基于互质阵列的信源数估计
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摘要
针对信号数大于物理阵元数情况下的信源数估计问题,提出一种基于互质阵列的信源数估计方法。首先利用互质阵列的特殊结构提高阵列自由度;然后估计阵列输出的向量化外积的概率密度函数的相关参数;最后利用得到的参数化概率模型的似然函数和最小描述长度(MDL)准则实现算法功能。仿真结果表明,本文方法在较低信噪比下对不相关的高斯信号的检测成功率仍可达到100%,检测性能优于其他算法。
To solve the problem of source detection in the case that the number of signals is larger than that of physical elements, a new method based on source number estimation of coprime array is proposed.First, the coprime array is used to exploit the degrees of freedom offered by the difference sets. Then, by applying the properties of the coprime array, the unknown parameters are estimated, which are critical to the probability density function of the vectorized outer-product of the array output. Finally, by using the likelihood function and MDL criterion of the parametric probability model, the function of the algorithm is realized. Simulation results show that the proposed method has good performance even at low signal-to-noise ratio when the number of snapshots is large enough.
To solve the problem of source detection in the case that the number of signals is larger than that of physical elements, a new method based on source number estimation of coprime array is proposed.First, the coprime array is used to exploit the degrees of freedom offered by the difference sets. Then, by applying the properties of the coprime array, the unknown parameters are estimated, which are critical to the probability density function of the vectorized outer-product of the array output. Finally, by using the likelihood function and MDL criterion of the parametric probability model, the function of the algorithm is realized. Simulation results show that the proposed method has good performance even at low signal-to-noise ratio when the number of snapshots is large enough.
引文
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[4]Huang L,Wu S,Li X.Reduced-rank MDL method for source enumeration in high-resolution array processing[J].IEEE Transactions on Signal Processing,2007,55(12):5658-5667.
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[11]毛维平,李国林,谢鑫,等.独立源与相干源并存的信源数估计[J].系统工程与电子技术,2014,36(3):422-428.Mao Wei-ping,Li Guo-lin,Xie Xin,et al.Source number estimation of coexisting uncorrelated and coherent sources[J].Systems Engineering and Electronics,2014,36(3):422-428.
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[17]张小飞,林新平,郑旺,等.互质阵中空间谱估计研究进展[J].南京航空航天大学学报,2017,49(5):636-644.Zhang Xiao-fei,Lin Xin-ping,Zheng Wang,et al.Research progress on spatial spectrum estimation based on coprime array[J].Journal of Nanjing University of Aeronautics&Astronautics,2017,49(5):636-644.
[18]Vaidyanathan P P,Pal P.Theory of sparse coprime sensing in multiple dimensions[J].IEEE Transactions on Signal Processing,2011,59(8):3592-3608.
[19]Shi Z,Zhou C,Gu Y,et al.Source estimation using coprime array:a sparse reconstruction perspective[J].IEEE Sensors Journal,2017,17(3):755-765.
[20]Liu C L,Vaidyanathan P P.Remarks on the spatial smoothing step in coarray MUSIC[J].IEEE Signal Processing Letters,2015,22(9):1438-1442.
[21]Jia T,Wang H,Shen X,et al.Direction of arrival estimation with co-prime arrays via compressed sensing methods[C]∥Oceans Conference,Shanghai,China,2016:1-5.
[22]Pal P,Vaidyanathan P P.Nested arrays:a novel approach to array processing with enhanced degrees of freedom[J].IEEE Transactions on Signal Processing,2010,58(8):4167-4181.
[23]Pal P,Vaidyanathan P P.Coprime sampling and the MUSIC algorithm[C]∥Digital Signal Processing and Signal Processing Education(DSP/SPE),Sedona,AZ,USA,2011:289-294.
[24]Chen W,Wong K M,Reilly J P.Detection of the number of signals:a predicted eigen-threshold approach[J].IEEE Transactions on Signal Processing,1991,39(5):1088-1098.
[25]Wu H T,Yang J F,Chen F K.Source number estimators using transformed Gerschgorin radii[J].IEEETransactions on Signal Processing,1995,43(6):1325-1333.
[2]Wax M,Kailath T.Detection of signals by information theoretic criteria[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1985,33(2):387-392.
[3]Fishler E,Messer H.On the use of order statistics for improved detection of signals by the MDL criterion[J].IEEE Transactions on Signal Processing,2000,48(8):2242-2247.
[4]Huang L,Wu S,Li X.Reduced-rank MDL method for source enumeration in high-resolution array processing[J].IEEE Transactions on Signal Processing,2007,55(12):5658-5667.
