2023-12-12
Tensor-Based Robust Adaptive Beamforming for Multiple-Input Multiple-Output Radar under Random Mismatch Scenarios
By
Progress In Electromagnetics Research M, Vol. 122, 53-62, 2023
Abstract
Adaptive beamforming for multiple-input multiple-output (MIMO) radar systems suffers from performance deterioration under the scenarios with multiple random mismatches. This paper explores the theory of tensor algebra and exploits the inherent multidimensional structure of data matrix received by MIMO radar systems. For dealing with the beamforming problem induced by multiple random mismatches including steering vector error, mutual coupling, sensor position error, and coherent local scattering, we develop a robust method based on a third-order tensor in conjunction with a gradient-based optimization process. The proposed method captures the multidimensional structure information embedded in the data matrix received by a MIMO radar and produces appropriate estimates for transmit and receive signal direction vectors required for beamforming. Using a third-order tensor helps to alleviate the effect of the multiple random mismatches in the tensor data domain. The gradient-based optimization process further enhances the capabilities of the third-order tensor in estimating transmit and receive signal direction vectors for adaptive beamforming of a MIMO radar. The main computational complexity of the proposed method is dominated by a trilinear alternating least squares algorithm and the well-known gradient-based algorithm. The proposed method provides better performance than the existing robust methods. Simulation results are presented to confirm the effectiveness of the proposed method.
Citation
Ju-Hong Lee, and Wei-Chi Lee, "Tensor-Based Robust Adaptive Beamforming for Multiple-Input Multiple-Output Radar under Random Mismatch Scenarios," Progress In Electromagnetics Research M, Vol. 122, 53-62, 2023.
doi:10.2528/PIERM23091205
References

1. Fishler, E., A. Haimovich, R. S. Blum, L. J. Cimini, D. Chizhik, and R. A. Valenzuela, "Spatial diversity in radars --- Models and detection performance," IEEE Transactions on Signal Processing, Vol. 54, No. 3, 823-838, Mar. 2006.
doi:10.1109/TSP.2005.862813        Google Scholar

2. Bekkerman, Ilya and Joseph Tabrikian, "Target detection and localization using MIMO radars and sonars," IEEE Transactions on Signal Processing, Vol. 54, No. 10, 3873-3883, Oct. 2006.
doi:10.1109/TSP.2006.879267        Google Scholar

3. Li, Jian, Petre Stoica, Luzhou Xu, and William Roberts, "On parameter identifiability of MIMO radar," IEEE Signal Processing Letters, Vol. 14, No. 12, 968-971, Dec. 2007.
doi:10.1109/LSP.2007.905051        Google Scholar

4. Li, Jian and Petre Stoica, MIMO Radar Signal Processing, John Wiley $$$&$$$ Sons, New York, 2008.
doi:10.1002/9780470391488

5. Hassanien, Aboulnasr and Sergiy A. Vorobyov, "Transmit/receive beamforming for MIMO radar with colocated antennas," 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol. 1- 8, 2089-2092, Apr. 19-24 2009.
doi:10.1109/ICASSP.2009.4960027

6. He, Jie, Da-Zheng Feng, Nicolas H. Younan, and Hui Lv, "Bi-capon beamforming for MIMO radar: A correlation matrix-based method," Proceedings of 2011 IEEE CIE International Conference on Radar, Vol. 1, 335-338, 2011.

7. Cheng, Sibei, Qingjun Zhang, Mingming Bian, and Xinhong Hao, "An improved adaptive received beamforming for nested frequency offset and nested array FDA-MIMO radar," Sensors, Vol. 18, No. 2, Feb. 2018.
doi:10.3390/s18020520        Google Scholar

8. Yu, Ze, Shusen Wang, Wei Liu, and Chunsheng Li, "Joint design of space-time transmit and receive weights for colocated MIMO radar," Sensors, Vol. 18, No. 8, 2722, Aug. 2018.
doi:10.3390/s18082722        Google Scholar

9. Chen, C.-Y., Signal processing algorithms for MIMO radar, Ph.D Thesis, Dept. Elect. Eng., California Institute of Technology, Pasadena, California, U.S.A., 2009.

10. Liao, B., K. M. Tsui, and S. C. Chan, "Robust beamforming with magnitude response constraints using iterative second-order cone programming," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 9, 3477-3482, Sep. 2011.
doi:10.1109/TAP.2011.2161445        Google Scholar

11. Yu, Zhu Liang, Zhenghui Gu, Jianjiang Zhou, Yuanqing Li, Wee Ser, and Meng Hwa Er, "A robust adaptive beamformer based on worst-case semi-definite programming," IEEE Transactions on Signal Processing, Vol. 58, No. 11, 5914-5919, Nov. 2010.
doi:10.1109/TSP.2010.2058107        Google Scholar

12. Khabbazibasmenj, Arash, Sergiy A Vorobyov, and Aboulnasr Hassanien, "Robust adaptive beamforming based on steering vector estimation with as little as possible prior information," IEEE Transactions on Signal Processing, Vol. 60, No. 6, 2974--2987, 2012.        Google Scholar

13. Jia, Weimin, Wei Jin, Shuhua Zhou, and Minli Yao, "Robust adaptive beamforming based on a new steering vector estimation algorithm," Signal Processing, Vol. 93, No. 9, 2539-2542, Sep. 2013.
doi:10.1016/j.sigpro.2013.03.015        Google Scholar

