通道均衡在宽带数字阵列雷达中的技术研究
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摘要
宽带数字阵列雷达是采用宽带信号波形、发射和接收都使用数字技术和波束形成技术的阵列天线雷达。其相对于传统相控阵来说,具有巨大的优势:易于实现超低副瓣,大的动态范围,波束扫描速度快,可同时多波束等。然而宽带数字阵列雷达阵列通道中的模拟器件及其构成的电路特性的差异会使多个发射通道和接收通道产生随频率变化的幅度和相位特性的不一致,即通道失配。通道失配会严重影响宽带数字阵列雷达所具有的优越性能。
本论文针对这一问题,分析了通道失配对雷达性能的影响,重点研究了宽带数字阵列雷达中的补偿通道失配的通道均衡技术。
首先从理论上推导了通道失配对数字波束形成以及脉冲压缩的影响。给出了FIR扰动模型,并通过仿真实验表明,不论是通道幅度失配,相位失配或者幅度相位均失配,通道失配对低旁瓣波束形成影响都非常大。工程上,为了得到低旁瓣波束需要精确地控制雷达通道在整个波形带宽内的频率响应。
然后研究了通道均衡的时域算法和频域算法。通道均衡的时域算法是基于维纳滤波理论和最小二乘理论,文中给出了时域均衡的基本算法,并基于给出的IIR零极点扰动模型进行了仿真。本论文重点讨论了通道均衡频域算法,并对基本算法作了适当的修正即采用加权的最小二乘拟合法,并且把参考通道幅度响应作为加权矩阵的对角元素,获得了更好的均衡性能。此外,还详细分析了通道频率响应的失配程度、校正信号信噪比、均衡器抽头数、带宽时间延迟积、FFT点数M等因素对均衡器性能的影响,为以后的工程实现提供了理论基础。
为了满足工程应用上计算复杂性和性能之间的折中,我们考虑在一定的条件下,用传统的窄带校正的方法来替代均衡。通过仿真实验,可以看出在对带宽、通道失配程度、BT值有一定约束时,以校正来代替均衡能够在减小计算量的情况下取得良好的性能。
最后,给出了通道均衡器在数字阵列雷达中的实现方案以及接收通道和发射通道的均衡器实现框图和流程。由于均衡器是复数的FIR滤波器。但是FPGA中只能实现实数FIR滤波器,因此在结构上,可以用四个FIR实数滤波器等效一个复数FIR滤波器。FIR滤波器的主要组成模块是乘/加单元(MAC),如果按照直观结构构造乘法器和系数寄存器来实现会占用大量的逻辑资源,显然不可取。因此考虑用分布式算法以利用FPGA高并行度的结构特点,同时利用整数最优表示法与离散化方法来对FIR滤波器的二进制系数作优化,在保证运算速度的前提下,进一步降低逻辑资源的消耗。
Wideband Digital Array Radar (WDAR) is a fully digitized array antenna radar in which wideband signal waveform is transmitted and digital beam forming (DBF) technology is used in receiving and transmitting. Compared with conventional phased array radar, it can offer significant advantages. Such as low side lobes, high dynamic range (DR), rapid multi-beams steering, etc. But the change in the characteristic of analog devices and circuits in the element channels will cause the frequency-dependent amplitude and phase difference of receiver channels and transmitter channels in WDAR. The differences among the frequency responses of the channels are called channel mismatch. Channel mismatch will affect the superior performance of the WDAR seriously.
In this thesis, the impact of the mismatch on WDAR’s performance is analyzed. Adaptive channel equalization in order to compensate for the channel mismatch is investigated.
First of all, the impact of channel mismatch on DBF and pulse compress is analyzed. The simulation based on FIR mismatch model is given. It shows that impact of mismatch on low-sidelobe beams is serious. Therefore, the real project requires precise control of the radar receiver’s frequency response across the entire signal waveform bandwidth.
Two channel equalization algorithms, named frequency-domain based and time-domain-based algorithms are investigated for compensating the channel mismatch. Channel equalization time-domain-based algorithm is based on Weiner filter theory and Least Squares theory. Basic algorithm of the time domain equalization is presented. And simulation based on IIR mismatch model is given. Frequency-domain based channel equalization algorithm is investigated mainly which is based on least squares fitting method. A modified method is presented which is weight least squares fitting method, and the diagonal elements are the reference channel magnitude response. Good equalization performances are achieved by using the improved method. Impacts of many factors on equalization performance are analyzed. Such as the mismatch extent of frequency response of the receive channel, SNR, the length of equalizer L, Bandwidth-Time delay product, FFT-points. All of these factors have references to real project.
