内置频率对Duffing振子微弱二进制相移键控信号盲检测影响
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摘要
采用Duffing振子实现对微弱二进制相移键控(Binary Phase Shift Keying, BPSK)信号的盲检测时,Duffing系统输出的周期态和混沌态转换之间存在过渡带。针对这一问题,推导出过渡带时长和Duffing系统内置频率之间的关系表达式;指出内置频率越高,过渡带时间越短;仿真实验给出时间频率响应曲线。内置频率的提高,会降低系统检测微弱信号的灵敏度。针对这一问题,推导出周期态下Duffing系统输出幅度作为因变量、内置频率作为自变量的表达式;仿真实验给出幅频响应曲线。针对微弱BPSK信号盲检测,建立变尺度方法和检测阵列相结合的基于S变换提取Duffing系统输出幅度包络的微弱BPSK信号盲检测模型,仿真实验验证了模型方法的有效性。
There are transition zones in the transitions between the chaotic and periodic states while blindly detecting weak BPSK(binary phase shift keying) signal by using Dufffing oscillator. The relationship expression between transition zone time length and forcing frequency of Duffing system was deduced, and the conclusion that higher forcing frequency leads to shorter transition zone time length was drawn. The simulation experiment gave the time-frequency response curve. The detection sensitivity of Duffing system will lower with the increasing of forcing frequency. The equations of output amplitude as dependent variable and the internal frequency as argument were deduced while Duffing system was in periodic state. The simulation experiment gave the amplitude-frequency response curve. Finally, by using S transform to extract the envelope of Duffing system output, the blind detection model of weak BPSK signal with the scale transformation method combined and the detection array was built. The simulation experiment results show the efficiency of the blind detection model.
There are transition zones in the transitions between the chaotic and periodic states while blindly detecting weak BPSK(binary phase shift keying) signal by using Dufffing oscillator. The relationship expression between transition zone time length and forcing frequency of Duffing system was deduced, and the conclusion that higher forcing frequency leads to shorter transition zone time length was drawn. The simulation experiment gave the time-frequency response curve. The detection sensitivity of Duffing system will lower with the increasing of forcing frequency. The equations of output amplitude as dependent variable and the internal frequency as argument were deduced while Duffing system was in periodic state. The simulation experiment gave the amplitude-frequency response curve. Finally, by using S transform to extract the envelope of Duffing system output, the blind detection model of weak BPSK signal with the scale transformation method combined and the detection array was built. The simulation experiment results show the efficiency of the blind detection model.
引文
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[19] Jordan D W, Smith P. Nonlinear ordinary differential equations: problems and solutions[M]. UK:Oxford University Press, 2007.
[20] 赖志慧, 冷永刚, 孙建桥, 等. Duffing振子的变尺度微弱特征信号检测方法研究[J]. 物理学报, 2012, 61(5): 60-68.LAI Zhihui, LENG Yonggang, SUN Jianqiao, et al. Weak characteristic signal detection based on scale transformation of Duffing oscillator[J]. Acta Physica Sinica, 2012, 61(5): 60-68. (in Chinese)
[21] Zhao W L, Zhao J X, Huang Z Q, et al. Weak signal detection technology based on Holmes Duffing oscillator[J]. Procedia Engineering, 2012, 29: 1796-1802.
[22] 王慧武, 丛超. 一种基于Duffing系统的信号检测与参数估计新方法[J]. 电子学报, 2016, 44(6): 1450-1457.WANG Huiwu, CONG Chao. A new signal detection and estimation method by using Duffing system[J]. Acta Electronica Sinica, 2016, 44(6): 1450-1457. (in Chinese)
[23] 徐艳春. 基于混沌振子的微弱光电信号检测技术研究[D]. 哈尔滨: 哈尔滨工业大学, 2010.XU Yanchun. Study of weak photo-electric signal detection based on chaotic oscillator[D]. Harbin: Harbin Institute of Technology, 2010. (in Chinese)
[2] 吴涛, 狄旻珉, 黄国策. 联合频偏估计与循环矩的MPSK信号调制识别算法[J]. 仪表技术与传感器, 2014, 12: 102-104.WU Tao, DI Minmin, HUANG Guoce. Joint frequency offset estimation and cyclic moments MPSK signal modulation recognition algorithm[J]. Instrument Technique and Sensor, 2014, 12: 102-104. (in Chinese)
[3] D′Amico A A. Efficient maximum-likelihood based clock and phase estimators for OQPSK signals[J]. IEEE Transactions on Communications, 2015, 63(7): 2647-2657.
[4] 王婷婷, 龚晓峰. 基于星座图的PSK、QAM信号联合识别算法应用[J]. 计算机应用研究, 2015, 32(7): 2116-2118.WANG Tingting, GONG Xiaofeng. Application of joint signal recognition on PSK and QAM based on constellation[J]. Application Research of Computers, 2015, 32(7): 2116-2118. (in Chinese)
[5] Zhen Y F, Duan C W. The Application of stochastic resonance in parameter estimation for PSK signals[C]//Proceedings of IEEE International Conference on Communication Software and Networks, 2015: 166-172.
