高自由度低互耦的广义二阶嵌套MIMO雷达DOA估计

doi:10.12305/j.issn.1001-506X.2021.10.15

Abstract

Abstract:

In view of low degree of freedom and high mutual coupling of traditional two-level nested array, this paper proposes a generalized two-level nested multiple input multiple output (MIMO) configuration with high degree of freedom and low mutual coupling, which is used for direction of arrival (DOA) estimation. Firstly, the traditional two-level nested array of the transmitting array and receiving array are introduced into the coprime extension factors to reduce mutual coupling and increase degree of freedom. Secondly, the close-form expressions of degree of freedom including the coprime expansion factors, the number of continuous virtual elements and the total number of virtual elements under the structures of "sum-difference co-array" are derived. Finally, for the discrete holes caused by the different coprime expansion factors, the virtual elements is filled at the discontinuous points and establishes the convex optimization model of reconstructing the equivalent received signal of the filling virtual array elements, and combining with multiple signal classification algorithm for DOA estimation. Simulation results demonstrate the rationality of the array structure and effectiveness of the algorithm.

Key words: direction of arrival (DOA) estimation, nested array, degree of freedom, mutual coupling, sum-difference co-array, atomic norm minimization

CLC Number:

TN953

Yule ZHANG, Guoping HU, Hao ZHOU, Shijie YUE, Feilong ZHAO. DOA estimation of generalized two-level nested MIMO radar with high degree of freedom and low mutual coupling[J]. Systems Engineering and Electronics, 2021, 43(10): 2819-2827.

