Compared with the worst-case optimization-based approach, the probability-constrained approach is a more flexible one to robust adaptive beamforming. In this paper, a precise relationship between the two approaches is built in the case of Gaussian steering vector mismatch, which shows that the probability-constrained beamformer design can be interpreted in terms of the worst-case beamformer design. Numerical simulations demonstrate that the precise version of the probability-constrained beamformer is more robust to the steering vector mismatch than the other popular robust adaptive beamformers.
"Robust Adaptive Beamforming for a Class of Gaussian Steering Vector Mismatch," Progress In Electromagnetics Research,
Vol. 81, 315-328, 2008. doi:10.2528/PIER08010202
1. Dessouky, M., H. Sharshar, and Y. Albagory, "Improving the cellular coverage from a high altitude platform by novel tapered beamforming technique," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1721-1731, 2007.
2. Gu, Y. J., et al. "Robust adaptive beamforming for steering vector uncertainties based on equivalent DOAs method," Progress In Electromagnetics Research, Vol. 79, 277-290, 2008. doi:10.2528/PIER07102202
3. Dessouky, M., H. Sharshar, and Y. Albagory, "A novel tapered beamforming window for uniform concentric circular arrays," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 2077-2089, 2006. doi:10.1163/156939306779322701
4. Abdelaziz, A. A., "Improving the performance of an antenna array by using radar absorbing cover," Progress In Electromagnetics Research Letters, Vol. 1, 129-138, 2008. doi:10.2528/PIERL07112503
5. Capineri, L., "Estimation of relative permittivity of shallow soils by using the ground penetrating radar response from different buried targets," Progress In Electromagnetics Research Letters, Vol. 2, 63-71, 2008.
6. Landesa, L., et al. "Bias of the maximum likelihood DOA estimation from inaccurate knowledge of the antenna array response," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 9, 1205-1217, 2007.
7. Zainud-Deen, S. H., et al. "Direction of arrival and state of polarization estimation using radial basis function neural network (RBFNN)," Progress In Electromagnetics Research B, Vol. 2, 137-150, 2008. doi:10.2528/PIERB07111801
8. Xiao, S., et al. "Spatial focusing characteristics of time reversal UWB pulse transmission with different antenna arrays," Progress In Electromagnetics Research B, Vol. 2, 223-232, 2008. doi:10.2528/PIERB07112203
9. Fakoukakis, F. E., et al. "Development of an adaptive and a switched beam smart antenna system for wireless communications," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 3, 399-408, 2006. doi:10.1163/156939306775701722
10. Guo, B., Y. Wang, J. Li, P. Stoica, and R. Wu, "Microwave imaging via adaptive beamforming methods for breast cancer detection," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 1, 53-63, 2006. doi:10.1163/156939306775777350
11. Vescovo, R., "Beam scanning with null and excitation constraints for linear arrays of antennas," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 2, 267-277, 2007. doi:10.1163/156939307779378817
12. Kazemi, S., et al. "Performance improvement in amplitude synthesis of unequally spaced array using least mean square method," Progress In Electromagnetics Research B, Vol. 1, 135-145, 2008. doi:10.2528/PIERB07103002
13. Seligson, C. D., "Comments on 'High resolution frequencywavenumber spectrum analysis'," Proc. of the IEEE, Vol. 58, 947-949, 1970.
14. Cox, H., "Resolving power and sensitivity to mismatch of optimum array processors," J. Acoust. Soc. Amer., Vol. 54, No. 3, 771-785, 1973. doi:10.1121/1.1913659
15. Mouhamadou, M., P. Vaudon, and M. Rammal, "Smart antenna array patterns synthesis: Null steering and multi-user beamforming by phase control," Progress In Electromagnetics Research, Vol. 60, 95-106, 2006. doi:10.2528/PIER05112801
16. Liu, Y.-T. and C.-W. Su, "Wideband omnidirectional operation monopole antenna," Progress In Electromagnetics Research Letters, Vol. 1, 255-261, 2008. doi:10.2528/PIERL07120903
17. Cox, H., R. M. Zeskind, and M. H. Owen, "Robust adaptive beamforming," IEEE Trans. Acoust., Vol. 35, No. 10, 1365-1376, 1987. doi:10.1109/TASSP.1987.1165054
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 Processing, Vol. 51, No. 2, 313-324, 2003. doi:10.1109/TSP.2002.806865
19. Li, J., P. Stoica, and Z. Wang, "On robust capon beamforming and diagonal loading," IEEE Trans. Signal Processing, Vol. 51, No. 7, 1702-1715, 2003. doi:10.1109/TSP.2003.812831
20. Lorenz, R. G. and S. P. Boyd, "Robust minimum variance beamforming," IEEE Trans. Signal Processing, Vol. 53, No. 5, 1684-1696, 2005. doi:10.1109/TSP.2005.845436
21. Vorobyov, S. A., Y. Rong, and A. B. Gershman, "Robust adaptive beamforming using probability-constrained optimization," Proc. IEEE Workshop on Statistical Signal Processing, 934-939, 2005.
22. Vorobyov, S. A., A. B. Gershman, and Y. Rong, "On the relationship between the worst-case optimization and probabilityconstrained approaches to Robust adaptive beamforming," Proc. 32nd IEEE Int. Conference on Acoustics, Vol. 2, 977-980, 2007.
23. Reed, I. S., J. D. Mallett, and L. E. Brennan, "Rapid convergence rate in adaptive arrays," IEEE Trans. Aerospace and Electron. Syst., Vol. 10, No. 6, 853-863, 1974. doi:10.1109/TAES.1974.307893
24. Capon, J., "High resolution frequency-wavenumber spectral analysis," Proc. of the IEEE, Vol. 57, No. 8, 1408-1418, 1969.
25. Besson, O. and F. Vincent, "Performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors," IEEE Trans. Signal Processing, Vol. 53, No. 2, 452-459, 2005. doi:10.1109/TSP.2004.840777
26. Proakis, J. G., Digital Communications, 4th edition, McGraw- Hill, 2001.
27. Papoulis, A., Probability, R andom Variables, and Stochastic Processes, 3rd edition, McGraw Hill Company, 1991.
28. Boyd, S. and L. Vandenberghe, Convex Optimization, Cambridge university press, Cambridge, 2004.
29. Chang, L. and C. C. Yeh, "Performance of DMI and eigenspacebased beamformers," IEEE Trans. Antennas Propagat., Vol. 40, No. 11, 1336-1347, 1992. doi:10.1109/8.202711