A New Rotation Measurement-based Method for Array Gain-phase Errors Calibration
CHENG Feng①② GONG Ziping② ZHANG Chi② WAN Xianrong②
①(The State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, Luoyang 471003, China) ②(School of Electronic Information, Wuhan University, Wuhan 430072, China)
It is not easy to accurately measure the direction angles of calibration-source signals, which limits the precision of array active-calibration methods. On the other hand, passive-calibration methods are difficult to apply to the presence of large array errors, which severely limits their practical applications. This paper proposes a rotation measurement-based method to calibrate array gain-phase errors, which can achieve high calibration precision without measuring the direction angles of calibration-source signals. Using the known array-rotation angles, the maximum likelihood-based method is able to simultaneously estimate the array gain-phase errors, direction angles and complex amplitudes of calibration-source signals without ambiguity. Compared with accurately measuring the direction angles of calibration-source signals, accurately measuring the array-rotation angles is much easier to be accomplished with a special test turntable, thus the proposed method can achieve quite high calibration precision at a low cost. Some simulation tests demonstrate the effectiveness and generality of the proposed method.
The Director Foundation of The State Key Laboratory of CEMEE (CEMEE2014Z0101B), The National Natural Science Foundation of China (U1333106, 61331012, 61371197), The National Key R&D Plan (2016YFB0502403)
KRIM H and VIBERG M. Two decades of array signal processing research[J]. IEEE Signal Processing Magazine, 1996, 13(4): 67-94. doi: 10.1109/79.526899.
[2]
SWINDLEHURST A and KAILATH T. A performance analysis of subspace based method in the presence of model errors, part I: The MUSIC algorithm[J]. IEEE Transactions on Signal Processing, 1992, 40(7): 1758-1774. doi: 10.1109/ 78.143447.
[3]
FERRÉOL A, LARZABAL P, and VIBERG M. Statistical analysis of the MUSIC algorithm in the presence of modeling errors, taking into account the resolution probability[J]. IEEE Transactions on Signal Processing, 2010, 58(8): 4156-4166. doi: 10.1109/TSP.2010.2049263.
CAO Shenghong. Direction of arrival estimation algorithms in the presence of array error[D]. [Ph.D. dissertation], University of Science and Technology of China, 2014.
WANG Yongliang, CHEN Hui, PENG Yingning, et al. Spatial Spectrum Estimation Theory and Algorithms[M]. Beijing: Tsinghua University Press, 2004: 415-465.
[7]
TUNCER E and FRIEDLANDER B. Classical and Modern Direction-of-Arrival Estimation[M]. Burlington, MA: Academic, 2009: 93-124.
[8]
刘书. 波达方向估计中阵列误差联合校正算法研究[D]. [硕士论文], 重庆大学, 2015.
LIU Shu. The research of joint calibration algorithms in DOA estimation[D]. [Master dissertation], Chongqing University, 2015.
[9]
张驰. 传感器阵列幅相误差校正方法研究[D]. [硕士论文], 武汉大学, 2015.
ZHANG Chi. Research on sensor array calibration techniques of amplitude and phase error[D]. [Master dissertation], Wuhan University, 2015.
[10]
NG B C and SEE C M S. Sensor-array calibration using a maximum likelihood approach[J]. IEEE Transactions on Antennas and Propagation, 1996, 44(6): 827-835. doi: 10.1109 /8.509886.
[11]
STAVROPOULOS K V and MANIKAS A. Array calibration in the presence of unknown sensor characteristics and mutual coupling[C]. Proceedings of the European Signal Processing Conference, Tampere, Finland, 2000, 3: 1417-1420.
WANG Ding and WU Ying. The multiplicative array errors calibration algorithms in the presence of multipath[J]. Scientia Sinica Informationis, 2015, 45(2): 270-288. doi: 10.1360/N112013-00060.
ZHANG Ke, CHENG Juming, and FU Jin. Fast active error calibration algorithm for array channel uncertainty[J]. Journal of Electronics & Information Technology, 2015, 37(9): 2110-2116. doi: 10.11999/JEIT141651.
WANG Min, MA Xiaochuan, YAN Shefeng, et al. New calibration method for array gain and phase errors with signal sources[J]. Journal of Signal Processsing, 2015, 31(11): 1389-1395. doi: 10.3969/j.issn.1003-0530.2015.11.001.
[15]
LI Qiong, GAN Long, and YE Zhongfu. An overview of self- calibration in sensor array processing[C]. 6th International Symposium on Antennas, Propagation and the EM Theory Proceedings, Beijing, 2003: 279-282. doi: 10.1109/ISAPE. 2003.1276682.
[16]
FRIEDLANDER B and WEISS A J. Direction finding in the presence of mutual coupling[J]. IEEE Transactions on Antennas and Propagation, 1991, 39(3): 273-284. doi: 10.1109 /8.76322.
[17]
LIU Aifei, LIAO Guisheng, ZENG Cao, et al. An eigenstructure method for estimating DOA and sensor gain- phase errors[J]. IEEE Transactions on Signal Processing, 2011, 59(12): 5944-5956. doi: 10.1109/TSP.2011.2165064.
[18]
DAI Zheng, SU Weimin, GU Hong, et al. Sensor gain-phase errors estimation using disjoint sources in unknown directions[J]. IEEE Sensors Journal, 2016, 16(10): 3724-3730. doi: 10.1109/JSEN.2016.2531282.
JING Xiaorong, YANG Yang, ZHANG Zufan, et al. Multiuser DOA estimation and mutual coupling error self-calibration in Gaussian noise backgrounds[J]. Journal of Electronics & Information Technology, 2014, 36(5): 1266-1270. doi: 10.3724 /SP.J.1146.2013.01042.
[20]
HUNG E K L. A critical study of a self-calibrating direction- finding method for arrays[J]. IEEE Transactions on Signal Processing, 1994, 42(2): 471-474. doi: 10.1109/78.275633.
[21]
FLIELLER A, FERRÉOL A, LARZABAL P, et al. Robust bearing estimation in the presence of direction-dependent modelling errors: Identiability and treatment[C]. IEEE International Conference on Acoustics, Speech and Signal Processing, Detroit, USA, 1995, 3: 1884-1887. doi: 10.1109 /ICASSP.1995.480579.
[22]
KAY S M. Fundamentals of Statistical Signal Processing: Estimation Theory[M]. Englewood Cliffs, NJ: Prentice-Hall, 1993: 254-260.
[23]
张贤达. 矩阵分析与应用[M]. 北京: 清华大学出版社, 2004: 101-105.
ZHANG Xianda. Matrix Analysis and Applications[M]. Beijing: Tsinghua University Press, 2004: 101-105.
ZHANG Jianxin. Structure design and alignment error analysis of the antenna test turntable[D]. [Master dissertation], Harbin Institute of Technology, 2015.
