Low-Complexity Phase Ambiguity Resolution DOA Estimation Algorithm for Composite Hierarchical Receiver Array Structure

CHEN Yiwen; DONG Yangze; CHEN Xiahua; LING Wenchang; XIONG Yiwen

doi:10.11999/JEIT260447

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CHEN Yiwen, DONG Yangze, CHEN Xiahua, LING Wenchang, XIONG Yiwen. Low-Complexity Phase Ambiguity Resolution DOA Estimation Algorithm for Composite Hierarchical Receiver Array Structure[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260447

Citation:

CHEN Yiwen, DONG Yangze, CHEN Xiahua, LING Wenchang, XIONG Yiwen. Low-Complexity Phase Ambiguity Resolution DOA Estimation Algorithm for Composite Hierarchical Receiver Array Structure[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260447

Citation:

CHEN Yiwen, DONG Yangze, CHEN Xiahua, LING Wenchang, XIONG Yiwen. Low-Complexity Phase Ambiguity Resolution DOA Estimation Algorithm for Composite Hierarchical Receiver Array Structure[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260447

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Low-Complexity Phase Ambiguity Resolution DOA Estimation Algorithm for Composite Hierarchical Receiver Array Structure

doi: 10.11999/JEIT260447 cstr: 32379.14.JEIT260447

Guangdong Provincial Laboratory of Southern Ocean Science and Engineering (Zhanjiang) Zhanjiang 524000, China

Funds: Item1, Item2, Item3

Accepted Date: 2026-06-24

Available Online: 2026-07-04

Abstract

Abstract

Objective Direction of Arrival (DOA) estimation is a key technique in sonar target localization. With the continuously increasing demand for high-precision direction estimation in complex environments, the number of array elements used for estimation is being scaled up. While the direction-finding accuracy and resolution are improved, a heavy computational burden is also imposed on conventional DOA estimation algorithms. To address this issue, a low-complexity composite hierarchical receiving array structure is constructed in this paper, and two rapidly phase ambiguity resolution methods are proposed: the composite hierarchical global nearest-neighbor matching (CHA-GNNM) and the composite hierarchical cross-correlation covariance merging (CHA-CCM). Methods The CHA-GNNM algorithm gets multiple candidate solution sets by exploiting the auto-covariance and cross-covariance relationships among the subarrays within each group. The true solution in each candidate set is identified according to nearest-neighbor matching and the consistency characteristics of the signal source. Then, the final DOA estimation is obtained through multilevel coherent combination. In this way, phase ambiguity resolution and angle matching are completed at a relatively low computational cost. However, since the correlation information among all array elements is not fully considered, some performance loss exists in the estimation results. To achieve better DOA estimation performance, the CHA-CCM adjusts the composite hierarchical structure into evenly partitioned groups, and these groups can be regarded as several large subarrays, and multiple large candidate solution sets can be obtained from the cross-correlation relationships among them. Then, the array elements in each group are divided into multiple small subarrays, and multiple small candidate solution sets are obtained by calculating the auto-covariance and cross-covariance relationships among the subarrays within each group. Furthermore, a rough solution is then determined through coprime clustering, and a more accurate initial DOA estimation is given by the small candidate solution sets. Finally, the pseudo-solutions in the large candidate solution sets are removed by the initial DOA estimation and an accurate DOA estimation is obtained. In this way, by combining a low-complexity covariance block-processing strategy, the high computational complexity is avoided and higher-accuracy direction estimation is achieved. Results and Discussions Simulation results show that, as the number of array elements increases, the two proposed algorithms significantly reduce the computational burden, and phase ambiguity is effectively eliminated through the special array construction (Fig.4). Among them, coarse direction estimation is achieved by the CHA-GNNM algorithm with a complexity reduction of nearly six orders of magnitude (Fig.6) relative to the conventional Root-MUSIC algorithm, and it is more suitable for scenarios that require high real-time performance. By contrast, with only a small increase in computational cost (Fig.6), the CHA-CCM algorithm attains DOA estimation performance close to the CRLB above a certain signal-to-noise ratio threshold (Fig.5), and a favorable balance is achieved between estimation accuracy and computational complexity. Conclusions To address the sharp increase in computational complexity caused by the increasing number of array elements, a composite hierarchical array structure for large-scale arrays is constructed in this paper. By hierarchically grouping the array elements, the structural characteristics of the hierarchical array are exploited, and a new implementation approach is provided for low-complexity direction finding. Based on the characteristics of the composite hierarchical array, two fast DOA estimation algorithms are proposed. In both algorithms, effective phase ambiguity resolution is achieved under low computational complexity by exploiting the inter-group differences of the array and the consistency of the observations of the same source across different groups, so that rapid direction estimation is accomplished. In the CHA-GNNM algorithm, the phase-difference relationships among subarrays in the composite hierarchical array are mainly utilized, and ambiguity resolution and angle matching are carried out in a relatively direct manner. This method is characterized by a relatively simple computational procedure, low implementation difficulty, and fast execution speed, and thus rapid target direction finding is achieved with high efficiency. However, since the cross-correlation information among all array elements is not fully exploited, and the statistical characteristics of the array are not sufficiently utilized, some performance degradation is incurred under complicated signal conditions. To further improve the estimation performance, the CHA-CCM algorithm is proposed. In this algorithm, the composite hierarchical array is adjusted to an evenly partitioned form. While the low-complexity advantage of the hierarchical structure is retained, cross-correlation information is further introduced at the group level, so that the intrinsic relationships among different groups are more fully utilized. In addition, the signal processing procedure is simplified in a targeted manner, and unnecessary computational steps are reduced. As a result, the robustness and accuracy of DOA estimation are improved while the computational complexity remains controllable. Compared with CHA-GNNM, a small amount of computational speed is sacrificed in CHA-CCM, and a more favorable balance between computational complexity and direction-finding performance is achieved. In summary, the proposed composite hierarchical structure and the two fast DOA estimation algorithms provide a new approach for efficient direction finding in large-scale arrays. CHA-GNNM is more suitable for applications with relatively real-time requirements, whereas CHA-CCM is more suitable for applications with higher demands on estimation accuracy and robustness. The proposed structure can achieve efficient phase ambiguity resolution and accurate target direction estimation, and it also has theoretical and practical value for engineering applications of large-scale array signal processing.
- DOA,
- Massive array,
- Computational complexity,
- Nearest neighbor matching

