ABSTRACT
Beamforming has been widely studied in wireless communications, radar, sonar, and other array systems. Digital beamforming is usually designed based on the array response and the estimation of the covariance matrix of the received signal. Various model mismatch issues can arise due to unequal antenna gains, phase errors, direction-or-arrival (DOA) mismatch and imperfect estimation of the covariance matrix. Different methods based on the shrinkage estimation of the covariance matrix and interference-plus-noise covariance matrix reconstruction have been proposed to address the challenges. In this paper, we investigate the robustness of several approaches in the presence of model uncertainties. We demonstrate the pros and cons of those approaches under different scenarios, based on which recommendation on the choice of the proper method may be made.
- Brennan, L., Mallett, J., and Reed, I. 1976. Adaptive arrays in airborne mti radar. IEEE Transactions on Antennas and Propagation. 24, 5 (Sept. 1976), 607--615.Google ScholarCross Ref
- Feldman, D. D. and Griffiths, L. J. 2002. A projection approach for robust adaptive beamforming. IEEE Transactions on Signal Processing. 42, 4 (Apr. 1994), 867--876. Google ScholarDigital Library
- Vorobyov, S. A., Gershman, A. B., and Luo, Z. Q. 2003. Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem. IEEE Trans. Signal Process. 51, 2 (Feb. 2003), 313--324. Google ScholarDigital Library
- Mestre, X., and Lagunas, M. Á. 2006. Finite sample size effect on minimum variance beamformers: Optimum diagonal loading factor for large arrays. IEEE Transactions on Signal Processing. 54, 1 (Jan. 2006), 69--82. Google ScholarDigital Library
- Serra, J., and Najar, M. 2014. Asymptotically optimal linear shrinkage of sample lmmse and mvdr filters. IEEE Transactions on Signal Processing. 62, 14 (Jul. 2014), 3552--3564. Google ScholarDigital Library
- Zhang, M., Zhang, A., and Yang, Q. 2016. Robust adaptive beamforming based on conjugate gradient algorithms. IEEE Transactions on Signal Processing. 64, 22 (Nov. 2016), 6046--6057. Google ScholarDigital Library
- Gu, Y., and Leshem, A. 2012. Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation. IEEE Transactions on Signal Processing. 60, 7 (Jul. 2012), 3881--3885. Google ScholarDigital Library
- Du, L., Li, J., and Stoica, P. 2010. Fully automatic computation of diagonal loading levels for robust adaptive beamforming. IEEE Transactions on Aerospace and Electronic Systems. 46, 1 (Jan. 2010), 449--458.Google ScholarCross Ref
- Yang, L., McKay, M. R., and Couillet, R. 2018. High-Dimensional MVDR Beamforming: Optimized Solutions Based on Spiked Random Matrix Models. IEEE Transactions on Signal Processing. 66, 7 (Apr. 2018), 1933--1947.Google ScholarCross Ref
- Vorobyov, S. A. 2013. Principles of minimum variance robust adaptive beamforming design. Signal Processing. 93, 12 (2013), 3264--3277.Google ScholarCross Ref
- Huang, L., Zhang, J., Xu, X., and Ye, Z. 2015. Robust adaptive beamforming with a novel interference-plus-noise covariance matrix reconstruction method. IEEE Transactions on Signal Processing. 63, 7 (Apr. 2015), 1643--1650.Google ScholarCross Ref
- Ledoit, O., and Wolf, M. 2012. Nonlinear shrinkage estimation of large-dimensional covariance matrices. The Annals of Statistics. 40, 2 (Apr. 2012), 1024--1060.Google ScholarCross Ref
- Chen, Y., Wiesel, A., Eldar, Y. C., and Hero, A. O. 2010. Shrinkage algorithms for mmse covariance estimation. IEEE Transactions on Signal Processing. 58, 10 (Oct. 2010), 5016--5029. Google ScholarDigital Library
- Tong, J., Hu, R., Xi, J., Xiao, Z., Guo, Q., and Yu, Y. 2018. Linear shrinkage estimation of covariance matrices using low-complexity cross-validation. Signal Processing. 148 (Jul. 2018), 223--233. Google ScholarDigital Library
- Wang, C., Pan, G., Tong, T., and Zhu, L. 2015. Shrinkage estimation of large dimensional precision matrix using random matrix theory. Statistica Sinica. 25, 3 (2015), 993--1008.Google Scholar
- Ito, T., and Kubokawa, T. 2015. Linear ridge estimator of high-dimensional precision matrix using random matrix theory. Technical Repore F-995, CIRJE, Faculty of Economics. University of Tokyo, (Nov. 2015).Google Scholar
- Bodnar, T., Gupta, A. K., and Parolya, N. 2016. Direct shrinkage estimation of large dimensional precision matrix. Journal of Multivariate Analysis. 146 (Apr. 2016), 223--236. Google ScholarDigital Library
- Tong, J., Xi, J., Guo, Q., and, Y. 2017. Low-complexity cross-validation design of a linear estimator. Electronics Letters. 53, 18 (Aug. 2017), 1252--1254.Google ScholarCross Ref
Index Terms
On the Robustness of Covariance Matrix Shrinkage-Based Robust Adaptive Beamforming
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