Direction of Arrival Estimation with Coprime Array Based on Toeplitz Covariance Matrix Reconstruction
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摘要: 针对基于互质阵列的欠定DOA估计方法对于虚拟阵元非连续部分利用率不高的问题，该文提出一种基于Toeplitz协方差矩阵重构的DOA估计方法。首先，从互质阵列差联合阵的角度分析虚拟阵元分布特性，结合其与协方差矩阵中各元素得到的波程差存在对应关系，将协方差矩阵进行扩展得到一个数据缺失的高维协方差矩阵；然后，根据矩阵填充理论，用迹范数代替秩范数进行松弛，对缺失元素进行填充；最后，利用现有root-MUSIC方法进行DOA估计。理论分析和仿真结果表明，该方法提升了虚拟阵元的利用率，从而增加了虚拟孔径和可估计信号数，同时无需对角度域进行离散化处理，有效消除了模型失配的影响，并且避免了正则化参数选取问题，提高了估计精度和分辨率。Abstract: In order to improve the utilization of non-contiguous virtual array elements in the underdetermined DOA estimation of the coprime array, a DOA estimation method based on Toeplitz covariance matrix reconstruction is proposed. First, the virtual array element distribution characteristics of the matrix are analyzed from the perspective of the difference coarray. Additionally, according to the correspondence between the difference coarray and the wave path difference, the covariance matrix is extended to a Toeplitz array covariance matrix, of which some elements are zero. Then, the Toeplitz matrix is recovered to the full covariance matrix according to the low rank matrix completion theory. Finally, the root-MUSIC method is employed for the DOA estimation. Theoretical analysis and simulation results show that this method can increase the number of the resolvable signals by increasing the number of virtual array elements, eliminate the effect of the off-grid effect without discretization of the angle domain, and avoid regularization parameter selection. Therefore, the estimation accuracy and resolution are improved.
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Key words:
- Direction Of Arrival (DOA) /
- Coprime array /
- Difference coarray /
- Matrix reconstruction
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VAIDYANATHAN P P and PAL P. Sparse sensing with co-prime samplers and arrays[J]. IEEE Transactions on Signal Processing, 2011, 59(2): 573–586. doi: 10.1109/TSP.2010.2089682 LIU Chunlin and VAIDYANATHAN P P. Remarks on the spatial smoothing step in coarray MUSIC[J]. IEEE Signal Processing Letters, 2015, 22(9): 1438–1442. doi: 10.1109/LSP.2015.2409153 LIU Jing, ZHOU Weidong, HUANG Defeng, et al. Covariance matrix based fast smoothed sparse DOA estimation with partly calibrated array[J]. AEU International Journal of Electronics and Communications, 2018, 84: 8–12. doi: 10.1016/j.aeue.2017.10.026 ALQADAH H F and SCHOLNIK D P. Stable DOA estimation with sparse sensor arrays[C]. 2017 IEEE Radar Conference, Washington, USA, 2017: 803–808. 赵季红, 马兆恬, 曲桦, 等. 冲击噪声下基于矩阵预处理的稀疏重构DoA估计[J]. 电子与信息学报, 2018, 40(3): 670–675. doi: 10.11999/JEIT170371ZHAO Jihong, MA Zhaotian, QU Hua, et al. DoA estimation based on matrix preconditioning through sparse reconstruction in impulsive noise[J]. Journal of Electronics &Information Technology, 2018, 40(3): 670–675. doi: 10.11999/JEIT170371 蔡晶晶, 宗汝, 蔡辉. 基于空域平滑稀疏重构的DOA估计算法[J]. 