大规模阵列Kronecker稳健波束形成器

doi:10.12305/j.issn.1001-506X.2024.06.03

系统工程与电子技术 ›› 2024, Vol. 46 ›› Issue (6): 1847-1854.doi: 10.12305/j.issn.1001-506X.2024.06.03

• 电子技术 • 上一篇

大规模阵列Kronecker稳健波束形成器

王德伍¹^,², 虞泓波²^,*, 袁耀辉², 廖胜男², 陈燕²

1. 北京理工大学信息与电子学院, 北京 100081
2. 北京无线电测量研究所, 北京 100854

收稿日期:2023-05-08 出版日期:2024-05-25 发布日期:2024-06-04
通讯作者: 虞泓波
作者简介:王德伍(1988—), 男, 高级工程师, 博士研究生, 主要研究方向为雷达系统总体设计、雷达信号处理与数据处理
虞泓波(1988—), 男, 高级工程师, 博士, 主要研究方向为雷达系统总体设计、阵列信号处理
袁耀辉(1995—), 男, 工程师, 硕士, 主要研究方向为雷达系统总体设计、电子对抗
廖胜男(1984—), 女, 高级工程师, 硕士, 主要研究方向为雷达系统总体设计、电子对抗
陈燕(1972—), 女, 研究员, 硕士, 主要研究方向为雷达系统总体设计

Kronecker robust adaptive beamformer for large array

Dewu WANG¹^,², Hongbo YU²^,*, Yaohui YUAN², Shengnan LIAO², Yan CHEN²

1. School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China
2. Beijing Institute of Radio Measurement, Beijing 100854, China

Received:2023-05-08 Online:2024-05-25 Published:2024-06-04
Contact: Hongbo YU

摘要/Abstract

摘要：

针对大规模阵列对样本需求量大、计算复杂度高的问题, 提出一种应用于大规模阵列的Kronecker自适应稳健波束形成器。首先, 将期望信号导向矢量分解成两个导向矢量的Kronecker乘积, 将原始导向矢量的失配问题转化为两个低维导向矢量的失配问题; 然后, 基于最坏情况性能最优原理建立双二次代价函数, 并利用双迭代算法求解该代价函数, 每次迭代过程只需求解两个低维的二阶锥规划问题。理论分析和仿真实验结果表明, 与传统全维稳健算法相比, 所提方法能够有效降低计算复杂度和样本需求量, 与现有的降维稳健算法相比, 由于具有更多自由度, 所提方法具有更高的输出信干噪比。

关键词: 大规模阵列, Kronecker积, 降维稳健波束形成器, 双迭代算法, 二阶锥规划

Abstract:

To solve the problems of the requirement of a large number of samples and high computational complexity for large array, a Kronecker robust adaptive beamformer is proposed in this paper. Firstly, the steering vector of the desired signal is decomposed into the Kronecker product of two low-dimension steering vectors, and the original steering vector mismatch problem is transformed into the corresponding two low-dimension steering vectors mismatch problem. Secondly, the bi-quadratic cost function is established based on the worst-case performance optimization principle, which is then solved by using the bi-iterative algorithm (BIA). Only two low-dimension second-order cone programming (SOCP) problems need to be solved in per iteration. Theoretic analysis and simulations results show that compared with the conventional full-dimension robust algorithms, the samples required and computational complexity are reduced efficiently in the proposed approach. In addition, the higher output signal to interference plus noise ratio (SINR) is obtained for the higher degrees of freedom (DoFs) compared with the existing reduced-dimension robust algorithms.

Key words: large array, Kronecker product, reduced-dimension robust beamformer, bi-iterative algorithm (BIA), second-order cone programming (SOCP)

中图分类号:

TN953

王德伍, 虞泓波, 袁耀辉, 廖胜男, 陈燕. 大规模阵列Kronecker稳健波束形成器[J]. 系统工程与电子技术, 2024, 46(6): 1847-1854.

Dewu WANG, Hongbo YU, Yaohui YUAN, Shengnan LIAO, Yan CHEN. Kronecker robust adaptive beamformer for large array[J]. Systems Engineering and Electronics, 2024, 46(6): 1847-1854.

