Affected by multipath propagation as well as the receiving conditions of an actual array, a distributed source model considering array uncertainties/errors is more consistent with the realistic scenarios. In this paper, a new direction finding method for coherently distributed (CD) sources in the presence of array gain-phase errors is proposed. By exploiting partly calibrated uniform linear arrays (ULA), the gain-phase errors are first estimated according to the relationship of elements of array covariance matrix, and then a two-step iterative procedure is introduced to achieve a joint estimation of nominal DOA and angular spread from sparse recovery perspective. Performance analysis and related Cramér-Rao bound (CRB) are also provided. Numerical examples show that the proposed method can provide improved resolution and estimation accuracy, and performs almost independently of gain-phase errors.
1. Jiang, Z., Z. Zhang, T. Zhao, H. Chen, and W. Wang, "Augmented quaternion MUSIC method for a uniform/sparse COLD array," Progress In Electromagnetics Research Letters, Vol. 95, 25-32, 2021. doi:10.2528/PIERL20102303
2. Zoubir, A. and Y. Wang, "Efficient DSPE algorithm for estimating the angular parameters of coherently distributed sources," Signal Processing, Vol. 88, No. 4, 1071-1078, 2008. doi:10.1016/j.sigpro.2007.11.002
3. Meng, Y., P. Stoica, and K. M. Wong, "Estimation of the directions of arrival of spatially dispersed signals in array processing," Proc. IEE Radar, Sonar, Navigat., Vol. 143, 1-9, 1996. doi:10.1049/ip-rsn:19960170
4. Wan, L., et al., "DOA estimation for coherently distributed sources considering circular and noncircular signals in massive MIMO systems," IEEE Systems Journal, Vol. 11, No. 1, 41-49, 2017. doi:10.1109/JSYST.2015.2445052
5. Tian, Y., H. Yue, and X. Rong, "Multi-parameters estimation of coherently distributed sources under coexistence of circular and noncircular signals," IEEE Communications Letters, Vol. 24, No. 6, 1254-1257, 2020. doi:10.1109/LCOMM.2020.2981028
6. Tian, Q., T. Qiu, and R. Cai, "DOA estimation for CD sources by complex cyclic correntropy in an impulsive noise environment," IEEE Communications Letters, Vol. 24, No. 5, 1015-1019, 2020. doi:10.1109/LCOMM.2020.2976957
7. Boujemaa, H., "Extension of COMET algorithm to multiple diffuse source localization in azimuth and elevation," European Transactions on Telecommunications, Vol. 16, No. 6, 557-566, 2005. doi:10.1002/ett.1021
8. Hu, A., et al., "An ESPRIT-based approach for 2-D localization of incoherently distributed sources in massive MIMO systems," IEEE Journal of Selected Topics in Signal Processing, Vol. 8, No. 5, 996-1011, 2014. doi:10.1109/JSTSP.2014.2313409
9. Zheng, Z., et al., "Efficient beanspace-based algorithm for two-dimensional DOA estimation of incoherently distributed sources in massive MIMO systems," IEEE Transactions on Vehicular Technology, Vol. 67, No. 12, 11776-11789, 2018. doi:10.1109/TVT.2018.2875023
10. Xu, H., Y. Tian, and S. Liu, "Linear-shrinkage-based DOA estimation for coherently distributed sources considering mutual coupling in massive MIMO systems," AEU — International Journal of Electronics and Communications, Vol. 126, 1-6, 2020.
11. Liu, A., et al., "An eigenstructure method for estimating DOA and sensor gain-phase errors," IEEE Transactions on Signal Processing, Vol. 59, No. 12, 5944-5956, 2011. doi:10.1109/TSP.2011.2165064
12. Cao, S., Z. Ye, D. Xu, and X. Xu, "A Hadamard product based method for DOA estimation and gain-phase error calibration," IEEE Transactions on Aerospace and Electronic Systems, Vol. 49, No. 2, 1224-1233, 2013. doi:10.1109/TAES.2013.6494409
13. Pesavento, M., A. B. Gershman, and K. M. Wong, "Direction finding in partly calibrated sensor arrays composed of multiple subarrays," IEEE Transactions on Signal Processing, Vol. 50, No. 9, 2103-2115, 2002. doi:10.1109/TSP.2002.801929
14. Tian, Y., J. Shi, H. Yue, and X. Rong, "Calibrating nested sensor arrays for DOA estimation utilizing continuous multiplication operator," Signal Processing, Vol. 176, 1-11, 2020.
15. Lin, M. and L. Yang, "Blind calibration and DOA estimation with uniform circular arrays in the presence of mutual coupling," IEEE Antennas Wireless Propagation Letters, Vol. 5, 315-318, 2006. doi:10.1109/LAWP.2006.878898
16. Liu, H., et al., "A sparse-based approach for DOA estimation and array calibration in uniform linear array," IEEE Sensors Journal, Vol. 16, No. 15, 6018-6027, 2016. doi:10.1109/JSEN.2016.2577712
17. Bresler, Y., "Maximum likelihood estimation of a linearly structured covariance with application to antenna array processing," Proc. 4th Annual ASSP Workshop Spectrum Estimation Model., 172-175, Minneapolis, MN, USA, Aug. 1988.
18. Arlot, A. and A. Cellsse, "A survey of cross-validation procedures for model selection," Statistics Survery, Vol. 4, 40-79, Institute of Mathematical Statistics (IMS), 2010.
19. Herman, M. A. and T. Strohmer, "General deviants: An analysis of perturbations in compressed sensing," IEEE Journal of Selected Topics in Signal Processing, Vol. 4, No. 2, 342-349, 2010. doi:10.1109/JSTSP.2009.2039170