利用FFT实现对LFM信号的快速稀疏分解
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摘要
针对传统稀疏分解算法致使冗余字典中原子数量巨大的缺陷,提出一种线性调频信号的快速稀疏分解算法。这种算法根据线性调频信号本身的特点构建冗余字典中的原子,构建了两个冗余字典,通过级联的方式,完成了线性调频信号的快速稀疏分解。通过分析,采用这种级联的方式使得总的原子数量远小于一个冗余字典中的原子数量。在利用第一个冗余字典进行稀疏分解时,该算法通过快速傅里叶变换寻找最大值在另一个冗余字典中同时得到最匹配的原子。实验结果证实这种算法比其他3种采用单一冗余字典的稀疏分解算法,不仅加快了稀疏分解速度,而且具有更好的收敛性。
This paper proposes a fast algorithm for sparse decomposition of linear FM(LFM)signal to solve the deficiency of traditional methods that there are a large number of atoms.The atoms in the overcomplete dictionary are structured based on linear FM signal,and fast sparse decomposition of LFM is completed by using combined dictionary.By analysis,the number of atoms in two over-complete dictionaries is much smaller than that in one over-complete dictionaries,and the most matched atom in another dictionary can be found with the use of searching the maximum based on fast Fourier transform.Simulation results show that the computational efficiency of the proposed method is better than that of three other algorithms using one over-completed dictionary,and the sparsity is better.
This paper proposes a fast algorithm for sparse decomposition of linear FM(LFM)signal to solve the deficiency of traditional methods that there are a large number of atoms.The atoms in the overcomplete dictionary are structured based on linear FM signal,and fast sparse decomposition of LFM is completed by using combined dictionary.By analysis,the number of atoms in two over-complete dictionaries is much smaller than that in one over-complete dictionaries,and the most matched atom in another dictionary can be found with the use of searching the maximum based on fast Fourier transform.Simulation results show that the computational efficiency of the proposed method is better than that of three other algorithms using one over-completed dictionary,and the sparsity is better.
引文
[1]Djurovic’M S.Parameter estimation of non-uniform sampled polynomial-phase signals using the HOCPF-WD[J].Signal Processing,2015,106(1):253-258.
[2]Ou G J,Yang S Z,Deng J X,et al.A refined estimator of multicomponent third-order polynomial phase signals[J].IEICETransactions on Communications,2016,E99-B(1):143-151.
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[5]Djukanovi’S,Djurovic’I.Aliasing detection and resolving in the estimation of polynomial-phase signal parameters[J].Signal Processing,2012,92(1):235-239.
[6]Guo Jinku,Zou Hongxing,Yang Xiaojun.Parameter estimation of multicomponent chirp signals via sparse representation[J].IEEE Transactions on Aerospace and Electronic Systems,2011,47(3):2261-2268.
[7]Djuric P M,Kay S M.Parameter estimation of chirp signals[J].IEEE Transaction on Signal Processing,1990,38(12):2118-2126.
[8]Yuan Weiming,Wang Min,Wu Shunjun.Algorithm for the detection and parameter estimation of multicomponent LFM signals[J].Journal of Electroniscs,2005,2(22):185-189.
[9]郭汉伟,王岩,杨风风,等.基于小波Radon变换检测线性调频信号[J].国防科技大学学报,2005,25(1):91-94.Guo Hanwei,Wang Yan,YANG Fengfeng,et al.Linear chirp signals detection by wavelet radon transform[J].Journal of National University of Defense Technology,2005,25(1):91-94.
[10]江宝安,万群.基于Gabor-Radon变换的低信噪比雷达LFM信号检测与估计[J].重庆邮电大学学报(自然科学版),2010,22(1):27-32.Jiang Baoan,Wan Qun.Radar LFM signal detection and estimation based on Gabor-radon transform in low SNR[J].Journal of Chongqing University of Posts and Telecommunications:Natural Science Edition,2010,22(1):27-32.
[11]王建英,吕雪,尹忠科,基于MP分解的宽带LFM信号参数估计[J].电波科学学报,2007,22(6):986-990.Wang Jianying,LüXue,Ying Zhongke.Parameter estimation of wideband LFM signals based on MP decomposition[J].Chinese Journal of Radio Science,2007,22(6):986-990.
[12]罗洁思,于德介,彭富强.基于多尺度线性调频基信号稀疏分解的多分量LFM信号检测[J].电子与信息学报,2009,31(11):2781-2785.Luo Jiesi,Yu Dejie,Peng Fuqiang.Multicomponent LFM signals detection based on multi-scale chirplet sparse signal decomposition[J].Journal of Electronics and Information Technology,2009,31(11):2781-2785.
[13]Mallat S,Zhang Z.Matching pursuits with time-frequency dictionaries[J].IEEE Trans Signal Processing,1993,41(12):3397-3415.
[14]Chen S,Donoho D,Saunders M.Atomic decomposition by basis pursuit[J].SIAM Journal on Scientific Computing,1999,20(1):33-61.
