雷达自适应波形优化设计研究
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摘要
雷达发射波形的选取影响着回波中包含的信息量,与雷达检测、估计、成像、跟踪及干扰抑制等方面性能有直接的关系。根据雷达工作环境自适应地选择发射波形,有利于使雷达以最佳方式从回波中提取更多更准确的目标信息,对于提高雷达的感知能力和适应能力,以及抗干扰能力有重要的理论意义和实用价值,自适应优化设计雷达发射波形近年来已成为国内外雷达界的研究热点。
本文围绕着改善雷达目标检测、抗干扰及成像方面的性能展开了发射波形自适应优化设计研究,主要研究内容包括以下几个方面：
(1)为了改善匹配照射下单输入单输出(SISO)雷达在加性噪声中的目标检测性能,进行了发射波形自适应优化设计研究。推导了匹配照射下SISO雷达滤波器输出信噪比(SNR)的时域向量表达式,结合工作于复高斯白噪声背景下的正交频分复用(OFDM)雷达,给出了在降低发射信号峰均比(PAPR)的约束下提高滤波器输出SNR的波形自适应优化设计方法。该方法采用凸优化算法求得近似最优OFDM信号子载波调制系数向量,所优化发射波形的检测性能接近最优匹配照射调制信号,同时其PAPR接近0dB,达到检测性能与PAPR性能的综合改善；结合工作于加性有色噪声背景下的SISO雷达,给出了目标信号子空间加权的波形自适应优化设计方法,该方法在提高SISO雷达滤波器输出SNR的同时,降低发射波形的PAPR和距离旁瓣,设计得到的波形可增强雷达系统对有色噪声的抑制能力,同时有利于降低系统设备复杂度,充分利用发射功率以及降低微弱目标被掩盖的几率。
(2)为了改善匹配照射下多输入多输出(MIMO)雷达在杂波及复高斯白噪声中的目标检测性能,进行了发射波形自适应优化设计研究。利用OFDM信号的频率分集特性,将其用于共址MIMO雷达,每个阵元发射一个子载波信号,依据匹配照射理论,给出了基于交替迭代算法联合优化子载波调制系数向量和滤波器系数向量的方法。该方法运算量小,收敛速度快,所优化波形可有效改善正交频分复用-多输入多输出(OFDM-MIMO)雷达对扩展目标的检测性能且具有较好的抗杂波稳健性；考虑到OFDM信号的高PAPR特性不利于实际工程应用,进一步提出了改进的交替迭代算法用于自适应优化设计随机相位编码发射波形。该算法在基于已知接收滤波器优化相位编码信号的问题上,采用半正定松弛将优化问题转换为凸问题,之后结合经典对分法与高斯随机算法求得原优化问题的近似最优解。设计得到的波形可进一步提高MIMO雷达的滤波器输出信杂噪比(SCNR),改善检测性能,且波形包络恒定,更具有工程适用性。
(3)针对宽带、超宽带雷达所面临的同频窄带干扰抑制问题,进行了稀疏频谱波形(SFW)自适应优化设计研究。提出了自适应优化设计低距离旁瓣SFW的随机相位编码方法。通过使波形功率谱密度(PSD)与期望PSD相匹配,优化波形的同频窄带干扰对抗性能。通过最小化波形自相关函数的积分旁瓣电平降低波形的距离旁瓣,基于Pareto优化理论,建立联合优化二者的目标函数,并给出基于快速傅里叶变换的循环迭代算法进行求解。所提波形优化方法计算复杂度低,易于工程实现,且灵活性较强。所优化波形的陷波性能和距离旁瓣性能均获得进一步改善,且可通过调节Pareto权值均衡二者性能；针对MIMO雷达,给出了自适应优化设计正交SFW的双阶段交替投影算法。该算法将波形优化问题分解为最优频谱求解与最优波形综合两个子优化问题依次求解,既可获得具有一定正交性及稀疏频谱的相位编码信号,也可通过调节参数设置获得正交性能和陷波性能进一步改善的低PAPR信号。该算法适用性较强、运算量较小、收敛速度快。
(4)针对MIMO雷达的距离-角度成像问题,进行了发射波形自适应优化设计研究。提出了将波形优化设计与目标雷达截面积(RCS)估计相结合的方法,基于最小均方误差准则,依次针对各距离-角度单元设计最优发射波形及接收滤波器,并将其用于相应距离-角度单元内散射点RCS的估计,此过程以递归的方式进行,在遍历目标场景内所有距离-角度单元后进行下一轮更新。该方法借助了自适应波形设计的优势,可有效提高MIMO雷达距离-角度成像精度及抗高斯白噪声稳健性。
The radar transmitting waveform influences the amount of information included in the echoes. It has a direct relationship with the radar performance with respect to detection, estimation, imaging, tracking, and interference mitigation. Choosing transmitting waveforms adaptively according to the operating environment is favorable for extracting more information from the echoes in the best way. This enjoys important theoretical significance and practical value in improving the sensing capability, adaptability, and anti-jamming ability for radars. Adaptive optimizing and designing radar transmitting waveforms has become a hot research topic internationally in recent years.