电子与信息学报, 2016, 38(1): 168–173. doi: 10.11999/JEIT150538CAI Jingjing, ZONG Ru, and CAI Hui. DOA estimation via sparse representation of the smoothed array covariance matrix[J]. Journal of Electronics &Information Technology, 2016, 38(1): 168–173. doi: 10.11999/JEIT150538 LV Wanghan, WANG Huali, LIU Feng, et al. Wideband DOA estimation based on co-prime arrays with sub-Nyquist sampling[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2016, E99-A(9): 1717–1720. doi: 10.1587/transfun.E99.A.1717 SHEN Qing, CUI Wei, LIU Wei, et al. Underdetermined wideband DOA estimation of off-grid sources employing the difference co-array concept[J]. Signal Processing, 2017, 130: 299–304. doi: 10.1016/j.sigpro.2016.07.022 CAI Jingjing, LIU Wei, ZONG Ru, et al. Sparse array extension for non-circular signals with subspace and compressive sensing based DOA estimation methods[J]. Signal Processing, 2018, 145: 59–67. doi: 10.1016/j.sigpro.2017.11.012 CHI Yuejie, SCHARF L L, PEZESHKI A, et al. Sensitivity to basis mismatch in compressed sensing[J]. IEEE Transactions on Signal Processing, 2011, 59(5): 2182–2195. doi: 10.1109/TSP.2011.2112650 LI Yuanxin and CHI Yuejie. Compressive parameter estimation with multiple measurement vectors via structured low-rank covariance estimation[C]. 2014 IEEE Workshop on Statistical Signal Processing, Gold Coast, Australia, 2014: 384–387. RAMIREZ J and KROLIK J. Multiple source localization with moving co-prime arrays[C]. 2015 IEEE International Conference on Acoustics, Speech and Signal Processing, Brisbane, Australia, 2015: 2374–2378. BOUDAHER E, JIA Yong, AHMAD F, et al. Multi-frequency co-prime arrays for high-resolution direction-of-arrival estimation[J]. IEEE Transactions on Signal Processing, 2015, 63(14): 3797–3808. doi: 10.1109/TSP.2015.2432734 BOUDAHER E, AHMAD F, and AMIN M G. Sparsity-based extrapolation for direction-of-arrival estimation using co-prime arrays[C]. Proceedings of SPIE 9857, Compressive Sensing V: from Diverse Modalities to Big Data Analytics, Baltimore, USA, 2016: 98570M. 王洪雁, 房云飞, 裴炳南. 基于矩阵补全的二阶统计量重构DOA估计方法[J]. 电子与信息学报, 2018, 40(6): 1383–1389. doi: 10.11999/JEIT170826WANG Hongyan, FANG Yunfei, and PEI Bingnan. Matrix completion based second order statistic reconstruction DOA estimation method[J]. Journal of Electronics &Information Technology, 2018, 40(6): 1383–1389. doi: 10.11999/JEIT170826 CHEN Caihua, HE Bingsheng, and YUAN Xiaoming. Matrix completion via an alternating direction method[J]. IMA Journal of Numerical Analysis, 2012, 32(1): 227–245. doi: 10.1093/imanum/drq039 MA Shiqian, GOLDFARB D, and CHEN Lifeng. Fixed point and Bregman iterative methods for matrix rank minimization[J]. Mathematical Programming, 2011, 128(1/2): 321–353. doi: 10.1007/s10107-009-0306-5 LI Bo and PETROPULU A. Spectrum sharing between matrix completion based MIMO radars and a MIMO communication system[C]. 2015 IEEE International Conference on Acoustics, Speech and Signal Processing, Brisbane, Australia, 2015: 2444–2448. HU Yao, ZHANG Debing, YE Jieping, et al. Fast and accurate matrix completion via truncated nuclear norm regularization[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(9): 2117–2130. doi: 10.1109/TPAMI.2012.271 WU Xiaohuan, ZHU Weiping, and YAN Jun. A Toeplitz covariance matrix reconstruction approach for direction-of-arrival estimation[J]. IEEE Transactions on Vehicular Technology, 2017, 66(9): 8223–8237. doi: 10.1109/TVT.2017.2695226 LIU Zhangmeng, HUANG Zhitao, and ZHOU Yiyu. Sparsity-inducing direction finding for narrowband and wideband signals based on array covariance vectors[J]. IEEE Transactions on Wireless Communications, 2013, 12(8): 1–12. doi: 10.1109/TWC.2013.071113.121305 -
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