一种基于Khatri-Rao子空间的非均匀稀疏阵列
|
摘要
基于Khatri-Rao(K-R)子空间提出一种提升阵列自由度的非均匀阵列排布方式,即新型嵌套阵列。新型嵌套阵列由大小2个均匀线阵(ULA)构成,较大ULA的阵元间隔取决于较小ULA的阵列长度。相较于自由度为O N()的N阵元ULA,N个阵元的新型嵌套阵可通过在K-R子空间中得到阵元数为N2(/2+N-1)的虚拟ULA,将阵列自由度提升至O N2(),大大提高了分辨多信源的能力。同时由于阵元稀疏排布,N个阵元的新型嵌套阵的有效孔径大于N阵元ULA,使新型嵌套阵列分辨临近目标的能力优于ULA。在通过K-R子空间得到虚拟ULA的稀疏阵列流型中,新型嵌套阵列是自由度提升最大的方式之一,且在低信噪比和小快拍数情况下依然有较好性能。
A novel sparse linear array geometry,i.e.a new nested array,is proposed based on Khatri-Rao(K-R)subspace,which is capable of increasing the degrees of freedom(DOF)of arrays.The new nested array consists of two uniform linear arrays(ULA),where the spacing of larger ULA is determined by the array length of smaller one.Compared with a ULA providing DOF with sensors,a new nested array is able to increase the DOF to by obtaining a virtual ULA with sensors through K-R product in K-R subspace,and thus the increased DOF makes it possible to resolve more sources.In addition,the new nested array is a sparse array,and has longer aperture than that of ULA in equal number of sensors to bring agood ability to resolve nearby targets.The new nested array is one of the arrays,which have the largest DOF increased by K-R product,and the performance of the new nested array is good even under the condition of low SNR and small snapshots.
A novel sparse linear array geometry,i.e.a new nested array,is proposed based on Khatri-Rao(K-R)subspace,which is capable of increasing the degrees of freedom(DOF)of arrays.The new nested array consists of two uniform linear arrays(ULA),where the spacing of larger ULA is determined by the array length of smaller one.Compared with a ULA providing DOF with sensors,a new nested array is able to increase the DOF to by obtaining a virtual ULA with sensors through K-R product in K-R subspace,and thus the increased DOF makes it possible to resolve more sources.In addition,the new nested array is a sparse array,and has longer aperture than that of ULA in equal number of sensors to bring agood ability to resolve nearby targets.The new nested array is one of the arrays,which have the largest DOF increased by K-R product,and the performance of the new nested array is good even under the condition of low SNR and small snapshots.
引文
[1]Schmidt R O.Multiple Emitter Location and Signal Parameter Specetral Estimation[J].IEEE Trans on AP,198634(3):276-280.
[2]Roy R,Kailath T.ESPRIT-Estimation of Signal Parameters via Rotational in Variance Techniques[J].IEEE Trans on ASSP,1986,37(7):984-995.
[3]Pillai S U,Bar-Ness Y,Haber F.A New Approach to Array Geometry for Improved Spatial Spectrum Estimation[J].Proceedings of the IEEE,1985,73(10):1522-1524.
[4]Pillai S,Haber F.Statistical Analysis of a High Resolution Spatial Spectrum Estimator Utilizing an Augmented Covariance Matrix[J].IEEE Trans Acoust Speech Signal Process,1987,35(11):1517–1523.
[5]Abramovich Y I,Gray D A,Gorokhov A Y,et al.Positive-denite Toeplitz Completion in DOA Estimation for Non-Uniform Linear Antenna Arrays[C]//Proc.SSAP-96.1996:550-553.
[6]Chevalier P,Albera L,Ferreol L,et al.Comon.On the Virtual Array Concept for Higher Order Array Processing[J].IEEE Trans Signal Process,2005,53(4):1254-1271.
[7]张小飞,汪飞,徐大专.阵列信号处理的理论和应用[M].北京:国防工业出版社,2010.ZHANG Xiaofei,WANG Fei,XU Dazhuan.Theory and Application of Array Signal Processing[M].Beijing:National Defense Industry Press,2010.(in Chinese)
[8]Ma W K,Hsieh T H,Chi C Y.DOA Estimation of Quasi-Stationary Signals ViaKhatri-Rao Subspace[C]//ICASSP.2009:2165-2168.
[9]Ma W,Hsieh T,Chi C.DOA Estimation of Quasi-Stationary Signals with Less Sensors than Sources and Unknown Spatial Noise Covariance:A Khatri–Rao Subspace Approach[J].IEEE Trans on Signal Processing,2010,58(4):2168-2180.
[10]Pal P,Vaidyanathan P.Nested Arrays:A Novel Approach to Array Processing With Enhanced Degrees of Freedom[J].IEEE Transactions on Signal Processing,2010,58(4):4167-4181.
[11]LiShuang,He Wei,Yang Xu-guang,Bao Ming,Wang Ying-guan.Direction of Arrival Estimation of Quasi-Stationary Signals Using twoLevel Khatri-Rao Subspace and Four-Level Nested Array[J].Springer,J Cent South Univ,2014,21:2743-2750.
