Detection and Parameter Estimation of Polyphase Code Signals Based on Fractional Fourier Transform

doi:10.3969/j.issn.1000-1093.2012.09.005

Abstract

Abstract: The polyphase code (Frank, P1, P2, P3 and P4 code) signals are a kind of typical low probability of intercept (LPI) radar signals. For the detection and parameter estimation of this kind of signals, the time-frequency distribution characteristics of the polyphase code signals were analyzed; the fractional spectrum characteristics of the polyphase code signals were also analyzed and the parameter estimation expressions of the polyphase code signals were deduced, taking Frank code signal for example. An algorithm for detection and parameters estimation of the polyphase code signals was proposed based on fractional Fourier transform (FRFT). And the algorithm first presents a method to estimate the carrier frequency of the polyphase code signals. Finally, simulations verifying the algorithm still has better signal detection and parameter estimation effect in low signal-to-noise ratios (SNR) condition.

CLC Number:

TN971
TN974

XU Hui-fa, HU Xiao-feng, ZHANG Ming-zhi₁. Detection and Parameter Estimation of Polyphase Code Signals Based on Fractional Fourier Transform[J]. Acta Armamentarii, 2012, 33(9): 1048-1054.

References

［1］ Pace P E. Detection and classifying low probability of intercept radar, second edition[M]. Boston： Artech House, 2009:81-119, 405-547.
[2] 徐海源, 周一宇, 黄知涛, 等. 一种Frank码脉压信号的检测与参数估计方法[J]. 系统工程与电子技术, 2007, 29(6):858-861.
XU Hai-yuan, ZHOU Yi-yu, HUANG Zhi-tao, et al. Detection and parameter estimation method for Frank code pulse compression wave- forms[J]. Systems Engineering and Electronics, 2007, 29(6):858-861. (in Chinese)
[3] 徐海源, 黄知涛, 周一宇. 基于Radon变换的具有线性调频特性的多相编码信号参数估计[J]. 信号处理, 2008, 24(2):172-176.
XU Hai-yuan, HUANG Zhi-tao, ZHOU Yi-yu. Parameter estimation methods for polyphase codes derived from LFM waveforms using the Radon transform [J]. Signal Processing, 2008,24(2):172-176. (in Chinese)
[4] 邓振淼, 刘渝. 多相码雷达信号识别与参数估计[J]. 电子与信息学报, 2009, 31(4):781-785.
DENG Zhen-miao, LIU Yu. Recognition and parameters estimation of polyphase-coded radar signals[J]. Journal of Electronics & Information Technology, 2009,31(4):781- 785. (in Chinese)
[5] 邓振淼. 雷达信号脉内分析与处理理论及算法研究[D]. 南京：南京航空航天大学, 2007:66-89.
DENG Zhen-miao. Study on theories and algorithms of intrapulse analysis and processing of radar signals[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2007:66-89. (in Chinese)
[6] Milne P R, Pace P E. Wigner distribution detection and analysis of FMCW and P-4 polyphase LPI waveforms［C］∥2002 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICA-SSP 02). Orlando: IEEE, 2002: 3944-3947.
[7] Copeland D B, Pace P E. Detection and analysis of FMCW and P-4 polyphase LPI waveforms using quadrature mirror filter trees［C］∥2002 IEEE International Conference on Acoustics, Speech, and Signal Processing. Orlando: IEEE, 2002:3960-3963.
[8] Jennison B K. Detection of polyphase pulse compression waveforms using the Radon-ambiguity transform［J］. IEEE Transaction on Aerospace and Electronic Systems, 2003, 39(1):335-343.
[9] 陶然, 邓兵, 王越. 分数阶傅里叶变换及其应用[M]. 北京: 清华大学出版社, 2009: 1-7.
TAO Ran, DENG Bing, WANG Yue. Fractional Fourier transform and its application[M]. Beijing: Tsinghua University Press, 2009:1-7. (in Chinese)
[10] 袁伟明, 王敏, 吴顺君. 对称三角线性调频连续波信号的检测与参数估计[J]. 电波科学学报, 2005,20(5): 594-597.
YUAN Wei-ming, WANG Min, WU Shun-jun. Detection and parameter estimation of symmetrical triangular linear frequency modulation continuous wave signal[J]. Chinese Journal of Radio Science, 2005,20(5):594-597. (in Chinese)
[11] Almeida L B. The fractional Fourier transform and time-frequency representations[J]. IEEE Transactions on Signal Processing, 1994, 42(11): 3084-3091.
[12] Ozaktas H M, Arikan O, Kutay M A, et al. Digital computation of the fractional Fourier transform[J]. IEEE Transactions on Signal Processing, 1996, 44(9):2141- 2150.
[13] Adhemar Bultheel, Héctor E, Martínez Sulbaran. Computation of the fractional Fourier transform[J]. Applied and Computational Harmonic Analysis, 2004, 16(3):182-202.
[14] 赵兴浩, 邓兵, 陶然. 分数阶傅立叶变换数值计算中的量纲归一化[J]. 北京理工大学学报, 2005,25(4): 360-364.
ZHAO Xing-hao, DENG Bing, TAO Ran. Dimensional normalization in the digital computation of the fractional Fourier transform[J]. Transactions of Beijing Institute of Technology, 2005,25(4): 360-364. (in Chinese)
[15] QI Lin, TAO Ran, ZHOU Si-yong, et al. Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform[J]. Science in China: Ser. F, Information Science, 2004, 47(2):184-198.
[16] 张贤达, 保铮. 非平稳信号分析与处理[M]. 北京: 国防工业出版社, 1998: 186-222.
ZHANG Xian-da, BAO Zheng. Non-stationary signal analysis and processing[M]. Beijing: National Defense Industry Press, 1998: 186-222. (in Chinese)
[17] Bernardo L M, Soates O D D. Fractional Fourier transforms and optical systems［J］. Optics Communication, 1994, 110(5-6):517-522.
[18] 齐林. 基于分数阶Fourier变换的线性调频信号的检测与处理[D]. 北京：北京理工大学, 2004.
QI Lin. Detection and processing of linear frequency modulation signals based on the fractional Fourier transform[D]. Beijing: Beijing Institute of Technology, 2004. (in Chinese)

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