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References(23)

References

[1]	ETTER P C. Underwater Acoustic Modeling and Simulation[M]. 5th ed. Boca Raton: CRC Press, 2018: 257–259.
[2]	ZEKAVAT R and BUEHRER R M. Handbook of Position Location[M]. Hoboken: Wiley-IEEE Press, 2012: 320–356.
[3]	梁国龙, 滕远鑫, 王晋晋, 等. 一种适用于半互质阵的高精度波达方向估计方法[J]. 电子与信息学报, 2024, 46(8): 3228–3237. doi: 10.11999/JEIT231139. LIANG Guolong, TENG Yuanxin, WANG Jinjin, et al. A high precision direction of arrival estimation method applied to semi-coprime arrays[J]. Journal of Electronics & Information Technology, 2024, 46(8): 3228–3237. doi: 10.11999/JEIT231139.
[4]	范旭慧, 王宇翼, 王安义, 等. 鲁棒自适应稀疏阵列波束形成[J]. 电子与信息学报, 2026, 48(1): 202–211. doi: 10.11999/JEIT250952. FAN Xuhui, WANG Yuyi, WANG Anyi, et al. Robust adaptive beamforming for sparse arrays[J]. Journal of Electronics & Information Technology, 2026, 48(1): 202–211. doi: 10.11999/JEIT250952.
[5]	商志刚, 曲星昊, 马璐, 等. 水声通信定位一体化研究综述[J]. 声学学报, 2026, 51(2): 465–477. doi: 10.12395/0371-0025.2025322. SHANG Zhigang, QU Xinghao, MA Lu, et al. A review of research on underwater acoustic integrated communication and localization[J]. Acta Acustica, 2026, 51(2): 465–477. doi: 10.12395/0371-0025.2025322.
[6]	刘帅, 许媛媛, 闫锋刚, 等. 泰勒展开与交替投影最大似然结合的离网格DOA估计算法[J]. 电子与信息学报, 2024, 46(8): 3219–3227. doi: 10.11999/JEIT231376. LIU Shuai, XU Yuanyuan, YAN Fenggang, et al. Off-grid DOA estimation algorithm based on Taylor-expansion and alternating projection maximum likelihood[J]. Journal of Electronics & Information Technology, 2024, 46(8): 3219–3227. doi: 10.11999/JEIT231376.
[7]	高山, 章伟裕, 郭良浩, 等. 分步波束形成和反卷积联合的面阵波达方向估计方法[J]. 声学学报, 2026, 51(3): 878–890. doi: 10.12395/0371-0025.2024011. GAO Shan, ZHANG Weiyu, GUO Lianghao, et al. Direction of arrival estimation jointing two-stage beamforming and deconvolution for an area array[J]. Acta Acustica, 2026, 51(3): 878–890. doi: 10.12395/0371-0025.2024011.
[8]	JIAO Lulu, YANG Xinghai, QUAN Tianqi, et al. High-precision DOA estimation for underwater acoustic signals based on sparsity adaptation[J]. Frontiers in Marine Science, 2022, 9: 1022494. doi: 10.3389/fmars.2022.1022494.
[9]	CAO Renzheng, LIU Binyue, GAO Feifei, et al. A low-complex one-snapshot DOA estimation algorithm with massive ULA[J]. IEEE Communications Letters, 2017, 21(5): 1071–1074. doi: 10.1109/LCOMM.2017.2652442.
[10]	LI Baobao, ZHANG Xiaofei, LI Jianfeng, et al. DOA estimation of non-circular source for large uniform linear array with a single snapshot: Extended DFT method[J]. IEEE Communications Letters, 2021, 25(12): 3843–3847. doi: 10.1109/LCOMM.2021.3120211.
[11]	YANG Xiao, LIU Licheng, and WANG Yide. A new low complexity DOA estimation algorithm for massive MIMO systems[C]. 2016 IEEE International Conference on Consumer Electronics-China (ICCE-China), Guangzhou, China, 2016: 1–4. doi: 10.1109/ICCE-China.2016.7849735.