To satisfy the request of less computation and better performance in real projects, calibration is considered to replace equalization to some extent. The simulation is given. It showed that calibration may achieve high performance with some restriction of the mismatch extent of frequency response, SNR, Bandwidth-Time delay product, equalizer length L, FFT-points M, etc.
Finally, the blue print of channel equalizer in WDAR is presented. The Flow of equalizer of both receiving and transmitting is described. For the coefficients of FIR filter in Matlab are complex number, but they can’t be implemented in FPGA. So the structure of FIR filter is modified in which four real FIR filters substitute for one complex FIR filter. FIR filters consist of MAC mainly. It’s wasteful and inefficient that FIR filters are simply constructed by multiplications and coefficient registers. So the Distributed Arithmetic which coverts the multiplications into some look-up operations is presented. In this thesis, an improved optimum representation of integer coefficient and a discrete coefficient method is introduced according to the FPGA structure. It can assure the decrease of hardware logic resource and the increase of compute performance.
本论文针对这一问题,分析了通道失配对雷达性能的影响,重点研究了宽带数字阵列雷达中的补偿通道失配的通道均衡技术。
首先从理论上推导了通道失配对数字波束形成以及脉冲压缩的影响。给出了FIR扰动模型,并通过仿真实验表明,不论是通道幅度失配,相位失配或者幅度相位均失配,通道失配对低旁瓣波束形成影响都非常大。工程上,为了得到低旁瓣波束需要精确地控制雷达通道在整个波形带宽内的频率响应。
然后研究了通道均衡的时域算法和频域算法。通道均衡的时域算法是基于维纳滤波理论和最小二乘理论,文中给出了时域均衡的基本算法,并基于给出的IIR零极点扰动模型进行了仿真。本论文重点讨论了通道均衡频域算法,并对基本算法作了适当的修正即采用加权的最小二乘拟合法,并且把参考通道幅度响应作为加权矩阵的对角元素,获得了更好的均衡性能。此外,还详细分析了通道频率响应的失配程度、校正信号信噪比、均衡器抽头数、带宽时间延迟积、FFT点数M等因素对均衡器性能的影响,为以后的工程实现提供了理论基础。
为了满足工程应用上计算复杂性和性能之间的折中,我们考虑在一定的条件下,用传统的窄带校正的方法来替代均衡。通过仿真实验,可以看出在对带宽、通道失配程度、BT值有一定约束时,以校正来代替均衡能够在减小计算量的情况下取得良好的性能。
最后,给出了通道均衡器在数字阵列雷达中的实现方案以及接收通道和发射通道的均衡器实现框图和流程。由于均衡器是复数的FIR滤波器。但是FPGA中只能实现实数FIR滤波器,因此在结构上,可以用四个FIR实数滤波器等效一个复数FIR滤波器。FIR滤波器的主要组成模块是乘/加单元(MAC),如果按照直观结构构造乘法器和系数寄存器来实现会占用大量的逻辑资源,显然不可取。因此考虑用分布式算法以利用FPGA高并行度的结构特点,同时利用整数最优表示法与离散化方法来对FIR滤波器的二进制系数作优化,在保证运算速度的前提下,进一步降低逻辑资源的消耗。
Wideband Digital Array Radar (WDAR) is a fully digitized array antenna radar in which wideband signal waveform is transmitted and digital beam forming (DBF) technology is used in receiving and transmitting. Compared with conventional phased array radar, it can offer significant advantages. Such as low side lobes, high dynamic range (DR), rapid multi-beams steering, etc. But the change in the characteristic of analog devices and circuits in the element channels will cause the frequency-dependent amplitude and phase difference of receiver channels and transmitter channels in WDAR. The differences among the frequency responses of the channels are called channel mismatch. Channel mismatch will affect the superior performance of the WDAR seriously.
In this thesis, the impact of the mismatch on WDAR’s performance is analyzed. Adaptive channel equalization in order to compensate for the channel mismatch is investigated.
First of all, the impact of channel mismatch on DBF and pulse compress is analyzed. The simulation based on FIR mismatch model is given. It shows that impact of mismatch on low-sidelobe beams is serious. Therefore, the real project requires precise control of the radar receiver’s frequency response across the entire signal waveform bandwidth.