This thesis centers on adaptive optimizing and designing radar transmitting waveforms for improving the detection, anti-interference, and imaging performances. The main works are illustrated as follows:
(1) To solve the problem of improving the detection performance in additive noise for Single Input Single Output (SISO) radar based on the principle of matched illumination, the method for adaptively designing the transmitting waveform is studied. The vector expression in time-domain of the output signal-to-noise ratio (SNR) of SISO radar according to the matched illumination theory is derived. Considering Orthogonal Frequency Division Multiplexing (OFDM) radar operating in complex Gaussian white noise, an adaptive waveform optimization method is given to improve the output SNR under the constraint of low peak-to-average power ratio (PAPR). This method employs convex optimization to acquire the sub-optimal coefficient vector for modulating the subcarriers of OFDM signal. The detection performance achieved by the optimized waveform approximates that realized by the optimum matched illumination modulation OFDM signal. The PAPR of optimized waveform approaches to0dB. The given method can make a comprehensive improvement in both detection and PAPR performances. Regarding the SISO radar performing in the additive colored noise, an adaptive waveform design method of weighted target signal subspace is provided. This method realizes improvements in the SISO radar output SNR as well as reductions in PAPR and range sidelobes. The optimized waveform can enhance the ability for suppressing the colored noise. Simultaneously, it is favorable to reduce the complexity of SISO radar system, make full use of transmitting power, and cut down the probability of weak targets being covered.
(2) To improve the detection performance of Multiple Input Multiple Output (MIMO) radar in clutter combined with complex Gaussian white noise, studies are conducted on adaptive waveform optimization based upon matched illumination. Taking advantages of the frequency diversity, OFDM signal is applied to MIMO radar with each transmitting antenna emitting one subcarrier. Under the instruction of matched illumination principle, a method adopting an alternate iterative algorithm is presented to jointly optimize subcarrier modulation coefficient vector and receiving filter vector. This method has a low computational complexity and fast convergence. The optimized waveform can improve the OFDM-MIMO radar detection performance effectively and has a good robustness against clutter. Since the OFDM signal usually has a high PAPR, not suitable for practical engineering application, a method is further proposed to adaptively design the random phase-coded transmitting waveforms. To optimize the phase-coded signal with regard to receiving filter, the proposed method transforms the optimization problem into a convex problem through semi-definite relaxation, and then recurs to the classical bisection procedure and Gaussian randomization. A sub-optimal solution can be obtained, and can make a further improvement in MIMO radar output signal-to-clutter-plus-noise ratio (SCNR), and improve the detection performance. In addition, the optimized waveform has a constant envelope, which has more adaptability in engineering.
(3) To deal with the problem of the narrow-band interference mitigation faced by wide band and ultra wide band radar, studies on the adaptive sparse frequency waveform (SFW) design are carried out. A method to design a phase-coded SFW with low range sidelobes is proposed. Through making the power spectrum density (PSD) of the waveform match the expected PSD, the anti-interference performance is optimized. The range sidelobes are reduced by minimizing the integrated sidelobe level (ISL) of the waveform autocorrelation. Then according to the Pareto theory, a target function jointly optimizing the PSD and ISL performances is constructed. A cyclic iterative algorithm (CIA) based on Fast Fourier Transformation is proposed to solve the optimization problem. CIA is computationally efficient, easy to be realized in engineering, and flexible. Further improvements can be brought into the performances of PSD and range sidelobes, which can be balanced by means of adjusting the value of Pareto weight. As the narrow band interferences also disturb MIMO radar, the two-stage alternate projection method is presented to design a set of orthogonal SFWs. This method decomposes the optimization problem into two subproblems, which are intended for solving the optimized spectrum and waveform synthesis. A set of phase-code orthogonal SFWs can be obtained, in addition, a set of orthogonal SFWs with low PAPR can also be acquired through parameter settings. The proposed method has good applicability, low computational complexity, and fast convergence.
(4) Aiming at increasing the range-angle imaging accuracy for MIMO radar, investigations of adaptive waveform design are made. A method combing waveform design and Radar Cross Section (RCS) estimation is proposed. The transmitting waveforms and the corresponding filters are optimized against each range-angle bin based on the criterion of MMSE. The RCS of the scatter in the corresponding range-angle bin is estimated with the optimized waveforms. The above process is conducted in a recursion way. When all the range-angles bins in the target scene are covered, a new round of updating is carried on. The proposed method takes the advantages of waveform design, and can improve range-angle imaging accuracy and robustness against Gaussian white noise for MIMO radar.
