基于双向传播算子的互质面阵二维波达方向估计
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摘要
针对谱峰搜索的二维波达方向估计中现有算法复杂度高,精度受搜索间隔影响较大的问题,给出了一种双向传播算子的互质面阵二维波达方向估计算法,实现了俯仰角和方位角的低复杂、高精度、无模糊联合估计.该方法首先将互质阵列引入到二维波达方向估计中,构造互质平面阵模型,然后采用两次旋转不变传播算子方法计算出不同阵列流型方向上的旋转因子矩阵,根据旋转因子矩阵解算出目标信号的俯仰角和方位角,同时利用互质理论消除了稀疏阵列角度估计的不确定性,证明了互质阵列模型下采用双向传播算子方法进行俯仰角和方位角估计的无模糊性.对算法的复杂度进行理论分析,并给出了平面阵列角度估计的克拉美罗界推导.理论分析与仿真结果表明,算法不需要进行角度匹配和谱峰搜索,在相同条件下的均方根误差性能优于均匀平面阵的多重信号分类算法,并且以较低的复杂度无模糊的达到了高维网格搜索的精度.
In the existing two-dimensional direction-of-arrival(DOA) estimation algorithms based on spectral peak search,the complexity is high and the accuracy is greatly influenced by the search interval.To overcome these problems,this paper examines a two-dimensional DOA estimation with coprime rectangular array using bi-directional propagator method,which realizes a low complexity,high accuracy,unambiguous for 2-D estimation.Firstly,this algorithm introduces coprime array into 2-D DOA estimation,and constructs a coprime rectangular array model.The two rotation factor matrices along the different directions for propagator method can be got,the elevation angle and azimuth angle for the sources can be obtained from the rotation factor matrices.Further more,the multi values of sparse array are eliminated by using coprime theory,and the proof of unambiguous for two-dimensional DOA estimation under the coprime array model is provided.This paper also analyzes the complexity and gives the Cramer Rao lower bounds(CRB) of coprime rectangular array.Theoretical analysis and simulation results show that this algorithm does not need to angle matching and spectrum peak search,under the same conditions,the root mean square error(RMSE) performance is better than the multiple signal classification(MUSIC) algorithm of uniform rectangular array.At the same time,the proposed algorithm can reach the same accuracy of high dimensional grid search with low complexity and without ambiguity.
In the existing two-dimensional direction-of-arrival(DOA) estimation algorithms based on spectral peak search,the complexity is high and the accuracy is greatly influenced by the search interval.To overcome these problems,this paper examines a two-dimensional DOA estimation with coprime rectangular array using bi-directional propagator method,which realizes a low complexity,high accuracy,unambiguous for 2-D estimation.Firstly,this algorithm introduces coprime array into 2-D DOA estimation,and constructs a coprime rectangular array model.The two rotation factor matrices along the different directions for propagator method can be got,the elevation angle and azimuth angle for the sources can be obtained from the rotation factor matrices.Further more,the multi values of sparse array are eliminated by using coprime theory,and the proof of unambiguous for two-dimensional DOA estimation under the coprime array model is provided.This paper also analyzes the complexity and gives the Cramer Rao lower bounds(CRB) of coprime rectangular array.Theoretical analysis and simulation results show that this algorithm does not need to angle matching and spectrum peak search,under the same conditions,the root mean square error(RMSE) performance is better than the multiple signal classification(MUSIC) algorithm of uniform rectangular array.At the same time,the proposed algorithm can reach the same accuracy of high dimensional grid search with low complexity and without ambiguity.
引文
[1] Yan F,Jin M,Qiao X.Low-complexity DOA estimation based on compressed MUSIC and its performance analysis[J].IEEE Transactions on Signal Processing,2013,61(8):1915-1930.
[2] 陈广东,黄海行,陈智.电磁矢量传感器阵列相干和独立信号DOA估计[J].电子学报,2017,45(9):2296-2301.Chen Guang-dong,Huang Hai-xing,Chen Zhi.DOA estimation with arrays of electromagnetic vector sensors under the coexistence of both uncorrelated and coherent signals[J].Acta Electronica Sinica,2017,45(9):2296-2301.(in Chinese)
[3] Huang Q,Zhang G,Yong F.DOAestimation using block variational sparse Bayesian learning[J].Chinese Journal of Electronics,2017,26(4):768-772.
[4] Shi J,Hu G,Zhang X,et al.Sparsity-based two-dimensional DOA estimation for coprime array:from sum-differencecoarray viewpoint[J].IEEE Transactions on Signal Processing,2017,65(21):5591-5604.
[5] 田野,练秋生,徐鹤.基于稀疏信号重构的DOA和极化角度估计算法[J].电子学报,2016,44(7):1548-1554.Tian Ye,Lian Qiu-sheng,Xu He.DOA and polarization angle estimation algorithm based on sparse signal reconstruction[J].Acta Electronica Sinica,2016,44(7):1548-1554.(in Chinese)
[6] Qin S,Zhang Y D,Amin M G.Generalizedcoprime array configurations for direction-of-arrival estimation[J].IEEE Transactions on Signal Processing,2015,63(6):1377-1390.