[6] 马腾跃. 多节点监测系统微弱信号检测算法研究[D]. 北京: 北京邮电大学, 2015.MA Tengyue. Research on detection method of weak signal in spectrum monitoring system[D]. Beijing: Beijing University of Posts and Telecommunications, 2015. (in Chinese)
[7] 靳晓艳, 周希元. 一种基于特定Duffing振子的MPSK信号调制识别算法[J]. 电子与信息学报, 2013, 35(8): 1882-1887.JIN Xiaoyan, ZHOU Xiyuan. A modulation classification algorithm for MPSK signals based on special Duffing oscillator[J]. Journal of Electronics & Information Technology, 2013, 35(8): 1882-1887. (in Chinese)
[8] 李月, 杨宝俊. 混沌振子系统(L-Y)与检测[M]. 北京: 科学出版社, 2007.LI Yue, YANG Baojun. Chaotic oscillator (L-Y) and detection[M]. Beijing: Science Press, 2007.(in Chinese)
[9] 吴彦华, 马庆力. Duffing振子微弱信号盲检测方法[J]. 系统工程与电子技术, 2017, 39(11): 2414-2421.WU Yanhua, MA Qingli. Blind detection method of weak signals with Duffing oscillator[J]. Systems Engineering and Electronics, 2017, 39(11): 2414-2421.(in Chinese)
[10] Huang Z L, Zhang J Z, Zhao T H, et al. Synchrosqueezing S-transform and its application in seismic spectral decomposition[J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(2): 817-825.
[11] 吴彦华. 改进的离散S变换快速算法与连续小波变换算法性能分析[J]. 信号处理, 2012, 28(7): 973-979.WU Yanhua. Compare of the performance between the improved discrete S transform fast algorithm and CWT[J]. Signal Processing, 2012, 28(7): 973-979. (in Chinese)
[12] Cai M X, Yang J P, Deng J. Bifurcations and chaos in duffing equation with damping and external excitations[J]. Acta Mathematicae Applicatae Sinica, 2014, 30(2): 483-504.
[13] Aghababa M P. A novel adaptive finite-time controller for synchronizing chaotic gyros with nonlinear inputs[J].Chinese Physics B, 2011, 20(9): 090505.
[14] 刘海波, 吴德伟, 金伟, 等. Duffing振子微弱信号检测方法研究[J]. 物理学报, 2013, 62(5): 34-39.LIU Haibo, WU Dewei, JIN Wei, et al. Study on weak signal detection method with Duffing oscillators[J]. Acta Physica Sinica, 2013, 62(5): 34-39. (in Chinese)
[15] 郑建华, 王基. 时间尺度函数法求解无阻尼达芬方程[J]. 力学季刊, 2013, 34(2): 256-261.ZHENG Jianhua, WANG Ji.Timescale function method to undamped Duffing equation[J]. Chinese Quarterly of Mechanics, 2013, 34(2): 256-261. (in Chinese)
[16] Guckenheimer J, Holmes P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields[M]. USA: Springer, 1983.
[17] Yagasaki K. Second-order averaging and chaos in quasiperiodically forced weakly nonlinear oscillators[J]. Physica D: Nonlinear Phenomena, 1990, 44(3): 445-458.
[18] 丛超, 李秀坤, 宋扬. 一种基于新型间歇混沌振子的舰船线谱检测方法[J]. 物理学报, 2014, 63(6): 064301.CONG Chao, LI Xiukun, SONG Yang. A method of detecting line spectrum of ship-radiated noise using a new intermittent chaotic oscillator[J]. Acta Physica Sinica, 2014, 63(6): 064301. (in Chinese)
[19] Jordan D W, Smith P. Nonlinear ordinary differential equations: problems and solutions[M]. UK:Oxford University Press, 2007.
[20] 赖志慧, 冷永刚, 孙建桥, 等. Duffing振子的变尺度微弱特征信号检测方法研究[J]. 物理学报, 2012, 61(5): 60-68.LAI Zhihui, LENG Yonggang, SUN Jianqiao, et al. Weak characteristic signal detection based on scale transformation of Duffing oscillator[J]. Acta Physica Sinica, 2012, 61(5): 60-68. (in Chinese)
[21] Zhao W L, Zhao J X, Huang Z Q, et al. Weak signal detection technology based on Holmes Duffing oscillator[J]. Procedia Engineering, 2012, 29: 1796-1802.
[22] 王慧武, 丛超. 一种基于Duffing系统的信号检测与参数估计新方法[J]. 电子学报, 2016, 44(6): 1450-1457.WANG Huiwu, CONG Chao. A new signal detection and estimation method by using Duffing system[J]. Acta Electronica Sinica, 2016, 44(6): 1450-1457. (in Chinese)
[23] 徐艳春. 基于混沌振子的微弱光电信号检测技术研究[D]. 哈尔滨: 哈尔滨工业大学, 2010.XU Yanchun. Study of weak photo-electric signal detection based on chaotic oscillator[D]. Harbin: Harbin Institute of Technology, 2010. (in Chinese)