[5]Huang L,So H C.Source Enumeration via MDL criterion based on linear shrinkage estimation of noise subspace covariance matrix[J].IEEE Transactions on Signal Processing,2013,61(19):4806-4821.
[6]Wu H T,Yang J F,Chen F K.Source number estimators using transformed Gerschgorin radii[J].IEEE Transactions on Signal Processing,1995,43(6):1325-1333.
[7]谢纪岭,司锡才.基于协方差矩阵对角加载的信源数估计方法[J].系统工程与电子技术,2008,30(1):46-49.Xie Ji-ling,Si Xi-cai.Determining the number of sources based on diagonal loading to the covariance matrix[J].Systems Engineering and Electronics,2008,30(1):46-49.
[8]郭立民,冯凯.非均匀噪声下基于BOOTSTRAP和特征空间投影的信源数估计[J].吉林大学学报:工学版,2015,45(5):1724-1730.Guo Li-min,Feng kai.Source detection based on characteristic subspace projection and Bootstrap technique in nonuniform noise[J].Journal of jilin University(Engineering and technology Edition),2015,45(5):1724-1730.
[9]Shan T J,Paulraj A,Kailath T.On smoothed rank profile tests in eigenstructure methods for directionsof-arrival estimation[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1987,35(10):1377-1385.
[10]Williams R T,Prasad S,Mahalanabis A K,et al.An improved spatial smoothing technique for bearing estimation in a multipath environment[J].IEEETransactions on Acoustics,Speech,and Signal Processing,1988,36(4):425-432.
[11]毛维平,李国林,谢鑫,等.独立源与相干源并存的信源数估计[J].系统工程与电子技术,2014,36(3):422-428.Mao Wei-ping,Li Guo-lin,Xie Xin,et al.Source number estimation of coexisting uncorrelated and coherent sources[J].Systems Engineering and Electronics,2014,36(3):422-428.
[12]Wax M,Ziskind I.Detection of the number of coherent signals by the MDL principle[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1989,37(8):1190-1196.
[13]Wax M.Detection and localization of multiple sources via the stochastic signals model[J].IEEE Transactions on Signal Processing,1991,39(11):2450-2456.
[14]Wax M.Detection and localization of multiple sources in noise with unknown covariance[J].IEEE Transactions on Signal Processing,1992,40(1):245-249.
[15]Abramovich Y I,Spencer N K,Gorokhov A Y.Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays.I.Fully augmentable arrays[J].IEEE Transactions on Signal Processing,2001,49(5):959-971.
[16]Moffet A.Minimum-redundancy linear arrays[J].IEEE Transactions on Antennas&Propagation,2003,16(2):172-175.
[17]张小飞,林新平,郑旺,等.互质阵中空间谱估计研究进展[J].南京航空航天大学学报,2017,49(5):636-644.Zhang Xiao-fei,Lin Xin-ping,Zheng Wang,et al.Research progress on spatial spectrum estimation based on coprime array[J].Journal of Nanjing University of Aeronautics&Astronautics,2017,49(5):636-644.
[18]Vaidyanathan P P,Pal P.Theory of sparse coprime sensing in multiple dimensions[J].IEEE Transactions on Signal Processing,2011,59(8):3592-3608.
[19]Shi Z,Zhou C,Gu Y,et al.Source estimation using coprime array:a sparse reconstruction perspective[J].IEEE Sensors Journal,2017,17(3):755-765.
[20]Liu C L,Vaidyanathan P P.Remarks on the spatial smoothing step in coarray MUSIC[J].IEEE Signal Processing Letters,2015,22(9):1438-1442.
[21]Jia T,Wang H,Shen X,et al.Direction of arrival estimation with co-prime arrays via compressed sensing methods[C]∥Oceans Conference,Shanghai,China,2016:1-5.
[22]Pal P,Vaidyanathan P P.Nested arrays:a novel approach to array processing with enhanced degrees of freedom[J].IEEE Transactions on Signal Processing,2010,58(8):4167-4181.
[23]Pal P,Vaidyanathan P P.Coprime sampling and the MUSIC algorithm[C]∥Digital Signal Processing and Signal Processing Education(DSP/SPE),Sedona,AZ,USA,2011:289-294.
[24]Chen W,Wong K M,Reilly J P.Detection of the number of signals:a predicted eigen-threshold approach[J].IEEE Transactions on Signal Processing,1991,39(5):1088-1098.
[25]Wu H T,Yang J F,Chen F K.Source number estimators using transformed Gerschgorin radii[J].IEEETransactions on Signal Processing,1995,43(6):1325-1333.