Finite Data Performance Analysis of Mvdr Antenna Array Beamformers with Diagonal Loading

doi:10.2528/PIER12092006

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Progress In Electromagnetics Research	ISSN: 1070-4698, E-ISSN: 1559-8985

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FINITE DATA PERFORMANCE ANALYSIS OF MVDR ANTENNA ARRAY BEAMFORMERS WITH DIAGONAL LOADING

By Y. L. Chen and J.-H. Lee

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Abstract:
Diagonal loading has been regarded as an efficient manner to tackle the finite sample effect or the steering vector imprecision problem on adaptive array beamforming. However, the reason of the robustness improvement by the loading factor is still unknown and rarely discussed. In this paper, we consider the finite sample effect and derive the approximated output signal-to-interference-plus-noise ratio (SINR) of minimum variance distortionless response (MVDR) beamformers with diagonal loading. The obtained SINR expression is more explicit and compact than the existing formulas in the literature. Based on the theoretical results, we investigate the effects of a loading factor on the output SINR of MVDR beamformers. The theoretical analysis shows the effectiveness of diagonal loading on alleviating finite sample effect. Moreover, the price of using diagonal loading is also discussed. Simulation results are presented for confirming the validity of the research work.

Citation:
Y. L. Chen 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
http://www.jpier.org/PIER/pier.php?paper=12092006

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

2. Reed, I. S., J. D. Mallett, and L. E. Brennan, "Rapid convergence rate in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst., Vol. 10, No. 6, 853-863, Nov. 1974.
doi:10.1109/TAES.1974.307893

3. Monzingo, R. A. and T. W. Miller, Introduction to Adaptive Arrays, Wiley, New York, 1980.

4. Chang, L. and C.-C. Yeh, "Performance of DMI and eigenspace-based beamformers," IEEE Trans. Antennas Propag., Vol. 40, No. 11, 1336-1347, Nov. 1992.
doi:10.1109/8.202711

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

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

7. Ganz, M. W., R. L. Moses, and S. L. Wilson, "Convergence of the SMI and the diagonally loaded SMI algorithms with weak interference," IEEE Trans. Antennas Propag., Vol. 38, No. 3, 394-399, Mar. 1990.
doi:10.1109/8.52247

8. Fertig, L. B., "Statistical performance of the MVDR beamformer in the presence of diagonal loading," Proc. First IEEE SAM Workshop, 77-81, 2000.

9. Liu, X., C. Liu, and G. Liao, "Diagonal loading for STAP and its performance analysis," Proc. 6th IEEE WiCOM, 2010.

10. Dilsavor, R. L. and R. L. Moses, "Analysis of modified SMI method for adaptive array weight control," IEEE Trans. Signal Process., Vol. 41, No. 2, 721-726, Feb. 1993.
doi:10.1109/78.193212

11. Mestre, X. and M. A. Lagunas, "Finite sample size effect on minimum variance beamformers: Optimum diagonal loading factor for large arrays," IEEE Trans. Signal Process., Vol. 54, No. 1, 69-82, Jan. 2006.
doi:10.1109/TSP.2005.861052

12. Chen, Y.-L. and J.-H. Lee, "Finite data performance analysis of LCMV antenna array beamformers with and without signal blocking," Progress In Electromagnetics Research, Vol. 130, 281-317, 2012.

13. Elnashar, A., S. M. Elnoubi, and H. A. El-Mikati, "Further study on robust adaptive beamforming with optimum diagonal loading," IEEE Trans. Antennas Propag., Vol. 54, No. 12, 3647-3658, Dec. 2006.
doi:10.1109/TAP.2006.886473

14. Lee, J.-H. and Y.-L. Chen, "Performance analysis of antenna array beamformers with mutual coupling effects," Progress In Electromagnetics Research B, Vol. 33, 291-295, 2011.
doi:10.2528/PIERB11052802

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

16. Li, J., P. Stoica, and Z. Wang, "On robust Capon beamforming and diagonal loading," IEEE Trans. Signal Process., Vol. 51, No. 7, 1702-1715, Jul. 2003.

17. Besson, O. and F. Vincent, "Performance analysis of beamformers sing generalized loading of the covariance matrix in the presence of random steering vector errors," IEEE Trans. Signal Process., Vol. 53, No. 2, 452-459, Feb. 2005.
doi:10.1109/TSP.2004.840777

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

19. Feldman, D. D. and L. J. Griffths, "A projection approach for robust adaptive beamforming," IEEE Trans. Signal Process., Vol. 42, No. 4, 867-876, Apr. 1994.
doi:10.1109/78.285650

20. Haimovich, A. M. and Y. Bar-Ness, "An eigenanalysis interference canceler," IEEE Trans. Signal Process., Vol. 39, No. 1, 76-84, Jan. 1991.
doi:10.1109/78.80767

21. Pillai, S. U., Array Signal Processing, Springer-Verlag, New York, 1989.

22. Widrow, B., K. M. Duvall, R. P. Gooch, and W. C. Newman, "Signal cancellation phenomena in adaptive antennas: Causes and cures," IEEE Trans. Antennas Propag., Vol. 30, No. 3, 469-478, May 1982.
doi:10.1109/TAP.1982.1142804

23. Hudson, J. E., Adaptive Array Principles, Peter Peregrinus, London, 1981.

24. Gabriel, W. F., "Using spectral estimation techniques in adaptive processing antenna systems," IEEE Trans. Antennas Propag., Vol. 34, No. 3, 291-300, Mar. 1986.
doi:10.1109/TAP.1986.1143827

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

26. Gu, J. and P. J. Wolfe, "Robust adaptive beamforming using variable loading," Proc. Fourth IEEE SAM Workshop, 1-5, 2006.

27. Gu, Y. J., Z. G. Shi, K. S. Chen, and Y. Li, "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

28. Liu, W. and S. Ding, "An efficient method to determine the diagonal loading factor using the constant modulus feature," IEEE Trans. Signal Process., Vol. 56, No. 12, 6102-6106, Dec. 2008.
doi:10.1109/TSP.2008.2005862

29. Du, L., J. Li, and P. Stoica, "Fully automatic computation of diagonal loading levels for robust adaptive beamforming," IEEE Trans. Aerosp. Electron. Syst., Vol. 46, No. 1, 449-458, Jan. 2010.
doi:10.1109/TAES.2010.5417174

30. Li, Y., Y. J. Gu, Z. G. Shi, and K. S. Chen, "Robust adaptive beamforming based on particle filter with noise unknown," Progress In Electromagnetics Research, Vol. 90, 151-169, 2009.
doi:10.2528/PIER09010302

31. Lee, J.-H. and C.-C. Lee, "Analysis of the performance and sensitivity of an eigenspace-based interference canceler," IEEE Trans. Antennas Propag., Vol. 48, No. 5, 826-835, May 2000.
doi:10.1109/8.855503

32. Trim, D., Calculus for Engineers, Prentice Hall, Toronto, 2008.

33. Sominskii, I. S., The Method of Mathematical Induction, Pergamon, London, 1961.