阵列结构是影响波达方向估计性能的重要因素，大孔径、高自由度的阵列拥有更强的空间分辨能力。互质阵列采用稀疏布阵的结构可有效增加阵列孔径，并且通过差联合处理产生的虚拟阵元极大提升了阵列的自由度。相比传统均匀线性阵列，有效降低成本同时实现高精度的波达方向估计，具有一定的现实意义。因此本文基于现有互质阵的波达方向估计方法开展以下研究：

为了改善小快拍情况下基于虚拟连续阵元中的稀疏重构类算法性能，提出一种基于噪声预估计的基追踪去噪稀疏重构的波达方向角估计方法。采用空间平滑算法消除虚拟信号中相关信息的影响，通过对真实噪声的预先估计，增加波达方向角估计方法的先验信息，提升了算法的稳健性。仿真结果表明，所提方法在信源数大于阵元数下能有效进行DOA估计，增强了非信源角度区域的干扰抑制效果，在小快拍时具有良好的参数估计性能。

针对互质虚拟阵列中存在空洞位置这一问题，提出一种基于加权截断核范数的矩阵填充的波达方向角估计方法。利用截断核范数约束实现虚拟阵元的填充，相比基于核范数的矩阵填充算法具有更精确的参数估计性能，其次考虑到待填充矩阵中每行缺失阵元数各不相同，将加权处理的方法引入到矩阵填充的过程中，提高了算法的估计精度及收敛速率，完成精确填充的同时有效地估计出各信源的方向。仿真结果表明，所提方法收敛速度较快，波达方向估计精度较高，而且对邻近信源也有效。

Array structure is the primary factor affecting direction-of-arrival estimation performance, large array aperture and high degrees of freedom of array has better spatial resolution.  Co-prime array adopts a sparse array structure, which can effectively increase the array aperture, and the virtual array elements generated by the differential joint processing greatly improve the degrees of freedom of the array. Compared with the uniform linear array, the coprime array can obtain an array with a high degrees of freedom and a large aperture with a small number of array elements, which can effectively reduce the cost and achieve high-precision DOA estimation, which has certain practical significance. Therefore, this article is based on the existing co-prime array DOA estimation method to carry out the following research:

In order to improve the performance of sparse reconstruction algorithms based on virtual continuous array elements in the case of low snapshots, a sparse reconstruction DOA estimation method based on actual noise estimation and basis pursuit do-nosing is proposed. The spatial smoothing algorithm is used to effectively eliminates the influence of coherent information in the virtual signal. By pre-estimating the actual noise, the prior information of the DOA estimation method is added, and the robustness of the algorithm is improved. The simulation results show that the proposed method can effectively perform DOA estimation when the number of sources is greater than the number of array elements, enhance the interference suppression effect in non-source angle regions, and has good parameter estimation performance in the case of low snapshots.

Aiming at the problem of holes in virtual array, put forward a kind of based on weighted truncated nuclear norm of covariance matrix reconstruction for DOA estimation method. Using the truncated nuclear norm constraint to realize the completion of virtual array elements has more accurate parameter estimation performance than the matrix completion algorithm based on nuclear norm. Considering that the number of holes in each row of the matrix to be completed is different, the method of weighting processing is introduced into the process of matrix completing. The estimation accuracy and convergence rate of the algorithm are improved, and the direction of each source can be effectively estimated at the same time as the accurate completion is completed. The simulation results show that, the proposed method has a fast convergence speed, high DOA estimation accuracy, and can accurately distinguish the source direction with a small difference between adjacent angles.

[1] 王龙涛,姜宁,戎华.舰载一体化雷达电子对抗系统无源侦察引导效能研究[J].兵器装备工程学报,2018,39(03):15-19.

[2] 石艳.雷达电子对抗技术及其应用研究[J].数字通信世界,2021(11):83-85+88.4.

[3] 郭永宁,李燕龙.无人机无线电监测混合定位算法[J].桂林电子科技大学学报,2021,41(05):362-367.

[4] 丘晟宏.无线电监测与定位技术的分析[J].电子测试,2021(04):99-100+76.

[5] 彭迎标,杨尊先,林志贤,等.基于传声器阵列的改进的PHAT-GCC语音定位算法[J].电声技术,2013,37(02):62-65.

[6] 王杰,黄丽霞,张雪英.改进DSB方法的语音信号多声源定位[J].计算机工程与应用,2021,57(01):173-180.

