volume | PIER Journals

Abstract

Sparse arrays have been extensively investigated for their capability to enhance degrees of freedom (DOFs). However, conventional nested array configuration is susceptible to strong mutual coupling (MC), while its achievable uniform DOFs (uDOFs) remains limited. To address these challenges, this paper proposes two optimized hierarchical nested arrays, designated as OHNA-I and OHNA-II. OHNA-I reconstructs the spatial arrangement of subarrays through a hierarchical shifting operation, effectively extending the continuous segment of the difference co-array (DCA). Building on this, OHNA-II further optimizes the subarray geometry via sensor displacement, achieving a better balance between uDOF enhancement and MC suppression, thereby maintaining higher uDOFs while reducing inter-sensor coupling interference. Numerical simulation results demonstrate that, under the same number of physical sensors, the proposed structures - particularly OHNA-II - achieve a greater number of uDOFs than existing classical sparse arrays. Furthermore, in scenarios with strong MC, the proposed structure exhibits superior robustness and lower root mean square error (RMSE) in DOA estimation.

1. Ling, Yun, Huotao Gao, Sang Zhou, Lijuan Yang, and Fangyu Ren, "Robust sparse Bayesian learning-based off-grid DOA estimation method for vehicle localization," Sensors, Vol. 20, No. 1, 302, Jan. 2020.
doi:10.3390/s20010302 Google Scholar

2. Sun, Haochen, Yifan Liu, Ahmed Al-Tahmeesschi, Avishek Nag, Mohadeseh Soleimanpour, Berk Canberk, Huseyin Arslan, and Hamed Ahmadi, "Advancing 6G: Survey for explainable AI on communications and network slicing," IEEE Open Journal of The Communications Society, Vol. 6, 1372-1412, 2025.
doi:10.1109/ojcoms.2025.3534626 Google Scholar

3. Shi, Junpeng, Zai Yang, and Yongxiang Liu, "On parameter identifiability of diversity-smoothing-based MIMO radar," IEEE Transactions on Aerospace and Electronic Systems, Vol. 58, No. 3, 1660-1675, Jun. 2022.
doi:10.1109/taes.2021.3126370 Google Scholar

4. Moffet, A., "Minimum-redundancy linear arrays," IEEE Transactions on Antennas and Propagation, Vol. 16, No. 2, 172-175, Mar. 1968.
doi:10.1109/tap.1968.1139138 Google Scholar

5. Pal, Piya and P. P. Vaidyanathan, "Nested arrays: A novel approach to array processing with enhanced degrees of freedom," IEEE Transactions on Signal Processing, Vol. 58, No. 8, 4167-4181, Aug. 2010.
doi:10.1109/tsp.2010.2049264 Google Scholar

6. Vaidyanathan, Palghat P. and Piya Pal, "Sparse sensing with co-prime samplers and arrays," IEEE Transactions on Signal Processing, Vol. 59, No. 2, 573-586, Feb. 2011.
doi:10.1109/tsp.2010.2089682 Google Scholar

7. Qin, Si, Yimin D. Zhang, and Moeness G. Amin, "Generalized coprime array configurations for direction-of-arrival estimation," IEEE Transactions on Signal Processing, Vol. 63, No. 6, 1377-1390, Mar. 2015.
doi:10.1109/tsp.2015.2393838 Google Scholar

8. Raza, Ahsan, Wei Liu, and Qing Shen, "Thinned coprime array for second-order difference co-array generation with reduced mutual coupling," IEEE Transactions on Signal Processing, Vol. 67, No. 8, 2052-2065, Apr. 2019.
doi:10.1109/tsp.2019.2901380 Google Scholar

9. Zheng, Wang, Xiaofei Zhang, Yunfei Wang, Jinqing Shen, and Benoit Champagne, "Padded coprime arrays for improved DOA estimation: Exploiting hole representation and filling strategies," IEEE Transactions on Signal Processing, Vol. 68, 4597-4611, 2020.
doi:10.1109/tsp.2020.3013389 Google Scholar