Two channel equalization algorithms, named frequency-domain based and time-domain-based algorithms are investigated for compensating the channel mismatch. Channel equalization time-domain-based algorithm is based on Weiner filter theory and Least Squares theory. Basic algorithm of the time domain equalization is presented. And simulation based on IIR mismatch model is given. Frequency-domain based channel equalization algorithm is investigated mainly which is based on least squares fitting method. A modified method is presented which is weight least squares fitting method, and the diagonal elements are the reference channel magnitude response. Good equalization performances are achieved by using the improved method. Impacts of many factors on equalization performance are analyzed. Such as the mismatch extent of frequency response of the receive channel, SNR, the length of equalizer L, Bandwidth-Time delay product, FFT-points. All of these factors have references to real project.
To satisfy the request of less computation and better performance in real projects, calibration is considered to replace equalization to some extent. The simulation is given. It showed that calibration may achieve high performance with some restriction of the mismatch extent of frequency response, SNR, Bandwidth-Time delay product, equalizer length L, FFT-points M, etc.
Finally, the blue print of channel equalizer in WDAR is presented. The Flow of equalizer of both receiving and transmitting is described. For the coefficients of FIR filter in Matlab are complex number, but they can’t be implemented in FPGA. So the structure of FIR filter is modified in which four real FIR filters substitute for one complex FIR filter. FIR filters consist of MAC mainly. It’s wasteful and inefficient that FIR filters are simply constructed by multiplications and coefficient registers. So the Distributed Arithmetic which coverts the multiplications into some look-up operations is presented. In this thesis, an improved optimum representation of integer coefficient and a discrete coefficient method is introduced according to the FPGA structure. It can assure the decrease of hardware logic resource and the increase of compute performance.
引文
[1]吴曼青.大有作为的数字阵列雷达.现代军事,2005,10:46-49
[2]吴曼青.数字阵列雷达及其进展.中国电子科学研究学报,2006, 1(1):11-16
[3]朱庆明.数字阵列雷达评述.雷达科学与技术,2004,2(3):136-146
[4] B. Cantrell, J. de Graff. Development of a Digital Array Radar(DAR). IEEE Aerospace and Electronic Systems Magazine, 2002,17(3):22-27
[5] D. J. Rabideau, R. J. Galejs, et al. An S-Band Digital Array Radar Testbed. 2003 IEEE Int. Symp. on Phased Array System and Technology, 2003, 113-118
[6]张光义,等.空间探测相控阵雷达.北京:科学出版社,2001, 106-248
[7] R. A. Monzigo, Thomas W. Miller. Introduction to Adaptive Arrays .New York: John Wiley & Sons, 1980:461-475
[8]束咸荣,何炳发,高铁.相控阵雷达天线.北京:国防工业出版社,2007,317-360
[9]龚耀寰.自适应滤波-时域自适应滤波和智能天线(第二版).北京:电子工业出版社,2003:308-333
[10]张贤达,保铮.通信信号处理.北京:国防工业出版社,2000:226-257
[11] K. A. Teitelbaum. A Flexible processor for a digital adaptive array radar. IEEE AES Magazine, 1991, 6(5):18-22
[12] Lars Pettersson, Magnuus Danestig, Ulf Sjostrom. An Experimental S-Band Digital Beamforming Antenna. IEEE AES systems Magazine, 1997, 12(11):19-29
[13]傅有光,唐纬,张倩.通道间幅相差异对旁瓣相消性能的影响与解决方法.现代雷达,2000, 22(6):50-55
[14]王峰,傅有光,孟兵,等.基于傅里叶变换的雷达通道均衡算法性能分析及改进.电子学报,2006, 34(9):1677-1680
[15]李建平.数字阵列雷达中的通道均衡算法研究:[硕士学位论文].成都:电子科技大学,2007
[16] M.Lanne, P.N.Drackner, T/R-Module mismatch and antenna pattern characteristics, IEEE,2003.