[7] Cheng Z F,Zhao Y,Zhu Y T,et al.Sparse representation based two-dimensional direction-of-arrival estimation method with L-shaped array[J].Iet Radar Sonar & Navigation,2016,10(5):976-982.
[8] Gu J F,Zhu W P,Swamy M N S.Joint 2-D DOA estimation via sparse L-shaped array[J].IEEE Transactions on Signal Processing,2015,63(5):1171-1182.
[9] Cao M Y,Huang L,Qian C,et al.Underdetermined DOA estimation of quasi-stationary signals via Khatri-Rao structure for uniform circular array[J].Signal Processing,2015,106(C):41-48.
[10] Na W,Qu Z,Si W,et al.DOA and polarization estimation using an electromagnetic vector sensor uniform circular array based on the ESPRIT algorithm[J].Sensors,2016,16(12):2109-2129.
[11] Li J,Zhang X,Chen H.Improved two-dimensional DOA estimation algorithm for two-parallel uniform linear arrays using propagator method[J].Signal Processing,2012,92(12):3032-3038.
[12] Wu H,Hou C,Chen H,et al.Direction finding and mutual coupling estimation for uniform rectangular arrays[J].Signal Processing,2015,117(C):61-68.
[13] Wang Q,Zhu X,Chen H,et al.Computationally efficient direction finding for a mixture of circular and strictly noncircular sources with uniform rectangular arrays[J].Sensors,2017,17(6):1269-1291.
[14] He X,Zhang Z,Wang W.DOA estimation with uniform rectangular array in thepresence of mutual coupling[A].2016 2nd IEEE International Conference on Computer and Communications (ICCC)[C].Chengdu,China:IEEE,2016.1854-1859.
[15] Zhang W,Liu W,Wang J,et al.Computationally efficient 2-D DOA estimation for uniform rectangular arrays[J].Multidimensional Systems & Signal Processing,2014,25(4):847-857.
[16] Chen Y M,Lee J H,Yeh C C.Two-dimensional angle-of-arrival estimation for uniform planar arrays with sensor position errors[J].Radar & Signal Processing IEE Proceedings F,1993,140(1):37-42.
[17] Chen H,Hou C,Zhu W P,et al.ESPRIT-like two-dimensional direction finding for mixed circular and strictly noncircular sources based on joint diagonalization[J].Signal Processing,2017,141:48-56.
[18] Zhou M,Zhang X,Qiu X,et al.Two-dimensional DOA estimation for uniform rectangular array using reduced-dimension propagator method[J].International Journal of Antennas & Propagation,2014,2014(1):1-10.
[19] Zheng W,Zhang X,Zhai H.Generalized coprime planar array geometry for 2-D DOA estimation[J].IEEE Communications Letters,2017,21(5):1075-1078.
[20] Wu Q,Sun F,Lan P,et al.Two-dimensional direction-of-arrival estimation for co-prime planar arrays:a partial spectral search approach[J].Sensors,2016,16(14):5660-5670.
[21] Zoltowski M D,Wong K T.ESPRIT-based 2-D direction finding with a sparse uniform array of electromagnetic vector sensors[J].IEEE Transactions on Signal Processing,2000,48(8):2195-2204.
[22] Hu A,Lv T,Gao H,et al.An ESPRIT-based approach for 2-D localization of incoherently distributed sources in massive MIMO systems[J].IEEE Journal of Selected Topics in Signal Processing,2014,8(5):996-1011.
[23] Filik T,Tuncer T E.A fast and automatically paired 2-D direction-of-arrival estimation with and without estimating the mutual coupling coefficients[J].Radio Science,2016,45(3):1-14.
[24] 巴斌,刘国春,李韬,等.基于哈达玛积扩展子空间的到达时间和波达方向联合估计[J].物理学报,2015,64(7):078403-9.Ba Bin,Liu GuoChun,Li Tao,et al.Joint for time of arrival and direction of arrival estimation algorithm based on the subspace of extended hadamard product[J].Acta Physica Sinica,2015,64(7):78403-078403.(in Chinese)
[25] Stoica P,Nehorai A.MUSIC,maximum likelihood,and Cramer-Rao bound[J].IEEE Transactions on Acoustics Speech & Signal Processing,1989,37(5):720-741.
[2] 陈广东,黄海行,陈智.电磁矢量传感器阵列相干和独立信号DOA估计[J].电子学报,2017,45(9):2296-2301.Chen Guang-dong,Huang Hai-xing,Chen Zhi.DOA estimation with arrays of electromagnetic vector sensors under the coexistence of both uncorrelated and coherent signals[J].Acta Electronica Sinica,2017,45(9):2296-2301.(in Chinese)
[3] Huang Q,Zhang G,Yong F.DOAestimation using block variational sparse Bayesian learning[J].Chinese Journal of Electronics,2017,26(4):768-772.