10. Liu, Jianyan, Yanmei Zhang, Yilong Lu, Shiwei Ren, and Shan Cao, "Augmented nested arrays with enhanced DOF and reduced mutual coupling," IEEE Transactions on Signal Processing, Vol. 65, No. 21, 5549-5563, Nov. 2017.
doi:10.1109/tsp.2017.2736493 Google Scholar

11. Shaalan, Ahmed M. A., Jun Du, and Yan-Hui Tu, "Dilated nested arrays with more degrees of freedom (DOFs) and less mutual coupling --- Part I: The fundamental geometry," IEEE Transactions on Signal Processing, Vol. 70, 2518-2531, 2022.
doi:10.1109/tsp.2022.3174451 Google Scholar

12. Zhang, Yule, Guoping Hu, Hao Zhou, Juan Bai, Chenghong Zhan, and Shuhan Guo, "Hole-free nested array with three sub-ULAs for direction of arrival estimation," Sensors, Vol. 23, No. 11, 5214, 2023.
doi:10.3390/s23115214 Google Scholar

13. Wei, Shuang, Gencun Zhu, and Ying Su, "A novel sparse array configuration for direction of arrival estimation with increased uniform degrees of freedom and reduced mutual coupling," Sensors, Vol. 24, No. 3, 808, Jan. 2024.
doi:10.3390/s24030808 Google Scholar

14. Wandale, Steven and Koichi Ichige, "A generalized extended nested array design via maximum inter-element spacing criterion," IEEE Signal Processing Letters, Vol. 30, 31-35, 2023.
doi:10.1109/lsp.2023.3238912 Google Scholar

15. Wang, Xiuwen, Lei Zhao, and Yuan Jiang, "Super augmented nested arrays: A new sparse array for improved DOA estimation accuracy," IEEE Signal Processing Letters, Vol. 31, 26-30, 2024.
doi:10.1109/lsp.2023.3340599 Google Scholar

16. Friedlander, B. and A. J. Weiss, "Direction finding in the presence of mutual coupling," IEEE Transactions on Antennas and Propagation, Vol. 39, No. 3, 273-284, Mar. 1991.
doi:10.1109/8.76322 Google Scholar

17. Liu, Chun-Lin and P. P. Vaidyanathan, "Super nested arrays: Linear sparse arrays with reduced mutual coupling --- Part I: Fundamentals," IEEE Transactions on Signal Processing, Vol. 64, No. 15, 3997-4012, Aug. 2016.
doi:10.1109/tsp.2016.2558159 Google Scholar

18. Wang, Min, Xiaochuan Ma, Shefeng Yan, and Chengpeng Hao, "An autocalibration algorithm for uniform circular array with unknown mutual coupling," IEEE Antennas and Wireless Propagation Letters, Vol. 15, 12-15, 2015.
doi:10.1109/lawp.2015.2425423 Google Scholar

19. Chen, Hua, Hongguang Lin, Wei Liu, Qing Wang, Qing Shen, and Gang Wang, "Augmented multi-subarray dilated nested array with enhanced degrees of freedom and reduced mutual coupling," IEEE Transactions on Signal Processing, Vol. 72, 1387-1399, 2024.
doi:10.1109/tsp.2024.3374557 Google Scholar

20. Lai, Xin, Xiaofei Zhang, Wang Zheng, Jianfeng Li, and Fuhui Zhou, "Fragmented coprime arrays with optimal inter subarray spacing for DOA estimation: Increased DOF and reduced mutual coupling," Signal Processing, Vol. 215, 109273, Feb. 2024.
doi:10.1016/j.sigpro.2023.109273 Google Scholar

21. Qi, Chongying, Yongliang Wang, Yongshun Zhang, and Ying Han, "Spatial difference smoothing for DOA estimation of coherent signals," IEEE Signal Processing Letters, Vol. 12, No. 11, 800-802, Nov. 2005.
doi:10.1109/lsp.2005.856866 Google Scholar

Professor Guibao Wang

Dr. Keyi Yu

Dr. Xianghui Wang

Dr. Shuzhen Wang