[17]申秋明.数字阵列雷达接收机通道均衡技术研究与实现:[硕士学位论文].成都:电子科技大学,2005
[18] Shunjun Wu, Yingjun Li. Adaptive channel equalization for space-time adaptive processing. IEEE International Conference, Alexadria, 1995:624-628
[19]吴洹,张玉洪,吴顺君.用于阵列信号处理的自适应均衡器的研究.现代雷达,1994, 16(1):49-56
[20]王振力,张雄伟,李荣锋.用于补偿高次畸变的一种自适应均衡法.通信学报,2005, 26(2):128-130
[21] R. J. Mailloux. Phased Array Antenna (Second Edition). Norwood: Artech House,2005, 353-377
[22] D. D. Aalfs, E. J. Holder. Impact of wideband channel-to-channel mismatch on adaptive array.2000 IEEE Proc. of SAMSP, Cambridge,2000:459-463
[23] A. Farina. Digital equalization in adaptive spatial filtering for radar system: a survey.Signal Processing 83,2003:11-29
[24]林茂庸.信号理论与应用.北京:高等教育出版社,1990:166-168
[25]张林让,保铮,张玉洪.通道失配对DBF天线旁瓣电平的影响.电子科学学刊,1995,17(3):268–275
[26] K. Gerlach. The effects of IF band pass mismatch errors on adaptive cancellation. IEEE Trans. on AES,1990, 26(3):455-468
[27] I. F. Progri, B. W. Nicholson, et al. Impacts of frequency dependent mutual coupling and channel errors on digital beaming antenna performance. Proc. of ION, Nashville, 1998:275-283
[28] K. A. Falcone, I. F. Progri, et al. Impact of frequency dependent mutual coupling and channel mismatch on closed loop digital adaptive nulling antenna performance. 1998
[29] Simon Haykin. Adaptive Filter Theory (Fourth Edition). Englewood Cliffs: Prentice Hall,2002:231-446
[30]王峰,傅有光,夏映玲.非最小相位雷达通道均衡算法研究.现代雷达,2004, 26(11):68-70
[31] A. Farina. Antenna Based Signal Processing Techniques for Radar System, Norwood: Artech House, 1992:25-260
[32] L. L. Horowitz. Convergence rate of the extended SMI algorithm for narrowband adaptive arrays. IEEE Trans. Aerosp. Electron. Syst., AES-16, 1980:738-740
[33]彭小亮,李荣锋,王永良,陈凤波.两种修正的自适应通道均衡方法.电子与信息学报,2006,4(28):658-662
[34] A.Agrawal,A.Jablon. A calibration technique for active phased array antennas.IEEE,2003.
[35] J.de Graff, G.Tavik,M.Bottoms.Calibration Overview of AMRFC TestBed.IEEE,2003.
[36] Xie Rong, Lin zheng,Zhang Shouhong.Design and implementation of channel equalization for a multi-frequency CW ranging radar.IEEE,2006
[37]冷红英,张扬,唐斌.阵列通道误差校正方法及DSP实现.电子科技大学学报,2004,5(33):511-514
[38]梁兵,陶海红,沈福民.提高旁瓣相消性能的自适应通道均衡技术.火控雷达技术,2004,3(33):34-39
[39]宋千,陆必应,梁甸农.基于FPGA的FIR滤波器高效实现.信号处理,2001,5(17): 385-391
[40]胡锦,彭成,孙晓宁. FIR数字滤波器的优化设计.宇航计测技术,2006,6(26):48-55
[2]吴曼青.数字阵列雷达及其进展.中国电子科学研究学报,2006, 1(1):11-16
[3]朱庆明.数字阵列雷达评述.雷达科学与技术,2004,2(3):136-146
[4] B. Cantrell, J. de Graff. Development of a Digital Array Radar(DAR). IEEE Aerospace and Electronic Systems Magazine, 2002,17(3):22-27
[5] D. J. Rabideau, R. J. Galejs, et al. An S-Band Digital Array Radar Testbed. 2003 IEEE Int. Symp. on Phased Array System and Technology, 2003, 113-118
[6]张光义,等.空间探测相控阵雷达.北京:科学出版社,2001, 106-248
[7] R. A. Monzigo, Thomas W. Miller. Introduction to Adaptive Arrays .New York: John Wiley & Sons, 1980:461-475
[8]束咸荣,何炳发,高铁.相控阵雷达天线.北京:国防工业出版社,2007,317-360
[9]龚耀寰.自适应滤波-时域自适应滤波和智能天线(第二版).北京:电子工业出版社,2003:308-333
[10]张贤达,保铮.通信信号处理.北京:国防工业出版社,2000:226-257
[11] K. A. Teitelbaum. A Flexible processor for a digital adaptive array radar. IEEE AES Magazine, 1991, 6(5):18-22
[12] Lars Pettersson, Magnuus Danestig, Ulf Sjostrom. An Experimental S-Band Digital Beamforming Antenna. IEEE AES systems Magazine, 1997, 12(11):19-29
[13]傅有光,唐纬,张倩.通道间幅相差异对旁瓣相消性能的影响与解决方法.现代雷达,2000, 22(6):50-55
[14]王峰,傅有光,孟兵,等.基于傅里叶变换的雷达通道均衡算法性能分析及改进.电子学报,2006, 34(9):1677-1680
[15]李建平.数字阵列雷达中的通道均衡算法研究:[硕士学位论文].成都:电子科技大学,2007
[16] M.Lanne, P.N.Drackner, T/R-Module mismatch and antenna pattern characteristics, IEEE,2003.
