Finite sample size effect on minimum variance beamformers: Optimum diagonal loading factor for large arrays

IEEE Transactions on Signal Processing

Volumn 54, Issue 1, 2006, Pages 69-82

  Mestre, Xavier ^a   Lagunas, Miguel Ángel ^a  

^a CENTRE TECNOLÒGIC DE TELECOMUNICACIONS DE CATALUNYA CTTC   (Spain)

Author keywords

Diagonal loading; G estimation; Minimum variance distortionless beamformer (MVDR); Random matrix theory; Sample matrix inversion algorithm

Indexed keywords

ALGORITHMS; ANTENNAS; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; SIGNAL INTERFERENCE; SIGNAL TO NOISE RATIO; STATISTICAL METHODS; VECTORS;

ASYMPTOTIC SIGNAL-TO-NOISE-PLUS-INTERFERENCE RATIO (SINR); DIAGONAL LOADING; G-ESTIMATION; MINIMUM VARIANCE DISTORTIONLESS BEAMFORMER (MVDR); RANDOM MATRIX THEORY; SAMPLE MATRIX INVERSION ALGORITHM;

SIGNAL PROCESSING;

EID: 30344437591     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2005.861052     Document Type: Article

References (38)

1. J. Capon, "High resolution frequency-wavenumber spectrum analysis," Proc. IEEE, vol. 57, pp. 1408-1418, Aug. 1969.
2. J. Hudson, Adaptive Array Principles. London, U.K.: IEE Press, 1981.
3. R. Monzingo and T. Miller, Introduction to Adaptive Arrays. New York: Wiley, 1980.
4. B. Widrow, K. Duvall, R, Gooch, and W. Newman, "Sigual cancellation phenomena in adaptive antennas: Causes and cures," IEEE Trans. Antennas Propag., vol. 30, no. 3, pp. 469-478, May 1982.
5. H. Cox, R. Zeskind, and M. Owen, "Robust adaptive beamforming," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-35, no. 10, pp. 1365-1376, Oct. 1987.
6. H. Van Trees, Optimum Array Processing. New York: Wiley, 2002, sec. Part IV of "Detection, Estimation and Modulation Theory".
7. S. Vorobyov, A. Gershman, and Z. Luo, "Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem," IEEE Trans. Signal Process., vol. 51, no. 2, pp. 313-324, Feb. 2003.
8. J. Li, P. Stoica, and Z. Wang, "On robust Capon beamforming and diagonal loading," IEEE Trans. Signal Process., vol. 51, no. 7, pp. 1702-1715, Jul. 2003.
9. S. Shahbazpanahi, A. Gershman, Z.-Q. Luo, and K. M. Wong, "Robust adaptive beamforming for general-rank signal models," IEEE Trans. Signal Process., vol. 51, no. 9, pp. 2257-2269, Sep. 2003.
10. Y. Abramovich, "A controlled method for adaptive optimization of filters using the criterion of maximum SNR," Radiotekh. Elektron. (Radio Engineering Electronic Physics), vol. 26, no. 3, pp. 87-95, 1981.
11. Y. Abramovich and A. Nevrev, "An analysis of effectiveness of adaptive maximization of the signal-to-noise ratio which utilizes the inversion of the estimated correlation matrix," Radiotekh. Elektro. (Radio Engineering Electronic Physics), vol. 26, no. 12, pp. 67-74, 1981.
12. V. Girko, Statistical Analysis of Observations of Increasing Dimension. Dordrecht, The Netherlands: Kluwer, 1995, vol. 28, Mathematical and Statistical Methods.
13. V. Girko, An Introduction to Statistical Analysis of Random Arrays. Leiden, The Netherlands: VSP, 1998.
14. O. Frost, "An algorithm for linearly constrained adaptive array processing," Proc. IEEE, vol. 60, pp. 926-935, 1972.
15. J. Magnus and H. Neudecker, Matrix Differential Calculus With Applications in Statistics and Econometrics. New York: Wiley, 1999.
16. J. Capon and N. Goodman, "Probability distributions for estimators of the frequency-wavenumber spectrum," Proc. IEEE, vol. 58, pp. 1785-1786, Oct. 1970.
17. I. Gupta, "SMI adaptive antenna arrays for weak interfering signals," IEEE Trans. Antennas Propag., vol. 34, no. 10, pp. 1237-1242, Oct. 1986.