本文围绕着改善雷达目标检测、抗干扰及成像方面的性能展开了发射波形自适应优化设计研究,主要研究内容包括以下几个方面：
(1)为了改善匹配照射下单输入单输出(SISO)雷达在加性噪声中的目标检测性能,进行了发射波形自适应优化设计研究。推导了匹配照射下SISO雷达滤波器输出信噪比(SNR)的时域向量表达式,结合工作于复高斯白噪声背景下的正交频分复用(OFDM)雷达,给出了在降低发射信号峰均比(PAPR)的约束下提高滤波器输出SNR的波形自适应优化设计方法。该方法采用凸优化算法求得近似最优OFDM信号子载波调制系数向量,所优化发射波形的检测性能接近最优匹配照射调制信号,同时其PAPR接近0dB,达到检测性能与PAPR性能的综合改善；结合工作于加性有色噪声背景下的SISO雷达,给出了目标信号子空间加权的波形自适应优化设计方法,该方法在提高SISO雷达滤波器输出SNR的同时,降低发射波形的PAPR和距离旁瓣,设计得到的波形可增强雷达系统对有色噪声的抑制能力,同时有利于降低系统设备复杂度,充分利用发射功率以及降低微弱目标被掩盖的几率。
(2)为了改善匹配照射下多输入多输出(MIMO)雷达在杂波及复高斯白噪声中的目标检测性能,进行了发射波形自适应优化设计研究。利用OFDM信号的频率分集特性,将其用于共址MIMO雷达,每个阵元发射一个子载波信号,依据匹配照射理论,给出了基于交替迭代算法联合优化子载波调制系数向量和滤波器系数向量的方法。该方法运算量小,收敛速度快,所优化波形可有效改善正交频分复用-多输入多输出(OFDM-MIMO)雷达对扩展目标的检测性能且具有较好的抗杂波稳健性；考虑到OFDM信号的高PAPR特性不利于实际工程应用,进一步提出了改进的交替迭代算法用于自适应优化设计随机相位编码发射波形。该算法在基于已知接收滤波器优化相位编码信号的问题上,采用半正定松弛将优化问题转换为凸问题,之后结合经典对分法与高斯随机算法求得原优化问题的近似最优解。设计得到的波形可进一步提高MIMO雷达的滤波器输出信杂噪比(SCNR),改善检测性能,且波形包络恒定,更具有工程适用性。
(3)针对宽带、超宽带雷达所面临的同频窄带干扰抑制问题,进行了稀疏频谱波形(SFW)自适应优化设计研究。提出了自适应优化设计低距离旁瓣SFW的随机相位编码方法。通过使波形功率谱密度(PSD)与期望PSD相匹配,优化波形的同频窄带干扰对抗性能。通过最小化波形自相关函数的积分旁瓣电平降低波形的距离旁瓣,基于Pareto优化理论,建立联合优化二者的目标函数,并给出基于快速傅里叶变换的循环迭代算法进行求解。所提波形优化方法计算复杂度低,易于工程实现,且灵活性较强。所优化波形的陷波性能和距离旁瓣性能均获得进一步改善,且可通过调节Pareto权值均衡二者性能；针对MIMO雷达,给出了自适应优化设计正交SFW的双阶段交替投影算法。该算法将波形优化问题分解为最优频谱求解与最优波形综合两个子优化问题依次求解,既可获得具有一定正交性及稀疏频谱的相位编码信号,也可通过调节参数设置获得正交性能和陷波性能进一步改善的低PAPR信号。该算法适用性较强、运算量较小、收敛速度快。
(4)针对MIMO雷达的距离-角度成像问题,进行了发射波形自适应优化设计研究。提出了将波形优化设计与目标雷达截面积(RCS)估计相结合的方法,基于最小均方误差准则,依次针对各距离-角度单元设计最优发射波形及接收滤波器,并将其用于相应距离-角度单元内散射点RCS的估计,此过程以递归的方式进行,在遍历目标场景内所有距离-角度单元后进行下一轮更新。该方法借助了自适应波形设计的优势,可有效提高MIMO雷达距离-角度成像精度及抗高斯白噪声稳健性。
The radar transmitting waveform influences the amount of information included in the echoes. It has a direct relationship with the radar performance with respect to detection, estimation, imaging, tracking, and interference mitigation. Choosing transmitting waveforms adaptively according to the operating environment is favorable for extracting more information from the echoes in the best way. This enjoys important theoretical significance and practical value in improving the sensing capability, adaptability, and anti-jamming ability for radars. Adaptive optimizing and designing radar transmitting waveforms has become a hot research topic internationally in recent years.