[7] 伍光新,姚元,祁琳琳.雷达通信波形一体化发展综述[J].现代雷达,2021,43(09):37-45.

[8] 罗骞,金琦珺.智能汽车激光雷达感知技术现状与发展分析[J].科技与创新,2020(17):4-6+9.

[9] 李迎春,高红卫,余继周.智能雷达发展研究[J].现代雷达,2019,41(11):1-5.

[10] 陈西洋,张恒.一种弹载共形阵天线的设计[J].微波学报,2016,32(S1):165-166.

[11] 彭志清,姜兴,谢跃雷.球面共形阵数字波束发射阵列的实现研究[J].电视技术,2015,39(03):89-92+106.

[12] 陈客松. 稀布天线阵列的优化布阵技术研究[D].电子科技大学,2006.

[13] Vaidyanathan P P, Pal P. Sparse Sensing With Co-Pprime Samplers and Arrays.[J]. IEEE Transactions on Signal Processing, 2011.

[14] 周成伟. 互质阵列信号处理算法研究[D]. 浙江大学, 2018.

[15] Moffet A. Minimum-redundancy linear arrays[J]. IEEE Transactions on antennas and propagation, 1968, 16(2): 172-175..

[16] Vertatschitsch E, Haykin S. Nonredundant arrays[J]. Proceedings of the IEEE, 1986, 74(1): 217-217.

[17] Pal P, Vaidyanathan P P. Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom[J]. IEEE Transactions on Signal Processing, 2010, 58(8):4167-4181.

[18] Adhikari K, Buck J R. Detection performance of coprime sensor arrays[J]. The Journal of the Acoustical Society of America, 2013, 134(5): 4169-4169.

[19] Adhikari K, Buck J R. Extending coprime sensor arrays to achieve the peak side lobe height of a full uniform linear array[J]. EURASIP Journal on Advances in Signal Processing, 2014, 2014(148).

[20] Si Q, Zhang Y D, Amin M G. Generalized Coprime Array Configurations for Direction-of-Arrival Estimation[J].IEEE Transactions on Signal Processing,2015,63(6):1377-1390.

[21] Liu Y, Buck J R. Super-resolution DOA estimation using a coprime sensor array with the min processor[C]//2016 50th Asilomar Conference on Signals, Systems and Computers. IEEE, 2016: 944-948.

[22] Liu C L, Vaidyanathan P P. Maximally economic sparse arrays and cantor arrays[C]//2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). IEEE, 2017: 1-5.

[23] Bush D, Xiang N. n-tuple coprime sensor arrays[J]. 2017, 142(6): EL567-EL572.

[24] Li J , Zhang X. Direction of Arrival Estimation of Quasi-Stationary Signals Using Unfolded Coprime Array[J]. IEEE Access, 2017, 5(99):6538-6545.

[25] Adhikari K .Sparse Sensing with Semi-Coprime Arrays[J]. The Journal of the Acoustical Society of America, 2018, 143(3):1851-1851.

[26] Elbir A M .Two-Dimensional DOA Estimation via Shifted Sparse Arrays with Higher Degrees of Freedom[J]. Circuits, Systems, and Signal Processing, 2019, 38(12):5549-5575.

[27] F Sun, Gao B ,Peng L. Partial spectral search-based DOA estimation method for co-prime linear arrays[J]. Electronics Letters, 2015, 51(24):2053-2055.

[28] Zhou C, Gu Y, Song W Z, et al. Robust adaptive beamforming based on DOA support using decomposed coprime subarrays[C]//2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016: 2986-2990.

[29] Dong Z, Zhang Y, Zheng G, et al. Improved DOA estimation algorithm for co-prime linear arrays using root-MUSIC algorithm[J]. Electronics Letters, 2017, 53(18):1277-1279.

[30] Yang X P, Wu X C, Shuai L, et al. A fast and robust DOA estimation method based on JSVD for co-prime array[J]. IEEE Access, 2018, PP:1-1.

[31] Pal P, Vaidyanathan P P. Coprime sampling and the MUSIC algorithm[C]//2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE). IEEE, 2011: 289-294.

[32] Zhang Y D, Amin M G, Himed B. Sparsity-based DOA estimation using co-prime arrays[C]//2013 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2013: 3967-3971.

[33] Tan Z, Eldar Y C, Nehorai A. Direction of Arrival Estimation Using Co-Prime Arrays: A Super Resolution Viewpoint[J]. IEEE Transactions on Signal Processing, 2014, 62(21):5565-5576.

