR image robustly by CS, andsome signal components tend to lose. To soften this constraint, BWE is combined with CSimaging to increase the degree of signal freedom while preserving its coherence. A refinedCS-based formation for ISAR image-resolution enhancement is then developed. Both real andsimulated data experiments are performed to evaluate the proposed approach, and an exampleof using this technique demonstrates the enhanced image resolution in application ofmaneuvering target imaging.
The dissertation also studies the design method of radar measurement matrix circuitbased on CS and the circuit realizing method of Orthogonal Matching Pursuit (OMP)optimization algorithm. The design of the random measurement matrix and the highlyefficient solution of the optimization problem are crucial for the successful application of CStheory in real-time radar signal processing. The design of the random measurement matrix involves the change and control of radar parameters, in this dissertation, the design method ofusing Field Programmable Gate Array (FPGA) and digital to analog converter to realize radarrandom measurement and the method of using FPGA and parallel-to-serial converter torealize the random modulation of broadband sparse signals are proposed. To solve theoptimization problem of sparse signal processing, a high-paralleled and deep-pipelinedcalculation circuit is designed on the basis of the high-performance FPGA platform developedby the lab. It compares the efficiency of the least squares problem based on ModifiedGram-Schmidt(MGS) QR decomposition and Conjugate Gradient(CG) iterative method. Thecircuit designed in the dissertation can be directly applied in real-time radar sparse signalprocessing.
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