图/表 5

参考文献 31

1	VAN TREES H L . Detection, estimation, and modulation theory, part iv: optimum array processing[M]. New York: Wiley, 2002.
2	VOROBYOV S A , GERSHMAN A B , LUO Z Q . Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem[J]. IEEE Trans.on Signal Processing, 2003, 51 (2): 313- 324. doi: 10.1109/TSP.2002.806865
3	LI J , STOICA P , WANG Z . On robust Capon beamforming and diagonal loading[J]. IEEE Trans.on Signal Processing, 2003, 51 (7): 1702- 1715. doi: 10.1109/TSP.2003.812831
4	VOROBYOV S A , CHEN H , GERSHMAN B . On the relationship between robust minimum variance beamformers with probabilistic and worst-case distortionless response of constraints[J]. IEEE Trans.on Signal Processing, 2008, 56 (11): 5719- 5724. doi: 10.1109/TSP.2008.929866
5	HASSANIEN A , VOROBYOV S A , WONG K M . Robust adaptive beamforming using sequential quadratic programming: an iterative solution to the mismatch problem[J]. IEEE Signal Processing Letters, 2008, (15): 733- 736.
6	KHABBAZIBASMENJ A , VOROBYOV S A , HASSANIEN A . Robust adaptive beamforming based on steering vector estimation with as little as possible prior information[J]. Proc.of the IEEE International Conference on Acoustics, Speech and Signal Processing, 2008,
7	GU Y , LESHEM A . Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation[J]. IEEE Trans.on Signal Processing, 2012, 60 (7): 3881- 3885. doi: 10.1109/TSP.2012.2194289
8	YANG H C , WANG P Y , YE Z F . Robust adaptive beamforming via covariance matrix reconstruction and interference power estimation[J]. IEEE Communications Letters, 2021, 25 (10): 3394- 3397. doi: 10.1109/LCOMM.2021.3103208
9	GONG C , HUANG L , XU D , et al. Knowledge-aided robust adaptive beamforming with small snapshots[J]. Electronics Letters, 2013, 49 (20): 1259- 1261. doi: 10.1049/el.2013.2447
10	YANG H C , WANG P Y , YE Z F . Robust adaptive beamforming via covariance matrix reconstruction and interference power estimation[J]. IEEE Communications Letters, 2021, 25 (10): 3394- 3397. doi: 10.1109/LCOMM.2021.3103208
11	吕岩, 曹菲, 杨剑, 等. 基于导向矢量双层估计和协方差矩阵重构的稳健波束形成算法[J]. 电子与信息学报, 2022, 44 (12): 4159- 4167. doi: 10.11999/JEIT211120
	LYU Y , CAO F , YANG J. , et al. Robust beamforming algorithm based on double-layer estimation of steering vector and covariance matrix reconstruction[J]. Journal of Electronics & Information Technology, 2022, 44 (12): 4159- 4167. doi: 10.11999/JEIT211120
12	张攀, 靖岗, 马腾. 期望信号稳健阻塞的协方差矩阵重构波束形成算法[J]. 系统工程与电子技术, 2020, 42 (7): 1464- 1470. doi: 10.3969/j.issn.1001-506X.2020.07.05
	ZHANG P , JING G , MA T . Covariance matrix reconstruction algorithm via desired signal robustly blocking for beamforming[J]. Systems Engineering and Electronics, 2020, 42 (7): 1464- 1470. doi: 10.3969/j.issn.1001-506X.2020.07.05
13	沈季, 万显荣, 易建新, 等. 复杂干扰场景下的稳健自适应波束形成[J]. 系统工程与电子技术, 2023, 45 (4): 941- 949. doi: 10.12305/j.issn.1001-506X.2023.04.01
	SHEN J , WAN X R , YI J X , et al. Robust adaptive beamforming in complex interference scenarios[J]. Systems Engineering and Electronics, 2023, 45 (4): 941- 949. doi: 10.12305/j.issn.1001-506X.2023.04.01
14	ZHANG X J , XIE H , FENG D Z , et al. Fast and robust adaptive beamforming algorithms for large-scale arrays with small samples[J]. Signal Processing, 2021, 188, 108223. doi: 10.1016/j.sigpro.2021.108223
15	SUN S C , YE Z F . Robust adaptive beamforming based on a method for steering vector estimation and interference covariance matrix reconstruction[J]. Proc.of the IEEE International Conference on Signal, Information and Data Processing, 2019,
16	FENG D Z , LI X M , LYU H . Two sided minimum-variance distortionless response beamformer for MIMO radar signal processing[J]. Signal Processing, 2009, 89 (3): 328- 332. doi: 10.1016/j.sigpro.2008.07.021
17	XIANG C , FENG D Z , LYU H , et al. Robust adaptive beamforming for MIMO radar[J]. Signal Processing, 2010, 90 (12): 3185- 3196. doi: 10.1016/j.sigpro.2010.05.022
18	ZHANG W , VOROBYOV S A . Joint robust transmit/receive adaptive beamforming for MIMO radar using probability-constrained optimization[J]. IEEE Signal Processing Letters, 2016, 23 (1): 112- 116. doi: 10.1109/LSP.2015.2504386
19	QIAN J , HE Z , ZHANG W , et al. Robust adaptive beamforming for multiple-input multiple-output radar with spatial filtering techniques[J]. Signal Processing, 2018, 143 (1): 152- 160.
20	YU H B , FENG D Z , NIE W K . Robust and fast beamforming with magnitude response constraints for multiple-input multiple-output radar[J]. IET Radar, Sonar and Navigation, 2016, 10 (3): 610- 616. doi: 10.1049/iet-rsn.2015.0384
21	ABRAMOVICH Y I , FRAZER G J , JOHNSON B A . Iterative adaptive kronecker MIMO radar beamformer: description and convergence analysis[J]. IEEE Trans.on Signal Processing, 2010, 58 (7): 3681- 3691. doi: 10.1109/TSP.2010.2046081
22	LASALLE J P . Stability theory for ordinary differential equations[J]. Journal of Differential Equations, 1968, 4 (1): 57- 65. doi: 10.1016/0022-0396(68)90048-X
23	LASALLE J P . The stability and control of discrete processes[M]. New York: Springer-Verlag, 1986.
24	HUANG Y W , VOROBYOV S A . An inner SOCP approximate algorithm for robust adaptive beamforming for general-rank signal model[J]. IEEE Signal Processing Letters, 2018, 25 (11): 1735- 1739.
25	SOMASUNDARAM S D. A framework for reduced dimension robust Capon beamforming[C]//Proc. of the IEEE Statistical Signal Processing Workshop, 2011: 425-428.
26	SOMASUNDARAM S D, PARSONS N H. Data-adaptive reduced-dimension robust Capon beamforming[C]//Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing, 2013.
27	SOMASUNDARAM S D , JAKOBSSON A , PARSONS N H . Robust and automatic data-adaptive beamforming for multi-dimensional arrays[J]. IEEE Trans.on Geoscience and Remote Sensing, 2012, 11 (50): 4642- 4656.
28	SOMASUNDARAM S D , PARSONS N H , LI P , et al. Reduced-dimension robust Capon beamforming using Krylov-subspace techniques[J]. IEEE Trans.on Aerospace and Electronic Systems, 2015, 51 (1): 270- 289. doi: 10.1109/TAES.2014.130485
29	虞泓波, 陈燕, 王琰. 降维MRC波束形成方法[C]//第十五届全国雷达学术年会, 2020: 1415-1420.
	YU H B, CHEN Y, WANG Y. A reduced-dimension MRC beamformer[C]//Proc. of the 15th National Radar Conference, 2020: 1415-1420.
30	李浩洋, 向建军, 彭芳, 等. 基于粒子群优化的波束空间广义旁瓣相消算法[J]. 系统工程与电子技术, 2022, 44 (10): 3037- 3045. doi: 10.12305/j.issn.1001-506X.2022.10.06
	LI H Y , XIANG J J , PENG F , et al. Beam space generalized sidelobe canceller algorithm based on particle swarm optimization[J]. Systems Engineering and Electronics, 2022, 44 (10): 3037- 3045. doi: 10.12305/j.issn.1001-506X.2022.10.06
31	GRANT M, BOYD S. CVX: Matlab software for disciplined convex programming[EB/OL]. [2023-06-22]. http://Stanford.edu/body/cvx.

