Virtual interpolation unitary transformation 2D DOA estimation&nbsp;method for parallel coprime arrays

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Journal of Vibration and Shock ›› 2025, Vol. 44 ›› Issue (11) : 163-171.

VIBRATION THEORY AND INTERDISCIPLINARY RESEARCH

Virtual interpolation unitary transformation 2D DOA estimation method for parallel coprime arrays

WANG Xuhu*, SUN Gaoli, FENG Honghao, HE Jinsong

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Abstract

Aiming at the problem that existing two-dimensional direction of arrival (DOA) estimation methods do not fully utilize the array received information, which leads to degradation of estimation performance, a two-dimensional DOA estimation method for virtual array interpolation under parallel coprime arrays is proposed. This method interpolates the extended virtual array of parallel coprime array. Then, using the relationship between the covariance matrix of the interpolated virtual array and the virtual measurement, a problem of minimizing the equivalent virtual measurement vector is proposed. Finally, the interpolated virtual array covariance matrix is reconstructed with convex optimization toolbox, and the DOA estimation is carried out with combining unitary transformation and total least squares method. Simulation results and lake experiments show that the method makes full use of all the virtual elements in the non-uniform virtual array, improves the degree of freedom and estimation accuracy, and is effective.

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two-dimensional direction of arrival estimation / parallel coprime arrays / virtual array interpolation / unitary transformation

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WANG Xuhu, SUN Gaoli, FENG Honghao, HE Jinsong. Virtual interpolation unitary transformation 2D DOA estimation method for parallel coprime arrays[J]. Journal of Vibration and Shock, 2025, 44(11): 163-171