[17]申秋明.数字阵列雷达接收机通道均衡技术研究与实现:[硕士学位论文].成都:电子科技大学,2005
[18] Shunjun Wu, Yingjun Li. Adaptive channel equalization for space-time adaptive processing. IEEE International Conference, Alexadria, 1995:624-628
[19]吴洹,张玉洪,吴顺君.用于阵列信号处理的自适应均衡器的研究.现代雷达,1994, 16(1):49-56
[20]王振力,张雄伟,李荣锋.用于补偿高次畸变的一种自适应均衡法.通信学报,2005, 26(2):128-130
[21] R. J. Mailloux. Phased Array Antenna (Second Edition). Norwood: Artech House,2005, 353-377
[22] D. D. Aalfs, E. J. Holder. Impact of wideband channel-to-channel mismatch on adaptive array.2000 IEEE Proc. of SAMSP, Cambridge,2000:459-463
[23] A. Farina. Digital equalization in adaptive spatial filtering for radar system: a survey.Signal Processing 83,2003:11-29
[24]林茂庸.信号理论与应用.北京:高等教育出版社,1990:166-168
[25]张林让,保铮,张玉洪.通道失配对DBF天线旁瓣电平的影响.电子科学学刊,1995,17(3):268–275
[26] K. Gerlach. The effects of IF band pass mismatch errors on adaptive cancellation. IEEE Trans. on AES,1990, 26(3):455-468
[27] I. F. Progri, B. W. Nicholson, et al. Impacts of frequency dependent mutual coupling and channel errors on digital beaming antenna performance. Proc. of ION, Nashville, 1998:275-283
[28] K. A. Falcone, I. F. Progri, et al. Impact of frequency dependent mutual coupling and channel mismatch on closed loop digital adaptive nulling antenna performance. 1998
[29] Simon Haykin. Adaptive Filter Theory (Fourth Edition). Englewood Cliffs: Prentice Hall,2002:231-446
[30]王峰,傅有光,夏映玲.非最小相位雷达通道均衡算法研究.现代雷达,2004, 26(11):68-70
[31] A. Farina. Antenna Based Signal Processing Techniques for Radar System, Norwood: Artech House, 1992:25-260
[32] L. L. Horowitz. Convergence rate of the extended SMI algorithm for narrowband adaptive arrays. IEEE Trans. Aerosp. Electron. Syst., AES-16, 1980:738-740
[33]彭小亮,李荣锋,王永良,陈凤波.两种修正的自适应通道均衡方法.电子与信息学报,2006,4(28):658-662
[34] A.Agrawal,A.Jablon. A calibration technique for active phased array antennas.IEEE,2003.
[35] J.de Graff, G.Tavik,M.Bottoms.Calibration Overview of AMRFC TestBed.IEEE,2003.
[36] Xie Rong, Lin zheng,Zhang Shouhong.Design and implementation of channel equalization for a multi-frequency CW ranging radar.IEEE,2006
[37]冷红英,张扬,唐斌.阵列通道误差校正方法及DSP实现.电子科技大学学报,2004,5(33):511-514
[38]梁兵,陶海红,沈福民.提高旁瓣相消性能的自适应通道均衡技术.火控雷达技术,2004,3(33):34-39
[39]宋千,陆必应,梁甸农.基于FPGA的FIR滤波器高效实现.信号处理,2001,5(17): 385-391
[40]胡锦,彭成,孙晓宁. FIR数字滤波器的优化设计.宇航计测技术,2006,6(26):48-55