[34] Tan Z, Nehorai A. Sparse Direction of Arrival Estimation Using Co-Prime Arrays with Off-Grid Targets[J]. IEEE Signal Processing Letters, 2013, 21(1):26-29.

[35] Gu Y, Zhou C, Goodman N A, et al. Coprime array adaptive beamforming based on compressive sensing virtual array signal[C]//2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016: 2981-2985.

[36] Zhou C, Gu Y, Zhang Y D, et al. Compressive Sensing Based Coprime Array Direction-of-Arrival Estimation[J]. Iet Communications, 2017, 11(11):1719-1724.

[37] Zhou C, Zhou J. Direction-of-Arrival Estimation with Coarray ESPRIT for Coprime Array[J]. Sensors, 2017, 17(8):1779-.

[38] Shi Z, Zhou C, Gu Y, et al. Source Estimation Using Coprime Array: A Sparse Reconstruction Perspective[J]. IEEE Sensors Journal, 2017, 17(3):755-765.

[39] Yanhua Q, Yumin L, Jianyi L, et al. Underdetermined Wideband DOA Estimation for Off-Grid Sources with Coprime Array Using Sparse Bayesian Learning[J]. Sensors, 2018, 18(1):253.

[40] Liu C L, Vaidyanathan P P, Pal P. Coprime coarray interpolation for DOA estimation via nuclear norm minimization[C]//2016 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2016: 2639-2642.

[41] Hosseini M R, Sebt M A. Array Interpolation Using Covariance Matrix Completion of Minimum-Size Virtual Array[J]. IEEE Signal Processing Letters, 2017:1063-1067.

[42] Zhou C, Gu Y, 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.

[43] Zheng Z, Yang T, Wang W Q, et al. Robust Adaptive Beamforming via Coprime Coarray Interpolation[J]. Signal Processing, 2019, 169:107382.

[44] Zheng Z, Huang Y, Wang W Q, et al. Direction-of-Arrival Estimation of Coherent Signals via Coprime Array Interpolation[J]. IEEE Signal Processing Letters, 2020, 27(99):585-589.

[45] Yadav S K, George N V. Fast Direction-of-Arrival Estimation via Coarray Interpolation Based on Truncated Nuclear Norm Regularization[J]. Circuits and Systems II: Express Briefs, IEEE Transactions on, 2020, PP(99):1-1.

[46] Fu M, Zheng Z, Wang W Q, et al. Coarray interpolation for DOA estimation using coprime EMVS array[J]. IEEE Signal Processing Letters, 2021, 28: 548-552.

[47] 刘梦波,胡国平,师俊朋,等.基于时间反转的MIMO雷达实值MUSIC算法[J].现代雷达,2018,40(11):21-26.

[48] 刘寅生,段洪涛,范振雄,等.基于改进MUSIC算法的短波非规则天线阵列测向系统[J].北京邮电大学学报,2019,42(05):42-47.

[49] 王晓庆,陶荣辉,甘露.基于贪婪算法的高分辨信号源DOA估计[J].信号处理,2012,28(05):705-710.

[50] 杨鹏,闫飞,张胜辉,等.基于FOCUSS算法的稀疏阵列综合[J].电子科技大学学报,2014,43(02):203-206.

[51] Candes E J, Tao T. Near-optimal signal recovery from random projections: Universal encoding strategies?[J]. IEEE transactions on information theory, 2006, 52(12): 5406-5425.

[52] 刘寅. 基于稀疏信号重构的空间谱估计算法研究[D].西安电子科技大学,2012.

[53] EJ Candès. The restricted isometry property and its implications for compressed sensing[J]. Comptes Rendus Mathematique, 2008, 346(9–10):589-592.

[54] 盘敏容,蒋留兵,车俐,等.基于协方差矩阵重构的互质阵列DOA估计[J].雷达科学与技术,2020,18(01):1-6+13.

[55] Huang H, Miao Y, Gong Y, et al. Toeplitz matrix completion for direction finding using a modified nested linear array[C]//ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2019 4474-4478.

[56] 艾明.基于互质阵列虚拟空洞填补的DOA估计算法研究[D].南昌大学,2020.

[57] Hu, Yao, Zhang, et al. Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization[J]. IEEE Transactions on Pattern Analysis & Machine Intelligence, 2013, 35(9):2117-2130.