18. M. Lagunas and M. Nájar, "Source reference in CIR beamforming," Signal Process., vol. 29, pp. 141-149, Nov. 1992.
19. I. Reed, J. Mallett, and L. Brennan, "Rapid convergence rate in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst., vol. 10, no. 6, pp. 853-863, Nov. 1974.
20. W. Gabriel, "Using spectral estimation techniques in adaptive processing antenna systems," IEEE Trans. Antennas Propag., vol. 34, no. 3, pp. 291-300, Mar. 1986.
21. B. Carlson, "Covariance matrix estimation errors and diagonal loading in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst., vol. 24, no. 4, pp. 397-401, Jul. 1988.
22. O. Cheremisin, "Efficiency of adaptive algorithms with regularized sample covariance matrix," Radiotekh. Elektron. (Radio Engineering Electronic Physics), vol. 27, no. 10, pp. 69-77, 1982.
23. D. Boroson, "Sample size considerations for adaptive arrays," IEEE Trans. Aerosp. Electron. Syst., vol. 16, no. 4, pp. 446-451, Jul. 1980.
24. M. Ganz, R. Moses, and S. Wilson, "Convergence of the SMI and the diagonally loaded SMI algorithms with weak interference," IEEE Trans. Antennas Propag., vol. 38, no. 3, pp. 394-399, Mar. 1990.
25. R. Dilsavor and R. Moses, "Analysis of modified SMI method for adaptive array weight control," IEEE Trans. Signal Process., vol. 41, no. 2, pp. 721-726, Feb. 1993.
26. L. Fertig, "Statistical performance of the MVDR beamformer in the presence of diagonal loading," in Proc. IEEE Sensor Array Multichannel Signal Processing Workshop, Mar. 2000, pp. 77-81.
27. Y. Abramovich, "Convergence analysis of linearly constrained SMI and LSMI adaptive algorithms," in Proc. IEEE Adaptive Systems Signal Processing, Communications, Control Symp., Oct. 2000, pp. 255-259.
28. O. Cheremisin, "The parameter selection for the controlled method of the adaptive optimization of filters," Radiotekh. Elektron. (Radio Engineering Electronic Physics), vol. 30, no. 12, pp. 2369-2377, 1985.
29. Y. Kim, S. Pillai, and J. Guerci, "Optimal loading factor for minimal sample support space-time adaptive radar," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, Seattle, WA, 1998, pp. 2505-2508.
30. N. Ma and J. Goh, "Efficient method to determine diagonal loading value," in Proc. IEEE Int. Conf. Acoustics, Speech Signal Processing, vol. V, 2003, pp. 341-344.
31. M. Viberg, B. Ottersten, and A. Nehorai, "Performance analysis of direction finding with large arrays and finite data," IEEE Trans. Signal Process., vol. 43, no. 2, pp. 469-477, Feb. 1995.
32. D. Feldman and L. Griffiths, "A constraint projection approach for robust adaptive beamforming," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, vol. 2, Apr. 1991, pp. 1381-1384.
33. V. Girko, "G2-estimators of the spectral functions of covariance matrices," in Theory Probab. Mathematical Statistics, vol. 35, 1987, pp. 27-30.
34. V. Girko, "G25-estimators of principal components," Theory Probab. Mathematical Statistics, vol. 40, pp. 1-10, 1990.
35. X. Mestre and M. Lagunas, "Finite sample size effect on minimum variance beamformers: Optimum diagonal loading factor for large arrays," Centre Tecnològic de Telecomunicacions de Catalunya, Catalunya, Spain, Tech. Rep. CTTC/RC/2004-01, 2004.
36. E. Hung and R. Turner, "A fast beamforming algorithm for large arrays," IEEE Trans. Aerosp. Electron. Syst., vol. 19, no. 4, pp. 598-607, Jul. 1983.
37. J. Silverstein and Z. Bai, "On the empirical distribution of eigenvalues of a class of large dimensional random matrices," J. Multivariate Anal., vol. 54, no. 2, pp. 175-192, 1995.
38. V. Girko, Theor. Stochastic Canonical Equations. Dordrecht, The Netherlands: Kluwer, 2001, vol. I.