[15]吴怡之,刘文轩,基于GA的心电信号稀疏分解MP算法改进[J].计算机工程,2013,39(9):250-253.Wu Yizhi,Liu Wenxuan.Improvement of electrocardio signal sparse decomposition MP algorithm based on GA[J].Computer Engineering,2013,39(9):250-253.
[16]张静,方辉,王建英,等.基于GA和MP的信号稀疏分解算法的改进[J].计算机工程与应用,2008,44(29):79-81.Zhang Jing,Fang Hui,Wang Jianying,et al.Improved GA-based MP algorithm for signal sparse decomposition[J].Computer Engineering and Application,2008,44(29):79-81.
[17]韩宁,尚朝轩.基于粒子群优化的稀疏分解变尺度快速算法[J].系统工程与电子技术,2012,34(1):46-49.Han Ning,Shang Chaoxuan.Fast variable matrix algorithm for sparse decomposition based on PSO[J].Systems Engineering and Electronic,2012,34(1):46-49.
[18]王丽,冯燕,基于粒子群优化的图像稀疏分解算法研究[J].计算机仿真,2015,32(11):363-367.Wang Li,Feng Yan.Sparse decomposition of images based on particle swarm optimization[J].Computer Simulation,2015,32(11):363-367.
[19]Zhao Y,Wu Z,Yang Z,et al.A novel signal sparse decomposition based on modulation correlation partition[J].Neurocomputing,2016,171:736-743.
[20]张天骐,全盛荣,强幸子,等.基于多尺度Chirplet稀疏分解和Wigner-Ville变换的时频分析方法[J].电子与信息学报,2017,39(6):1333-1339.Zhang Tianqi,Quan Shengrong,Qiang Xingzi,et al.Time-frequency analysis method based on multi-scale chirplet time-frequency analysis method based on multi-scale chirplet sparse decomposition and wigner-Ville transform[J].Journal of Electronics&Information Technology,2017,39(6):1333-1339.
[21]于凤芹,董希林,曹家麟.匹配追逐算法中三参数Chirp原子及搜索方法[J].系统工程与电子技术,2005,27(10):1711-1713.Yu Fengqin,Dong Xilin,Cao Jialin.Three parameter chirp atoms and the searching method in matching pursuit[J].Systems Engineering and Electronics,2005,27(10):1711-1713.
[22]Yi Chen,Nasrabadi N M,Tran D.Sparse representation for target detection in hyper-spectral imagery[J].IEEE Journal of Selected Topics in Signal Processing,2011,5(3):629-640.
[23]胡国兵,徐立中,金明.基于NP准则的LFM信号盲处理结果可靠性检验[J].电子学报,2013,41(4):739-743.Hu Guobing,Xu Lizhong,Jin Ming.Reliability testing for blind processing results of LFM signals based on NP criterion[J].Acta Electronica Sinica 2013,41(4):739-743.
[24]邵君,尹忠科,王建英,等.信号稀疏分解中过完备原子库的集合划分[J].铁道学报,2006,28(1):68-71.Shao Jun,Yin Zhongke,Wang Jianying,et al.Set partitioning of the over-complete dictionary in sparse decomposition[J].Journal of The China Railway Society,2006,28(1):68-71.
[2]Ou G J,Yang S Z,Deng J X,et al.A refined estimator of multicomponent third-order polynomial phase signals[J].IEICETransactions on Communications,2016,E99-B(1):143-151.
[3]Djurovic’I,Djukanovic’S,Simeunovic’M,et al.An efficient joint estimation of wideband polynomial-phase signal parameters and direction-of-arrival in sensor array[J].EURASIP Journal on Advances in Signal Processing,2012,2012(43):1-19.
[4]Robby G,McKilliam I,Vaughan L,et al.The asymptotic properties of polynomial phase estimation by least[C]∥Acoustics,Speech and Signal Processing(ICASSP),2011IEEE International Conference on.[S.l]:IEEE,2011:3592-3595.
[5]Djukanovi’S,Djurovic’I.Aliasing detection and resolving in the estimation of polynomial-phase signal parameters[J].Signal Processing,2012,92(1):235-239.
[6]Guo Jinku,Zou Hongxing,Yang Xiaojun.Parameter estimation of multicomponent chirp signals via sparse representation[J].IEEE Transactions on Aerospace and Electronic Systems,2011,47(3):2261-2268.
[7]Djuric P M,Kay S M.Parameter estimation of chirp signals[J].IEEE Transaction on Signal Processing,1990,38(12):2118-2126.
[8]Yuan Weiming,Wang Min,Wu Shunjun.Algorithm for the detection and parameter estimation of multicomponent LFM signals[J].Journal of Electroniscs,2005,2(22):185-189.