References

[1] 王伟东, 李向水, 李辉, 等. 非均匀噪声下基于稀疏重构的声矢量传感器阵列方位估计方法[J]. 振动与冲击, 2023, 42(13): 127-136.
WANG Wei-dong, LI Xiang-shui, LI Hui, et al. A method of DOA estimation of acoustic vector sensor array based on sparse reconstruction under non-uniform noiseel[J]. Journal of Vibration and Shock, 2023, 42(13): 127-136..
[2] 王绪虎, 白浩东, 张群飞, 等. 阵列互耦情况下基于稀疏贝叶斯学习的离网格DOA估计[J]. 振动与冲击, 2022, 41(17): 303-312.
WANG Xu-hu, BAI Hao-dong, ZHANG Qun-fei, et al. Off-grid DOA estimation based on sparse Bayesian learning under interaction among array elements[J]. Journal of Vibration and Shock, 2022, 41(17): 303-312.
[3] TIAN Y, QIN Y B, DONG Z Y, et al. DOA estimation of coherently distributed sources in massive MIMO systems with unknown mutual coupling[J]. Digital Signal Processing, 2021, 111(2): 102987-102994.
[4] MORADKHAN S, HOSSEINZADEH S, ZAKER R. Deep-learning based DOA estimation in the presence of multiplicative noise[J]. Wireless Personal Communications, 2022, 126(4): 3093-3101.
[5] CHEN Y H, YAN L F, HAN C. Millidegree-level direction-of-arrival (DOA) estimation and tracking for terahertz wireless communications[C]//Proceedings of 2020 17th Annual IEEE International Conference on Sensing, Communication, and Networking (SECON). Como, Italy: IEEE, 2020: 1-9.
[6] FU X W, CAO R Z, WEN F Q. A de-noising 2D-DOA estimation method for uniform rectangle array[J]. IEEE Communications Letters, 2018, 22(9): 1854-1857.
[7] ZHANG Z, GUO Y, HUANG Y Z, et al. A 2-D DOA estimation method with reduced complexity in unfolded coprime L-shaped array[J]. IEEE Systems Journal, 2021, 15(1): 407-410.
[8] 高晓峰, 栗苹, 李国林等. 基于互协方差的L型嵌套阵列二维波达方向估计[J]. 兵工学报, 2019, 40(06): 1207-1215.
GAO Xiao-feng, LI Ping, LI Guo-lin, et al. Two-dimensional direction-of-arrival estimation for L-shaped nested array based on cross-covariance matrix[J]. Acta Armamentarii, 2019, 40(06): 1207-1215.
[9] YUE Y X, ZHANG Z Y, ZHOU C W, et al. Closed-form two-dimensional DOA and polarization joint estimation using parallel non-collocated sparse COLD arrays[C]//2022 IEEE 12th Sensor Array and Multichannel Signal Processing Workshop (SAM). Trondheim, Norway: IEEE, 2022: 16-20.
[10] YIN Q Y, NEWCOMB R W, MUNJAL S, et al. Relation between the DOA matrix method and the ESPRIT method[C]//Proceedings of IEEE International Symposium on Circuits and Systems. New Orleans, USA: IEEE, 1990: 1561-1564.
[11] CHEN X Q, WANG C H, ZHANG X F. A real-valued 2D DOA estimation algorithm of noncircular signal via euler transformation and rotational invariance property[J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2018, 35(03): 47-58.
[12] DAI X R, ZHANG X F, WANG Y F. Extended DOA-Matrix method for DOA estimation via two parallel linear arrays[J]. IEEE Communications Letters, 2019, 23(11): 1981-1984.
[13] LI J, ZHAO J, DING Y H, et al. An improved co-prime parallel array with conjugate augmentation for 2-D DOA estimation[J]. IEEE Sensors Journal, 2021, 21(20): 23400-23411.
[14] LI X L, ZHANG W J, SHU T, et al. Two-dimensional direction finding with parallel nested arrays using DOA matrix method[J]. IEEE Sensors Letters, 2019, 3(7): 2475-1472.
[15] ZHANG X F, LAI X, ZHENG W, et al. Sparse array design for DOA estimation of non-circular signals: reduced co-array redundancy and increased DOF[J]. IEEE Sensors Journal, 2021, 21(24): 27928-27937.
[16] SUN F G, OUYANG S Q, LAN P, et al. Reduced dimensional 2-D DOA estimation via least partial search with automatic pairing for parallel co-prime arrays[C]// Proceedings of 2020 IEEE 11th Sensor Array and Multichannel Signal Processing Workshop (SAM). Hangzhou, China: IEEE, 2020: 1-5.
[17] CHEN T, SHI L, GUO L M. Sparse DOA estimation algorithm based on fourth-order cumulants vector exploiting restricted non-uniform linear array[J]. IEEE Access, 2019, 7: 9980-9988.
[18] DAI Z H, ZHANG L, WANG C, et al. Enhanced second-order off-grid DOA estimation method via sparse reconstruction based on extended coprime array under impulsive noise[J]. IEEE Transactions on Instrumentation and Measurement Tccess, 2024, 73: 1-17.
[19] ZHOU C W, GU Y J, FAN X, et al. Direction-of-arrival estimation for coprime array via virtual array interpolation[J]. IEEE Transactions on Signal Processing, 2018, 66(22): 5956-5971.
[20] 李建峰, 蒋德富, 沈明威. 基于平行嵌套阵互协方差的二维波达角联合估计算法[J]. 电子与信息学报, 2017, 39(03): 670-676.
LI Jian-feng, JIANG De-fu, SHEN Ming-wei. Joint two-dimensional direction of arrival estimation based on cross covariance matrix of parallel nested array[J]. Journal of Electronics & Information Technology, 2017, 39(03): 670-676.
[21] LIU S H，MAO Z H，ZHANG Y M， et al． Rank minimization based toeplitz reconstruction for DOA estimation using coprime array[J]. IEEE Communications Letters，2021, 25(7): 2265-2269.
[22] LI J F, HE Y, MA P H, et al. Direction of arrival estimation using sparse nested arrays with coprime displacement[J]. IEEE Sensors Journal, 2021, 21(4): 5282-5291.
[23] 李林, 余玉龙, 韩慧. 基于平行互质虚拟阵列的低复杂度二维DOA联合估计算法[J]. 电子与信息学报, 2021, 43(06): 1653-1658.
LI Li, YU Yu-long, HAN Hu. A low complexity two-demensional DOA joint estimation algorithm based on parallel coprime virtual array[J]. Journal of Electronics & Information Technology, 2021, 43(06): 1653-1658.
[24] SUN L. A novel displaced coprime parallel array for two-dimensional direction of arrival estimation[J]. International Journal of Electronics, 2022, 110(11): 2100-2116.
[25] 王绪虎, 田雨, 张群飞等. 基于互质阵列的近场源位置估计方法[J]. 兵工学报, 2023, 44(10): 3227-3236.
WANG Xu-hu, TIAN Yu, ZHANG Qun-fei, et al. Near-field source location estimation method based on coprime arrays[J]. Acta Armamentarii, 2023, 44(10): 3227-3236.