多维阵列张量模型的鲁棒波束成形方法

doi:10.12305/j.issn.1001-506X.2024.07.01

摘要/Abstract

摘要：

传统波束成形算法在应对维数较高的多维阵列时, 训练快拍数难以满足远大于信号维数这一要求, 从而导致波束成形器性能急剧下降。针对这一问题, 本文给出了多维阵列输出数据的张量模型, 基于多维阵列子维度的可分离性, 引入张量波束成形方法, 分析了其在训练快拍数需求上具有的优势。然后, 基于张量波束成形中子维度干扰协方差矩阵的模型, 通过直接估计干扰协方差矩阵实现了一种鲁棒张量波束成形方法。分析表明: 该方法可更好地应对非均匀杂波环境以及相干干扰, 并得到更高的输出信干噪比, 以给出的二维极化敏感阵列为例, 所提方法的训练快拍数需求为传统方法的1/3, 相干干扰下输出信干噪比提高了约2.5 dB, 仿真验证了分析的有效性。

关键词: 鲁棒波束成形, 张量波束成形, 多维阵列, 相干干扰

Abstract:

Traditional beamforming performance will significantly degrade with insufficient training samples on multi-dimensional arrays with much higher dimensions. In this paper, a tensor beamforming method that has advantages in the number of training snapshots required is introduced based on the proposed tensor model and the separability of sub-dimensions for multi-dimensional arrays. Then, for coherent interference, based on the model of the sub-dimension' s interference covariance matrix in tensor beamforming, a robust tensor beamforming method is proposed by directly estimating the interference covariance matrix. Analysis shows that the proposed method could overcome the non-homogeneous clutter environment and coherent interference and obtain a higher output signal-to-interference-noise ratio. Taking the given two-dimensional polarization-sensitive array as an example, the number of training snaps required by the proposed method is 1/3 of the traditional method, and the output signal-to-interference-to-noise ratio increases by about 2.5 dB under coherent interference scenario. The simulation results verify the effectiveness of the analysis.

Key words: robust beamforming, tensor beamforming, multi-dimensional array, coherent interference

中图分类号:

V243.2

毕权杨, 李旦, 张建秋. 多维阵列张量模型的鲁棒波束成形方法[J]. 系统工程与电子技术, 2024, 46(7): 2175-2183.

Quanyang BI, Dan LI, Jianqiu ZHANG. Robust beamforming method for multi-dimensional array tensor models[J]. Systems Engineering and Electronics, 2024, 46(7): 2175-2183.

