Vol. 37
Latest Volume
All Volumes
PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2014-06-16
Magnitude Constraint Minimum Variance Beamformer with Conjugate Symmetric Constraint and Norm Constraint
By
Progress In Electromagnetics Research M, Vol. 37, 41-50, 2014
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.
Citation
Lulu Zhao Guang Liang Huijie Liu , "Magnitude Constraint Minimum Variance Beamformer with Conjugate Symmetric Constraint and Norm Constraint," Progress In Electromagnetics Research M, Vol. 37, 41-50, 2014.
doi:10.2528/PIERM14042808
http://www.jpier.org/PIERM/pier.php?paper=14042808
References

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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