[12]王毅,陈伯孝,杨明磊,等.分布式nested阵列及其高精度DOA估计[J].系统工程与电子技术,2015,37(2):253-258.WANG Yi,CHEN Boxiao,YANG Minglei,et al.High Accuracy DOA Estimation Using Separated Nested Array[J].System Engineering and Electronics,2015,37(2):253-258.(in Chinese)
[13]张璐.最小冗余阵波束合成技术及应用[D].哈尔滨:哈尔滨工业大学,2009.ZHANG Lu.Beam Forming Technology and Its Applications in Minimum Redundancy Arrays[D].Harbin:Harbin Institute of Technology,2009.(in Chinese)
[14]Evans J E,Johnson J R,Sun D f.High Resolution Angular Spectrum Estimation Techniques for Terrain Scattering Analysis and Angle of Arrival Estimation[C]//Processing 1st ASSP Workshop Specteal Estimation.Hamilton,Ontario,1981:134-139.
[15]沈堤,童宁宁,郭艺夺,等.基于盲信号分离的波达方向估计[J].空军工程大学学报:自然科学版,2010,11(2):47-51.SHEN Di,TONG Ningning,GUO Yiduo,et al.DOA Estimation Method Based on Blind Signal Separation[J].Journal of Air Force Engineering University:Natural Science Edition,2010,11(2):47-51.(in Chinese)
[2]Roy R,Kailath T.ESPRIT-Estimation of Signal Parameters via Rotational in Variance Techniques[J].IEEE Trans on ASSP,1986,37(7):984-995.
[3]Pillai S U,Bar-Ness Y,Haber F.A New Approach to Array Geometry for Improved Spatial Spectrum Estimation[J].Proceedings of the IEEE,1985,73(10):1522-1524.
[4]Pillai S,Haber F.Statistical Analysis of a High Resolution Spatial Spectrum Estimator Utilizing an Augmented Covariance Matrix[J].IEEE Trans Acoust Speech Signal Process,1987,35(11):1517–1523.
[5]Abramovich Y I,Gray D A,Gorokhov A Y,et al.Positive-denite Toeplitz Completion in DOA Estimation for Non-Uniform Linear Antenna Arrays[C]//Proc.SSAP-96.1996:550-553.
[6]Chevalier P,Albera L,Ferreol L,et al.Comon.On the Virtual Array Concept for Higher Order Array Processing[J].IEEE Trans Signal Process,2005,53(4):1254-1271.
[7]张小飞,汪飞,徐大专.阵列信号处理的理论和应用[M].北京:国防工业出版社,2010.ZHANG Xiaofei,WANG Fei,XU Dazhuan.Theory and Application of Array Signal Processing[M].Beijing:National Defense Industry Press,2010.(in Chinese)
[8]Ma W K,Hsieh T H,Chi C Y.DOA Estimation of Quasi-Stationary Signals ViaKhatri-Rao Subspace[C]//ICASSP.2009:2165-2168.
[9]Ma W,Hsieh T,Chi C.DOA Estimation of Quasi-Stationary Signals with Less Sensors than Sources and Unknown Spatial Noise Covariance:A Khatri–Rao Subspace Approach[J].IEEE Trans on Signal Processing,2010,58(4):2168-2180.
[10]Pal P,Vaidyanathan P.Nested Arrays:A Novel Approach to Array Processing With Enhanced Degrees of Freedom[J].IEEE Transactions on Signal Processing,2010,58(4):4167-4181.
[11]LiShuang,He Wei,Yang Xu-guang,Bao Ming,Wang Ying-guan.Direction of Arrival Estimation of Quasi-Stationary Signals Using twoLevel Khatri-Rao Subspace and Four-Level Nested Array[J].Springer,J Cent South Univ,2014,21:2743-2750.
[12]王毅,陈伯孝,杨明磊,等.分布式nested阵列及其高精度DOA估计[J].系统工程与电子技术,2015,37(2):253-258.WANG Yi,CHEN Boxiao,YANG Minglei,et al.High Accuracy DOA Estimation Using Separated Nested Array[J].System Engineering and Electronics,2015,37(2):253-258.(in Chinese)
[13]张璐.最小冗余阵波束合成技术及应用[D].哈尔滨:哈尔滨工业大学,2009.ZHANG Lu.Beam Forming Technology and Its Applications in Minimum Redundancy Arrays[D].Harbin:Harbin Institute of Technology,2009.(in Chinese)
[14]Evans J E,Johnson J R,Sun D f.High Resolution Angular Spectrum Estimation Techniques for Terrain Scattering Analysis and Angle of Arrival Estimation[C]//Processing 1st ASSP Workshop Specteal Estimation.Hamilton,Ontario,1981:134-139.
[15]沈堤,童宁宁,郭艺夺,等.基于盲信号分离的波达方向估计[J].空军工程大学学报:自然科学版,2010,11(2):47-51.SHEN Di,TONG Ningning,GUO Yiduo,et al.DOA Estimation Method Based on Blind Signal Separation[J].Journal of Air Force Engineering University:Natural Science Edition,2010,11(2):47-51.(in Chinese)