volume | PIER Journals

Abstract

In this paper, an improved robust minimum variance beamformer against direction of arrival (DOA) mismatch and finite sample effect is proposed. Multiple inequality magnitude constraints are imposed to broaden the main lobe of beampattern. The conjugate symmetric structure of the optimal weight is utilized to transform the non-convex inequality magnitude constraints into convex ones. A quadratic constraint on the norm of weight is introducing to make further improvement on robustness against DOA mismatch and finite sample effect. The proposed beamforming problem can be reformulated in the form of the second order cone programming and solved efficiently by interior point method. Simulation results show that the proposed beamformer outperforms several other adaptive beamformers.

1. Van Veen, B. D. and K. M. Buckley, "Beamforming: A versatile approach to spatial filtering," IEEE Acoust., Speech, Signal Process. Mag., Vol. 5, No. 2, 4-24, 1988. Google Scholar

2. Godara, L. C., "Application of antenna arrays to mobile communications, Part II: Beam-forming and direction-of-arrival considerations," Proc. IEEE, Vol. 85, No. 8, 1195-1245, 1997.
doi:10.1109/5.622504 Google Scholar

3. Qu, Y., G. S. Liao, S. Q. Zhu, and X. Y. Liu, "Pattern synthesis of planar antenna array via convex optimization for airborne forward looking radar," Progress In Electromagnetics Research, Vol. 84, 1-10, 2008.
doi:10.2528/PIER08060301 Google Scholar

4. Capon, J., "High-resolution frequency-wavenumber spectrum analysis," Proc. IEEE, Vol. 57, No. 8, 1408-1418, 1969.
doi:10.1109/PROC.1969.7278 Google Scholar

5. Wax, M. and Y. Anu, "Performance analysis of the minimum variance beamformer in the presence of steering vectors errors," IEEE Trans. Signal Process., Vol. 44, No. 4, 938-947, 1996.
doi:10.1109/78.492546 Google Scholar

6. Van Trees, H. L., Detection, Estimation and Modulation Theory, Part IV: Optimum Array Processing, Wiley, New York, 2002.

7. Carlson, B. D., "Covariance matrix estimation errors and diagonal loading in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst., Vol. 24, No. 4, 397-401, 1988.
doi:10.1109/7.7181 Google Scholar

8. Wax, M. and Y. Anu, "Performance analysis of the minimum variance beamformer," IEEE Trans. Signal Process., Vol. 44, No. 4, 928-937, 1996.
doi:10.1109/78.492545 Google Scholar

9. Stoica, P., Z. Wang, and J. Li, "Robust Capon beamforming," IEEE Signal Process. Lett., Vol. 10, No. 6, 172-175, 2003.
doi:10.1109/LSP.2003.811637 Google Scholar

10. Lorenz, R. G. and S. P. Boyd, "Robust minimum variance beamforming," IEEE Trans. Signal Process., Vol. 53, No. 5, 1684-1696, 2005.
doi:10.1109/TSP.2005.845436 Google Scholar

11. Lie, J. P., W. Ser, and C. M. S. See, "Adaptive uncertainty based iterative robust Capon beamformer using steering vector mismatch estimation," IEEE Trans. Signal Process., Vol. 59, No. 9, 4483-4488, 2011.
doi:10.1109/TSP.2011.2157500 Google Scholar

12. Nai, S. E., W. Ser, Z. L. Yu, and H. Chen, "Iterative robust minimum variance beamforming," IEEE Trans. Signal Process., Vol. 59, No. 4, 1601-1611, 2011.
doi:10.1109/TSP.2010.2096222 Google Scholar

13. Zaharis, Z. D., C. Skeberis, and T. D. Xenos, "Improved antenna array adaptive beamforming with low side lobe level using a novel adaptive invasive weed optimization method," Progress In Electromagnetics Research, Vol. 124, 137-150, 2012.
doi:10.2528/PIER11120202 Google Scholar

14. Liu, C. F. and J. Yang, "Robust LCMP beamformer with negative loading," Progress In Electromagnetics Research, Vol. 130, 541-561, 2012.
doi:10.2528/PIER12061909 Google Scholar

15. Chen, Y. L. and J. H. Lee, "Finite data performance analysis of MVDR antenna array beamformers with diagonal loading," Progress In Electromagnetics Research, Vol. 134, 475-507, 2013.
doi:10.2528/PIER12092006 Google Scholar

16. Yang, K., Z. Q. Zhao, and Q. H. Liu, "Robust adaptive beamforming against array calibration errors," Progress In Electromagnetics Research, Vol. 140, 341-351, 2013.
doi:10.2528/PIER13042203 Google Scholar

17. Li, J., P. Stoica, and Z.Wang, "On robust Capon beamforming and diagonal loading," IEEE Trans. Signal Process., Vol. 51, No. 7, 1702-1715, 2003.
doi:10.1109/TSP.2003.812831 Google Scholar

18. Vorobyov, S. A., A. B. Gershman, and Z. Q. Luo, "Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem," IEEE Trans. Signal Process., Vol. 51, No. 2, 313-324, 2003.
doi:10.1109/TSP.2002.806865 Google Scholar

19. Li, J., P. Stoica, and Z. Wang, "Doubly constrained robust Capon beamformer," IEEE Trans. Signal Process., Vol. 52, No. 7, 2407-2423, 2004.
doi:10.1109/TSP.2004.831998 Google Scholar

20. Booker, A. and C. Y. Ong, "Multiple constraint adaptive filtering," Geophysics, Vol. 36, No. 3, 498-509, 1971.
doi:10.1190/1.1440187 Google Scholar

21. Frost III, O. L., "An algorithm for linearly constrained adaptive array processing," Proc. IEEE, Vol. 60, No. 8, 926-935, 1972.
doi:10.1109/PROC.1972.8817 Google Scholar

22. Huarng, K. C. and C. C. Yeh, "Adaptive beamforming with conjugate symmetric weights," IEEE Trans. Signal Process., Vol. 39, No. 7, 926-932, 1991. Google Scholar

23. Boyd, S. and L. Vandenberghe, Convex Optimization, Cambrideg University Press, Cambridge, UK, 2004.
doi:10.1017/CBO9780511804441

24. Cox, H., R. M. Zeskind, and M. M. Owen, "Robust adaptive beamforming," IEEE Trans. Acoust., Speech, Signal Process, Vol. 35, No. 10, 1365-1376, 1987.
doi:10.1109/TASSP.1987.1165054 Google Scholar

25. Tian, Z., K. L. Bell, and H. L. Van Trees, "A recursive least squares implementation for LCMP beamforming under quadratic constraint," IEEE Trans. Signal Process., Vol. 49, No. 6, 1138-1145, 2001.
doi:10.1109/78.923296 Google Scholar

26. Liu, J., A. B. Gershman, Z. Q. Luo, and K. M. Wong, "Adaptive beamforming with sidelobe control: A second-order cone programming approach," IEEE Signal Process. Lett., Vol. 10, No. 11, 331-334, 2003.
doi:10.1109/LSP.2003.817852 Google Scholar

27. Strum, J. F., "Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones," Optimization Methods and Software, Vol. 11, No. 1-4, 625-653, 1999.
doi:10.1080/10556789908805766 Google Scholar

28. Luenberger, D. G. and Y. Y. Ye, Linear and Nonlinear Programming, Springer, New York, 2008.

Dr. Lulu Zhao

Professor Guang Liang

Dr. Huijie Liu