Figures/Tables 12

Fig.1

Table 1

Fig.2

Table 2

Table 3

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

References 29

1	赵永波, 刘宏伟. MIMO雷达技术综述[J]. 数据采集与处理, 2018, 33 (3): 389- 399.
	ZHAO Y B , LIU H W . Overview on MIMO radar[J]. Journal of Data Acquisition and Processing, 2018, 33 (3): 389- 399.
2	LIU B B , ERCAN E K , ZHANG J Y , et al. Angle estimation in MIMO radar using a new sparse representation approach[J]. International Journal of Electronics, 2019, 106 (11): 1694- 1709. doi: 10.1080/00207217.2019.1608588
3	师俊朋, 文方青, 艾琳, 等. 空域色噪声背景下双基地MIMO雷达角度估计[J]. 系统工程与电子技术, 2021, 43 (6): 1477- 1485.
	SHI J P , WEN F Q , AI L , et al. Angle estimation for bistatic MIMO radar with spatially colored noise[J]. Systems Engineering and Electronics, 2021, 43 (6): 1477- 1485.
4	BOUDAHER E , AHMAD F , AMIN M G , et al. Mutual coupling effect and compensation in non-uniform arrays for direction-of-arrival estimation[J]. Digital Signal Processing, 2017, 61 (1): 3- 14.
5	SHI J P , HU G P , ZHANG X F , et al. Generalized nested array: Optimization for degrees of freedom and mutual coupling[J]. IEEE Communications Letters, 2018, 22 (6): 1208- 1211. doi: 10.1109/LCOMM.2018.2821672
6	MOFFET A . Minimum-redundancy linear arrays[J]. IEEE Trans.on Antennas and Propagation, 1968, 16 (3): 172- 175.
7	PAL P , VAIDYANATHAN P P . Nested arrays: a novel approach to array processing with enhanced degrees of freedom[J]. IEEE Trans.on Signal Processing, 2010, 58 (8): 4167- 4181. doi: 10.1109/TSP.2010.2049264
8	VAIDYANATHAN P P , PAL P . Sparse sensing with co-prime samplers and arrays[J]. IEEE Trans.on Signal Processing, 2011, 59 (2): 573- 586. doi: 10.1109/TSP.2010.2089682
9	CHEN C, VAIDYANATHAN P P. Minimum redundancy MIMO radars[C]//Proc. of the IEEE International Symposium on Circuits Systems (ISCAS), 2008: 45-48.
10	HUANG Y , LIAO G S , LI J , et al. Sum and difference coarray based MIMO radar array optimization with its application for DOA estimation[J]. Multidimensional System Signal Processing, 2017, 28 (4): 1183- 1202. doi: 10.1007/s11045-016-0387-2
11	LI J F , JIANG D F , ZHANG D F . DOA estimation based on combined unitary ESPRIT for coprime MIMO radar[J]. IEEE Communications Letters, 2017, 21 (1): 96- 99. doi: 10.1109/LCOMM.2016.2618789
12	BOUDAHER E , AHMAD F , AMIN M G . Sparsity-based direction finding of coherent and uncorrelated targets using active nonuniform arrays[J]. IEEE Signal Processing Letters, 2015, 22 (10): 1628- 1632. doi: 10.1109/LSP.2015.2417807
13	SHI J P , HU G P , ZHANG X F , et al. Generalized co-prime MIMO radar for DOA estimation with enhanced degrees of freedom[J]. IEEE Sensors Journal, 2018, 18 (3): 1203- 1212. doi: 10.1109/JSEN.2017.2782746
14	SHI J P , HU G P , ZHANG X F , et al. Symmetric Sum coarray based co-prime MIMO configuration for direction of arrival estimation[J]. International Journal of Electronics and Communication, 2018, 94 (1): 339- 347.
15	QIN S, ZHANG Y D, AMIN M G. DOA estimation of mixed coherent and uncorrelated signals exploiting a nested MIMO radar[C]//Proc. of the IEEE Benjamin Franklin Symposium on Microwave and Antenna Sub-systems for Radar, 2016.
16	ZHENG G M , TANG J . DOD and DOA estimation in bistatic MIMO radar for nested and coprime array with closed-form DOF[J]. International Journal of Electronics, 2016, 104 (5): 885- 897.
17	YANG M L , SUN L , YUAN X , et al. A new nested MIMO array with increased degrees of freedom and hole-free difference coarray[J]. IEEE Signal Processing Letters, 2018, 25 (1): 40- 44. doi: 10.1109/LSP.2017.2766294
18	ZHENG W , ZHANG X F , SHI J P . Sparse extension array geometry for DOA estimation with nested MIMO radar[J]. IEEE Access, 2017, 5, 9580- 9586. doi: 10.1109/ACCESS.2017.2710212
19	LIU Q G, WANG B H, LI X, et al. An optimizing nested MIMO array with hole-free difference coarray[C]//Electronic Information Technology and Computer Engineering, 2018
20	YANG M L , SUN L , YUAN X , et al. Improved nested array with hole-free DCA and more degrees of freedom[J]. Electro-nics Letters, 2016, 52 (25): 2068- 2070. doi: 10.1049/el.2016.3197
21	LIU C L , VAIDYANATHAN P P . Remarks on the spatial smoothing step in coarray MUSIC[J]. IEEE Signal Processing Letters, 2015, 22 (9): 1439- 1442.
22	孙兵, 阮怀林, 吴晨曦, 等. 基于Toeplitz协方差矩阵重构的互质阵列DOA估计方法[J]. 电子与信息学报, 2019, 41 (8): 1924- 1930.
	SUN B , RUAN H L , WU C X , et al. Direction of arrival estimation with coprime array based on toeplitz covariance matrix reconstruction[J]. Journal of Electronics and Information Technology, 2019, 41 (8): 1924- 1930.
23	王凌, 潘华, 赵维. 互耦效应下低复杂度的二维DOA估计算法[J]. 系统工程与电子技术, 2021, 43 (7): 1819- 1823.
	WANG L , PAN H , ZHAO W . Reduced-dimensional unitary ESPRIT algorithm for monostatic MIMO radar[J]. Systems Engineering and Electronics, 2021, 43 (7): 1819- 1823.
24	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 Y , CHEN B X , YANG M L , et al. High accuracy DOA estimation using separated nested array[J]. Systems Engineering and Electronics, 2015, 37 (2): 253- 258.
25	LIU C L, VAIDYANATHAN P P, PAL P. Coprime coarray interpolation for DOA estimation via nuclear norm minimization[C]//Proc. of the IEEE International Symposium on Circuits and Systems, 2016: 2639-2642.
26	艾明, 虞贵财, 王志强. 互质阵列空洞中内插虚拟阵元的DOA估计算法[J]. 南昌大学学报(工科版), 2019, 41 (4): 398- 403. doi: 10.3969/j.issn.1006-0456.2019.04.015
	AI M , YU G C , WANG Z Q . DOA estimation algorithm with interpolated array elements for coprime array holes[J]. Journal of Nanchang University(Engineering and Technology), 2019, 41 (4): 398- 403. doi: 10.3969/j.issn.1006-0456.2019.04.015
27	占成宏, 胡国平, 周豪, 等. 基于虚拟阵元内插的互质阵列目标DOD和DOA联合估计算法[J]. 系统工程与电子技术, 2020, 42 (7): 1455- 1463.
	ZHAN C H , HU G P , ZHOU H , et al. Joint DOD and DOA estimation algorithm for coprime array based on virtual array element interpolation[J]. Systems Engineering and Electro-nics, 2020, 42 (7): 1455- 1463.
28	ZHOU C W , GU Y J , FAN X , et al. Direction-of-arrival estimation for coprime array via virtual array interpolation[J]. IEEE Trans.on Signal Processing, 2018, 66 (22): 5956- 5971. doi: 10.1109/TSP.2018.2872012
29	李慧启, 李立春, 刘志鹏. 无网格压缩感知下结合傅里叶变换的FT-ANM算法[J]. 信息工程大学学报, 2018, 19 (4): 475- 479.
	LI H Q , LI L C , LIU Z P . FT-ANM algorithm combined with fourier transform in gridless compressive sensing[J]. Journal of Information Engineering University, 2018, 19 (4): 475- 479.