14. Huang, Chia-Cheng and Ju-Hong Lee, "Robust adaptive beamforming using a fully data-dependent loading technique," Progress In Electromagnetics Research B, Vol. 37, 307--325, 2012.        Google Scholar

15. Xiang, Cong, Da-Zheng Feng, Hui Lv, Jie He, and Yang Cao, "Robust adaptive beamforming for MIMO radar," Signal Processing, Vol. 90, No. 12, 3185-3196, Dec. 2010.
doi:10.1016/j.sigpro.2010.05.022        Google Scholar

16. Zhang, Wei, Ju Wang, and Siliang Wu, "Robust minimum variance multiple-input multiple-output radar beamformer," IET Signal Processing, Vol. 7, No. 9, 854--862, 2013.        Google Scholar

17. Zhang, Weiyu and Sergiy A. Vorobyov, "Joint robust transmit/receive adaptive beamforming for MIMO radar using probability-constrained optimization," IEEE Signal Processing Letters, Vol. 23, No. 1, 112-116, Jan. 2016.
doi:10.1109/LSP.2015.2504386        Google Scholar

18. Yu, Hongbo, Dazheng Feng, and Xiaokun Yao, "Robust adaptive beamforming against large DOA mismatch with linear phase and magnitude constraints for multiple-input-multiple-output radar," IET Signal Processing, Vol. 10, No. 9, 1062-1072, Dec. 2016.
doi:10.1049/iet-spr.2015.0521        Google Scholar

19. Qian, Junhui, Zishu He, Wei Zhang, Yulong Huang, Ning Fu, and Jonathon Chambers, "Robust adaptive beamforming for multiple-input multiple-output radar with spatial filtering techniques," Signal Processing, Vol. 143, 152-160, Feb. 2018.
doi:10.1016/j.sigpro.2017.09.004        Google Scholar

20. Huang, Junsheng, Hongtao Su, and Yang Yang, "Low-complexity robust adaptive beamforming method for MIMO radar based on covariance matrix estimation and steering vector mismatch correction," IET Radar Sonar and Navigation, Vol. 13, No. 5, 712-720, May 2019.
doi:10.1049/iet-rsn.2018.5416        Google Scholar

21. Huang, Junsheng, Hongtao Su, and Yang Yang, "Robust adaptive beamforming for MIMO radar in the presence of covariance matrix estimation error and desired signal steering vector mismatch," IET Radar Sonar and Navigation, Vol. 14, No. 1, 118-126, Jan. 2020.
doi:10.1049/iet-rsn.2019.0086        Google Scholar

22. Astély, D and B Ottersten, "The effects of local scattering on direction of arrival estimation with MUSIC," IEEE Transactions on Signal Processing, Vol. 47, No. 12, 3220-3234, Dec. 1999.
doi:10.1109/78.806068        Google Scholar

23. De Lathauwer, L, B De Moor, and J Vandewalle, "A multilinear singular value decomposition," SIAM Journal on Matrix Analysis and Applications, Vol. 21, No. 4, 1253-1278, May 16 2000.
doi:10.1137/S0895479896305696        Google Scholar

24. Kolda, Tamara G. and Brett W. Bader, "Tensor decompositions and applications," SIAM Review, Vol. 51, No. 3, 455-500, Sep. 2009.
doi:10.1137/07070111X        Google Scholar

25. Nion, Dimitri and Nicholas D. Sidiropoulos, "Tensor algebra and multidimensional harmonic retrieval in signal processing for MIMO radar," IEEE Transactions on Signal Processing, Vol. 58, No. 11, 5693-5705, Nov. 2010.
doi:10.1109/TSP.2010.2058802        Google Scholar

26. Van Trees, Harry L, Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory, John Wiley $$$&$$$ Sons, 2002.
doi:10.1002/0471221104

27. Zhidong, Zheng, Zhang Jianyun, and Niu Chaoyan, "Angle estimation of bistatic MIMO radar in the presence of unknown mutual coupling," Proceedings of 2011 IEEE CIE International Conference on Radar, Vol. 1, 55--58, 2011.

28. Xu, Baoqing, Yongbo Zhao, Zengfei Cheng, and Hui Li, "A novel unitary PARAFAC method for DOD and DOA estimation in bistatic MIMO radar," Signal Processing, Vol. 138, 273-279, Sep. 2017.
doi:10.1016/j.sigpro.2017.03.016        Google Scholar

29. Kruskal, Joseph B, "Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics," Linear Algebra and Its Applications, Vol. 18, No. 2, 95-138, 1977.        Google Scholar

30. Sidiropoulos, N. D., R. Bro, and G. B. Giannakis, "Parallel factor analysis in sensor array processing," IEEE Transactions on Signal Processing, Vol. 48, No. 8, 2377-2388, Aug. 2000.
doi:10.1109/78.852018        Google Scholar

31. Du, Lin, Jian Li, and Petre Stoica, "Fully automatic computation of diagonal loading levels for robust adaptive beamforming," IEEE Transactions on Aerospace and Electronic Systems, Vol. 46, No. 1, 449-458, Jan. 2010.
doi:10.1109/TAES.2010.5417174        Google Scholar

32. Mohammadzadeh, Saeed and Osman Kukrer, "Adaptive beamforming based on theoretical interference-plus-noise covariance and direction-of-arrival estimation," IET Signal Processing, Vol. 12, No. 7, 819-825, Sep. 2018.
doi:10.1049/iet-spr.2017.0462        Google Scholar