[12]	CHEN Yiwen, JIE Qijuan, ZHANG Yiqiao, et al. Two rapid power iterative DOA estimators for UAV emitter using massive/ultra-massive receive array[J]. Drones, 2023, 7(6): 361. doi: 10.3390/drones7060361.
[13]	CHEN Yiwen, ZHAN Xichao, SHU Feng, et al. Two low-complexity DOA estimators for massive/ultra-massive MIMO receive array[J]. IEEE Wireless Communications Letters, 2022, 11(11): 2385–2389. doi: 10.1109/LWC.2022.3204173.
[14]	CHUANG Shengfu, WU Wenrong, and LIU Yenting. High-resolution AoA estimation for hybrid antenna arrays[J]. IEEE Transactions on Antennas and Propagation, 2015, 63(7): 2955–2968. doi: 10.1109/TAP.2015.2426795.
[15]	SHU Feng, QIN Yaolu, LIU Tingting, et al. Low-complexity and high-resolution DOA estimation for hybrid analog and digital massive MIMO receive array[J]. IEEE Transactions on Communications, 2018, 66(6): 2487–2501. doi: 10.1109/TCOMM.2018.2805803.
[16]	ZHANG Ruoyu, SHIM B, and WU Wen. Direction-of-arrival estimation for large antenna arrays with hybrid analog and digital architectures[J]. IEEE Transactions on Signal Processing, 2022, 70: 72–88. doi: 10.1109/TSP.2021.3119768.
[17]	SHU Feng, SHI Baihua, CHEN Yiwen, et al. A new heterogeneous hybrid massive MIMO receiver with an intrinsic ability of removing phase ambiguity of DOA estimation via machine learning[J]. IEEE Transactions on Machine Learning in Communications and Networking, 2025, 3: 17–29. doi: 10.1109/TMLCN.2024.3506874.
[18]	HUANG Hongji, YANG Jie, HUANG Hao, et al. Deep learning for super-resolution channel estimation and DOA estimation based massive MIMO system[J]. IEEE Transactions on Vehicular Technology, 2018, 67(9): 8549–8560. doi: 10.1109/TVT.2018.2851783.
[19]	CHEN Yiwen, ZHENG Yuxiang, ZHANG Yiqiao, et al. Deep-learning-aided low-complexity DOA estimators for ultra-massive MIMO overlapped receive array[C]. 2023 IEEE 6th International Conference on Pattern Recognition and Artificial Intelligence (PRAI), Haikou, China, 2023: 1201–1205. doi: 10.1109/PRAI59366.2023.10332046.
[20]	HU Die, ZHANG Yonghao, HE Lianghua, et al. Low-complexity deep-learning-based DOA Estimation for hybrid massive MIMO systems with uniform circular arrays[J]. IEEE Wireless Communications Letters, 2020, 9(1): 83–86. doi: 10.1109/LWC.2019.2942595.
[21]	RAO B D and HARI K V S. Performance analysis of root-MUSIC[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989, 37(12): 1939–1949. doi: 10.1109/29.45540.
[22]	STOICA P and NEHORAI A. MUSIC, maximum likelihood, and Cramer-Rao bound[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1989, 37(5): 720–741. doi: 10.1109/29.17564.
[23]	HUNGER R and REPORT T. Floating Point Operations in Matrix-Vector Calculus[M]. München: Technische Universität München, 2007: 5–14.