T	最优M₁, M₂, N₁, N₂	自由度2l+1
T=4k	M₁=M₂=N₁=N₂=T/4	(T⁴+8T³-64T+64)/64
T=4k+1	M₁=N₁=N₂=(T-1)/4, M₂=(T+3)/4	(T⁴+8T³+2T²-64T-11)/64
T=4k+2	M₁=N₁=(T-2)/4, M₂=N₂=(T+2)/4	(T⁴+8T³+8T²-32T+16)/64
T=4k+3	M₁=M₂=N₂=(T+1)/4, N₁=(T-3)/4	(T⁴+8T³+2T²-48T+21)/64

阵列结构	互质扩展因子α, β	Ω_t	Ω_r
传统二阶嵌套阵	α=1, β=1	0.531 2	0.531 2
广义二阶嵌套阵1	α=1, β=17	0.531 2	0
广义二阶嵌套阵2	α=2, β=17	0.388 4	0
广义二阶嵌套阵3	α=4, β=17	0.174 1	0

[1]	Jialei LIU, Jiazhi MA, Longfei SHI. DOA estimation algorithm based on fourth-order cumulant using virtual beam forming [J]. Systems Engineering and Electronics, 2022, 44(7): 2134-2142.
[2]	Zhiyu QU, Meng SUN, Huanyao DAI. Joint estimation algorithm of DOA and polarization information based on conformal array [J]. Systems Engineering and Electronics, 2022, 44(6): 1798-1804.
[3]	Juan WEI, Shian YAN, Fangli NING. DOA estimation method for coherent signals based on coprime array virtual array spatial smoothing [J]. Systems Engineering and Electronics, 2022, 44(4): 1069-1077.
[4]	Baohua FAN, Le ZUO, Yong TANG, Zehua HU. DOA estimation of multiple time-varying signals with expectation-maximization algorithm [J]. Systems Engineering and Electronics, 2022, 44(2): 420-426.
[5]	Tao CHEN, Lin SHI, Mengyu SHEN. Gridless DOA estimation algorithm based on M-FIPM [J]. Systems Engineering and Electronics, 2022, 44(2): 427-433.
[6]	Zhiyuan YOU, Guoping HU, Hao ZHOU. Bistatic nested MIMO radar based on redundant element optimization joint estimation method of target DOD and DOA [J]. Systems Engineering and Electronics, 2022, 44(12): 3696-3702.
[7]	Yili HU, Yongbo ZHAO, Sheng CHEN, Chenghu CAO. Blind polarization DOA estimation of parabolic conformal array based on interpolation fitting [J]. Systems Engineering and Electronics, 2021, 43(8): 2037-2044.
[8]	Ling WANG, Hua PAN, Wei ZHAO. Low complexity 2D-DOA estimation algorithm in the presence of mutual coupling [J]. Systems Engineering and Electronics, 2021, 43(7): 1819-1823.
[9]	Junpeng SHI, Fangqing WEN, Lin AI, Gong ZHANG, Zhenghui GONG. Angle estimation for bistatic MIMO radar with spatially colored noise [J]. Systems Engineering and Electronics, 2021, 43(6): 1477-1485.
[10]	Jian LU, Jian YANG, Bo HOU, Zhiyong YU, Guangbin LIU. Robust beamforming of nested array based on virtual elements signal reconstruction [J]. Systems Engineering and Electronics, 2021, 43(5): 1161-1168.
[11]	Zixin ZHANG, Guoping HU, Hao ZHOU, Chenghong ZHAN. Low elevation angle estimation algorithm for MIMO radar based on sparse reconstruction of cross-covariance [J]. Systems Engineering and Electronics, 2021, 43(5): 1218-1223.
[12]	Silei CAO, Weigui ZENG, Huiqi XU. Broadband DOA estimation method based on eigenvector space focusing [J]. Systems Engineering and Electronics, 2021, 43(2): 294-299.
[13]	Liyang QIAO, Zhongma CUI, Yunxiu YANG, Qin SHU. Estimation of targets' range, angle and unknown mutual coupling parameters for FDA-MIMO radar [J]. Systems Engineering and Electronics, 2021, 43(10): 2797-2802.
[14]	Juan SHI, Qunfei ZHANG, Linlin MAO, Wentao SHI. Wideband DOA estimation with deficient snapshots via joint sub-band atomic norm minimization [J]. Systems Engineering and Electronics, 2020, 42(4): 733-739.
[15]	Shanhong HE, Mengqian JI, Liangyu XIE, Jin FAN. Two-dimensional DOA estimation for multi-beam reflector antenna based on focal-plane field [J]. Systems Engineering and Electronics, 2020, 42(1): 23-29.

DOA estimation of generalized two-level nested MIMO radar with high degree of freedom and low mutual coupling

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 12

References 29

Related Articles 15

Recommended Articles

Metrics

Comments

广义二阶嵌套MIMO雷达DOA估计算法
步骤1 根据式(5)获取向量化的协方差矩阵r;
步骤2 在不连续点处填补0, 根据式(22)建立新的单快拍测量矢量r′;
步骤3 根据式(33), 求前向空间平滑协方差矩阵R_x;
步骤4 定义二值向量z, 求得二值矩阵Z;
步骤5 求解式(31)所示的凸优化问题, 得到重构的协方差矩阵${\rm{\bar R}}$_x;
步骤6 对${\rm{\bar R}}$_x进行特征值分解, 结合式(32)进行谱峰搜索, 得到目标角度。