[4] Shi J,Hu G,Zhang X,et al.Sparsity-based two-dimensional DOA estimation for coprime array:from sum-differencecoarray viewpoint[J].IEEE Transactions on Signal Processing,2017,65(21):5591-5604.
[5] 田野,练秋生,徐鹤.基于稀疏信号重构的DOA和极化角度估计算法[J].电子学报,2016,44(7):1548-1554.Tian Ye,Lian Qiu-sheng,Xu He.DOA and polarization angle estimation algorithm based on sparse signal reconstruction[J].Acta Electronica Sinica,2016,44(7):1548-1554.(in Chinese)
[6] Qin S,Zhang Y D,Amin M G.Generalizedcoprime array configurations for direction-of-arrival estimation[J].IEEE Transactions on Signal Processing,2015,63(6):1377-1390.
[7] Cheng Z F,Zhao Y,Zhu Y T,et al.Sparse representation based two-dimensional direction-of-arrival estimation method with L-shaped array[J].Iet Radar Sonar & Navigation,2016,10(5):976-982.
[8] Gu J F,Zhu W P,Swamy M N S.Joint 2-D DOA estimation via sparse L-shaped array[J].IEEE Transactions on Signal Processing,2015,63(5):1171-1182.
[9] Cao M Y,Huang L,Qian C,et al.Underdetermined DOA estimation of quasi-stationary signals via Khatri-Rao structure for uniform circular array[J].Signal Processing,2015,106(C):41-48.
[10] Na W,Qu Z,Si W,et al.DOA and polarization estimation using an electromagnetic vector sensor uniform circular array based on the ESPRIT algorithm[J].Sensors,2016,16(12):2109-2129.
[11] Li J,Zhang X,Chen H.Improved two-dimensional DOA estimation algorithm for two-parallel uniform linear arrays using propagator method[J].Signal Processing,2012,92(12):3032-3038.
[12] Wu H,Hou C,Chen H,et al.Direction finding and mutual coupling estimation for uniform rectangular arrays[J].Signal Processing,2015,117(C):61-68.
[13] Wang Q,Zhu X,Chen H,et al.Computationally efficient direction finding for a mixture of circular and strictly noncircular sources with uniform rectangular arrays[J].Sensors,2017,17(6):1269-1291.
[14] He X,Zhang Z,Wang W.DOA estimation with uniform rectangular array in thepresence of mutual coupling[A].2016 2nd IEEE International Conference on Computer and Communications (ICCC)[C].Chengdu,China:IEEE,2016.1854-1859.
[15] Zhang W,Liu W,Wang J,et al.Computationally efficient 2-D DOA estimation for uniform rectangular arrays[J].Multidimensional Systems & Signal Processing,2014,25(4):847-857.
[16] Chen Y M,Lee J H,Yeh C C.Two-dimensional angle-of-arrival estimation for uniform planar arrays with sensor position errors[J].Radar & Signal Processing IEE Proceedings F,1993,140(1):37-42.
[17] Chen H,Hou C,Zhu W P,et al.ESPRIT-like two-dimensional direction finding for mixed circular and strictly noncircular sources based on joint diagonalization[J].Signal Processing,2017,141:48-56.
[18] Zhou M,Zhang X,Qiu X,et al.Two-dimensional DOA estimation for uniform rectangular array using reduced-dimension propagator method[J].International Journal of Antennas & Propagation,2014,2014(1):1-10.
[19] Zheng W,Zhang X,Zhai H.Generalized coprime planar array geometry for 2-D DOA estimation[J].IEEE Communications Letters,2017,21(5):1075-1078.
[20] Wu Q,Sun F,Lan P,et al.Two-dimensional direction-of-arrival estimation for co-prime planar arrays:a partial spectral search approach[J].Sensors,2016,16(14):5660-5670.
[21] Zoltowski M D,Wong K T.ESPRIT-based 2-D direction finding with a sparse uniform array of electromagnetic vector sensors[J].IEEE Transactions on Signal Processing,2000,48(8):2195-2204.
[22] Hu A,Lv T,Gao H,et al.An ESPRIT-based approach for 2-D localization of incoherently distributed sources in massive MIMO systems[J].IEEE Journal of Selected Topics in Signal Processing,2014,8(5):996-1011.
[23] Filik T,Tuncer T E.A fast and automatically paired 2-D direction-of-arrival estimation with and without estimating the mutual coupling coefficients[J].Radio Science,2016,45(3):1-14.
[24] 巴斌,刘国春,李韬,等.基于哈达玛积扩展子空间的到达时间和波达方向联合估计[J].物理学报,2015,64(7):078403-9.Ba Bin,Liu GuoChun,Li Tao,et al.Joint for time of arrival and direction of arrival estimation algorithm based on the subspace of extended hadamard product[J].Acta Physica Sinica,2015,64(7):78403-078403.(in Chinese)
[25] Stoica P,Nehorai A.MUSIC,maximum likelihood,and Cramer-Rao bound[J].IEEE Transactions on Acoustics Speech & Signal Processing,1989,37(5):720-741.