算法	计算复杂度
F-Worst-Case	O(M⁶)
LSMI	O(M⁶)
本文方法	O(M³)
O-PoR-Spherical	O(M³)
RD-RCB	O(M³)

[1]	禹永植, 侯培迟, 陈涛, 张未坤. 多用户双向AF MIMO中继系统的联合预编码算法[J]. 系统工程与电子技术, 2020, 42(6): 1379-1385.
[2]	王旭东, 董文杰, 吴楠. 基于TDOA/AOA混合的高精度室内可见光定位算法[J]. 系统工程与电子技术, 2019, 41(10): 2371-2377.
[3]	黄中瑞, 牛朝阳, 张剑云. 基于序列锥规划的MIMO雷达正交连续相位编码波形设计[J]. 系统工程与电子技术, 2015, 37(9): 2000-2009.
[4]	陈阳，张艺朦，赵安邦，余赟，冯烨旻. 基于二阶锥规划的自适应均衡算法[J]. Journal of Systems Engineering and Electronics, 2011, 33(4): 904-907.
[5]	何学辉, 曾操, 苏涛, 吴顺君. 基于二阶锥规划的峰值旁瓣抑制滤波器设计[J]. Journal of Systems Engineering and Electronics, 2009, 31(11): 2567-2570 .

大规模阵列Kronecker稳健波束形成器

Kronecker robust adaptive beamformer for large array

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 5

参考文献 31

相关文章 5

编辑推荐

Metrics

本文评价