[9]郭汉伟,王岩,杨风风,等.基于小波Radon变换检测线性调频信号[J].国防科技大学学报,2005,25(1):91-94.Guo Hanwei,Wang Yan,YANG Fengfeng,et al.Linear chirp signals detection by wavelet radon transform[J].Journal of National University of Defense Technology,2005,25(1):91-94.
[10]江宝安,万群.基于Gabor-Radon变换的低信噪比雷达LFM信号检测与估计[J].重庆邮电大学学报(自然科学版),2010,22(1):27-32.Jiang Baoan,Wan Qun.Radar LFM signal detection and estimation based on Gabor-radon transform in low SNR[J].Journal of Chongqing University of Posts and Telecommunications:Natural Science Edition,2010,22(1):27-32.
[11]王建英,吕雪,尹忠科,基于MP分解的宽带LFM信号参数估计[J].电波科学学报,2007,22(6):986-990.Wang Jianying,LüXue,Ying Zhongke.Parameter estimation of wideband LFM signals based on MP decomposition[J].Chinese Journal of Radio Science,2007,22(6):986-990.
[12]罗洁思,于德介,彭富强.基于多尺度线性调频基信号稀疏分解的多分量LFM信号检测[J].电子与信息学报,2009,31(11):2781-2785.Luo Jiesi,Yu Dejie,Peng Fuqiang.Multicomponent LFM signals detection based on multi-scale chirplet sparse signal decomposition[J].Journal of Electronics and Information Technology,2009,31(11):2781-2785.
[13]Mallat S,Zhang Z.Matching pursuits with time-frequency dictionaries[J].IEEE Trans Signal Processing,1993,41(12):3397-3415.
[14]Chen S,Donoho D,Saunders M.Atomic decomposition by basis pursuit[J].SIAM Journal on Scientific Computing,1999,20(1):33-61.
[15]吴怡之,刘文轩,基于GA的心电信号稀疏分解MP算法改进[J].计算机工程,2013,39(9):250-253.Wu Yizhi,Liu Wenxuan.Improvement of electrocardio signal sparse decomposition MP algorithm based on GA[J].Computer Engineering,2013,39(9):250-253.
[16]张静,方辉,王建英,等.基于GA和MP的信号稀疏分解算法的改进[J].计算机工程与应用,2008,44(29):79-81.Zhang Jing,Fang Hui,Wang Jianying,et al.Improved GA-based MP algorithm for signal sparse decomposition[J].Computer Engineering and Application,2008,44(29):79-81.
[17]韩宁,尚朝轩.基于粒子群优化的稀疏分解变尺度快速算法[J].系统工程与电子技术,2012,34(1):46-49.Han Ning,Shang Chaoxuan.Fast variable matrix algorithm for sparse decomposition based on PSO[J].Systems Engineering and Electronic,2012,34(1):46-49.
[18]王丽,冯燕,基于粒子群优化的图像稀疏分解算法研究[J].计算机仿真,2015,32(11):363-367.Wang Li,Feng Yan.Sparse decomposition of images based on particle swarm optimization[J].Computer Simulation,2015,32(11):363-367.
[19]Zhao Y,Wu Z,Yang Z,et al.A novel signal sparse decomposition based on modulation correlation partition[J].Neurocomputing,2016,171:736-743.
[20]张天骐,全盛荣,强幸子,等.基于多尺度Chirplet稀疏分解和Wigner-Ville变换的时频分析方法[J].电子与信息学报,2017,39(6):1333-1339.Zhang Tianqi,Quan Shengrong,Qiang Xingzi,et al.Time-frequency analysis method based on multi-scale chirplet time-frequency analysis method based on multi-scale chirplet sparse decomposition and wigner-Ville transform[J].Journal of Electronics&Information Technology,2017,39(6):1333-1339.
[21]于凤芹,董希林,曹家麟.匹配追逐算法中三参数Chirp原子及搜索方法[J].系统工程与电子技术,2005,27(10):1711-1713.Yu Fengqin,Dong Xilin,Cao Jialin.Three parameter chirp atoms and the searching method in matching pursuit[J].Systems Engineering and Electronics,2005,27(10):1711-1713.
[22]Yi Chen,Nasrabadi N M,Tran D.Sparse representation for target detection in hyper-spectral imagery[J].IEEE Journal of Selected Topics in Signal Processing,2011,5(3):629-640.
[23]胡国兵,徐立中,金明.基于NP准则的LFM信号盲处理结果可靠性检验[J].电子学报,2013,41(4):739-743.Hu Guobing,Xu Lizhong,Jin Ming.Reliability testing for blind processing results of LFM signals based on NP criterion[J].Acta Electronica Sinica 2013,41(4):739-743.
[24]邵君,尹忠科,王建英,等.信号稀疏分解中过完备原子库的集合划分[J].铁道学报,2006,28(1):68-71.Shao Jun,Yin Zhongke,Wang Jianying,et al.Set partitioning of the over-complete dictionary in sparse decomposition[J].Journal of The China Railway Society,2006,28(1):68-71.