This thesis centers on adaptive optimizing and designing radar transmitting waveforms for improving the detection, anti-interference, and imaging performances. The main works are illustrated as follows:
(1) To solve the problem of improving the detection performance in additive noise for Single Input Single Output (SISO) radar based on the principle of matched illumination, the method for adaptively designing the transmitting waveform is studied. The vector expression in time-domain of the output signal-to-noise ratio (SNR) of SISO radar according to the matched illumination theory is derived. Considering Orthogonal Frequency Division Multiplexing (OFDM) radar operating in complex Gaussian white noise, an adaptive waveform optimization method is given to improve the output SNR under the constraint of low peak-to-average power ratio (PAPR). This method employs convex optimization to acquire the sub-optimal coefficient vector for modulating the subcarriers of OFDM signal. The detection performance achieved by the optimized waveform approximates that realized by the optimum matched illumination modulation OFDM signal. The PAPR of optimized waveform approaches to0dB. The given method can make a comprehensive improvement in both detection and PAPR performances. Regarding the SISO radar performing in the additive colored noise, an adaptive waveform design method of weighted target signal subspace is provided. This method realizes improvements in the SISO radar output SNR as well as reductions in PAPR and range sidelobes. The optimized waveform can enhance the ability for suppressing the colored noise. Simultaneously, it is favorable to reduce the complexity of SISO radar system, make full use of transmitting power, and cut down the probability of weak targets being covered.
(2) To improve the detection performance of Multiple Input Multiple Output (MIMO) radar in clutter combined with complex Gaussian white noise, studies are conducted on adaptive waveform optimization based upon matched illumination. Taking advantages of the frequency diversity, OFDM signal is applied to MIMO radar with each transmitting antenna emitting one subcarrier. Under the instruction of matched illumination principle, a method adopting an alternate iterative algorithm is presented to jointly optimize subcarrier modulation coefficient vector and receiving filter vector. This method has a low computational complexity and fast convergence. The optimized waveform can improve the OFDM-MIMO radar detection performance effectively and has a good robustness against clutter. Since the OFDM signal usually has a high PAPR, not suitable for practical engineering application, a method is further proposed to adaptively design the random phase-coded transmitting waveforms. To optimize the phase-coded signal with regard to receiving filter, the proposed method transforms the optimization problem into a convex problem through semi-definite relaxation, and then recurs to the classical bisection procedure and Gaussian randomization. A sub-optimal solution can be obtained, and can make a further improvement in MIMO radar output signal-to-clutter-plus-noise ratio (SCNR), and improve the detection performance. In addition, the optimized waveform has a constant envelope, which has more adaptability in engineering.
(3) To deal with the problem of the narrow-band interference mitigation faced by wide band and ultra wide band radar, studies on the adaptive sparse frequency waveform (SFW) design are carried out. A method to design a phase-coded SFW with low range sidelobes is proposed. Through making the power spectrum density (PSD) of the waveform match the expected PSD, the anti-interference performance is optimized. The range sidelobes are reduced by minimizing the integrated sidelobe level (ISL) of the waveform autocorrelation. Then according to the Pareto theory, a target function jointly optimizing the PSD and ISL performances is constructed. A cyclic iterative algorithm (CIA) based on Fast Fourier Transformation is proposed to solve the optimization problem. CIA is computationally efficient, easy to be realized in engineering, and flexible. Further improvements can be brought into the performances of PSD and range sidelobes, which can be balanced by means of adjusting the value of Pareto weight. As the narrow band interferences also disturb MIMO radar, the two-stage alternate projection method is presented to design a set of orthogonal SFWs. This method decomposes the optimization problem into two subproblems, which are intended for solving the optimized spectrum and waveform synthesis. A set of phase-code orthogonal SFWs can be obtained, in addition, a set of orthogonal SFWs with low PAPR can also be acquired through parameter settings. The proposed method has good applicability, low computational complexity, and fast convergence.
(4) Aiming at increasing the range-angle imaging accuracy for MIMO radar, investigations of adaptive waveform design are made. A method combing waveform design and Radar Cross Section (RCS) estimation is proposed. The transmitting waveforms and the corresponding filters are optimized against each range-angle bin based on the criterion of MMSE. The RCS of the scatter in the corresponding range-angle bin is estimated with the optimized waveforms. The above process is conducted in a recursion way. When all the range-angles bins in the target scene are covered, a new round of updating is carried on. The proposed method takes the advantages of waveform design, and can improve range-angle imaging accuracy and robustness against Gaussian white noise for MIMO radar.
引文
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