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参考文献 28

1	KROLIK J L . The performance of matched-field beamformers with Mediterranean vertical array data[J]. IEEE Trans.on Signal Processing, 1996, 44 (10): 2605- 2611. doi: 10.1109/78.539043
2	GERSHMAN A B , TURCHIN V I , ZVEREV V A . Experimental results of localization of moving underwater signal by adaptive beamforming[J]. IEEE Trans.on Signal Processing, 1995, 43 (10): 2249- 2257. doi: 10.1109/78.469863
3	GODARA L C . Application of antenna arrays to mobile communications. Ⅱ. Beamforming and direction-of-arrival considerations[J]. Proceedings of the IEEE, 1997, 85 (8): 1195- 1245. doi: 10.1109/5.622504
4	CAPON J . High-resolution frequency-wavenumber spectrum analysis[J]. Proceedings of the IEEE, 1969, 57 (8): 1408- 1418. doi: 10.1109/PROC.1969.7278
5	VAN TREES H L . Optimum array processing: part IV of detection, estimation, and modulation theory[M]. New Jersey: John Wiley & Sons, 2004.
6	BOROSON D M . Sample size considerations for adaptive arrays[J]. IEEE Trans.on Aerospace and Electronic Systems, 1980, 16 (4): 446- 451.
7	GUO J Y , YANG H C , YE Z F . A novel robust adaptive beamforming algorithm based on subspace orthogonality and projection[J]. IEEE Sensors Journal, 2023, 11, 12076- 12083.
8	HUANG Y W , FU H , VOROBYOV S A , et al. Robust adaptive beamforming via worst-case SINR maximization with nonconvex uncertainty sets[J]. IEEE Trans.on Signal Processing, 2023, 71, 218- 232. doi: 10.1109/TSP.2023.3240312
9	LIU C , ZHEN J . Diagonal loading beamforming based on aquila optimizer[J]. IEEE Access, 2023, 11, 69091- 69100. doi: 10.1109/ACCESS.2023.3293403
10	MUHAMMAD M , LI M , ABBASI Q H , et al. Adaptive diago- nal loading technique to improve direction of arrival estimation accuracy for linear antenna array sensors[J]. IEEE Sensors Journal, 2022, 22 (11): 10986- 10994. doi: 10.1109/JSEN.2022.3168785
11	LI Z Z, CAO S L, ZENG W G, et al. Robust beamforming algorithm based on steering vector estimation and interference plus noise covariance matrix reconstruction[C]//Proc. of the IEEE Signal Processing: Algorithms, Architectures, Arrangements, and Applications, 2022: 24-27.
12	LIAO B , CHAN S C , TSUI K M . Recursive steering vector estimation and adaptive beamforming under uncertainties[J]. IEEE Trans.on Aerospace and Electronic Systems, 2013, 49 (1): 489- 501. doi: 10.1109/TAES.2013.6404116
13	LIAO B , TSUI K M , CHAN S C . Robust beamforming with magnitude response constraints using iterative second-order cone programming[J]. IEEE Trans.on Antennas and Propagation, 2011, 59 (9): 3477- 3482. doi: 10.1109/TAP.2011.2161445
14	ZHANG P , YANG Z , LIAO G , et al. An RCB-like steering vector estimation method based on interference matrix reduction[J]. IEEE Trans.on Aerospace and Electronic Systems, 2020, 57 (1): 636- 646.
15	ZHENG Z , YANG T , WANG W Q , et al. Robust adaptive beamforming via simplified interference power estimation[J]. IEEE Trans.on Aerospace and Electronic Systems, 2019, 55 (6): 3139- 3152. doi: 10.1109/TAES.2019.2899796
16	HAARDT M , ROEMER F , DEL G G . Higher-order SVD-based subspace estimation to improve the parameter estimation accuracy in multidimensional harmonic retrieval problems[J]. IEEE Trans.on Signal Processing, 2008, 56 (7): 3198- 3213. doi: 10.1109/TSP.2008.917929
17	BRIGUI F , BOIZARD M , GINOLHAC G , et al. New low-rank filters for MIMO-STAP based on an orthogonal tensorial decomposition[J]. IEEE Trans.on Aerospace and Electronic Systems, 2018, 54 (3): 1208- 1220. doi: 10.1109/TAES.2017.2776679
18	毕权杨, 李旦, 张建秋. 空时自适应处理张量波束成形器的外积合成法[J]. 航空学报, 2019, 40 (10): 158- 170.
	BI Q Y , LI D , ZHANG J Q . An outer product synthesis approach to tensor beamformer for space-time adaptive processing[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40 (10): 158- 170.
19	XIE D , PENG H P , LI L X , et al. Semi-tensor compressed sensing[J]. Digital Signal Processing, 2016, 58, 85- 92. doi: 10.1016/j.dsp.2016.07.003
20	QIAN C , FU X , SIDIROPOULOS N D , et al. Tensor-based channel estimation for dual-polarized massive MIMO systems[J]. IEEE Trans.on Signal Processing, 2018, 66 (24): 6390- 6403. doi: 10.1109/TSP.2018.2873506
21	GONG X F, LIN Q H. Spatially constrained parallel factor analysis for semi-blind beamforming[C]//Proc. of the IEEE 7th International Conference on Natural Computation, 2011, 1: 416-420.
22	MIRANDA R K, DA COSTA J P C L, ROEMER F, et al. Generalized sidelobe cancellers for multidimensional separable arrays[C]//Proc. of the IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2015: 193-196.
23	RIBEIRO L N, DE ALMEIDA A L F, MOTA J C M. Tensor beamforming for multilinear translation invariant arrays[C]// Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing, 2016: 2966-2970.
24	LIU L , XIE J , WANG L , et al. Robust tensor beamforming for polarization sensitive arrays[J]. Multidimensional Systems and Signal Processing, 2019, 30 (2): 727- 748. doi: 10.1007/s11045-018-0580-6
25	SHARMA R , COHEN I , BENESTY J . Adaptive and hybrid Kronecker product beamforming for far-field speech signals[J]. Speech Communication, 2020, 120, 42- 52. doi: 10.1016/j.specom.2020.04.001
26	虞翔, 李旦, 张建秋. 鲁棒成形极化敏感阵列波束的方法及极化估计[J]. 航空学报, 2017, 38 (6): 234- 241.
	YU X , LI D , ZHANG J Q . A robust beamformer with a pola-rization sensitive array and polarization estimation[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38 (6): 234- 241.
27	YANG L , MCKAY M R , COUILLET R . High-dimensional MVDR beamforming: optimized solutions based on spiked random matrix models[J]. IEEE Trans.on Signal Processing, 2018, 66 (7): 1933- 1947. doi: 10.1109/TSP.2018.2799183
28	MA N, GOH J T. Efficient method to determine diagonal loading value[C]//Proc. of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003, 5: V-341.

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