Statistical inference in large antenna arrays under unknown noise pattern

IEEE Transactions on Signal Processing

Volumn 61, Issue 22, 2013, Pages 5633-5645

  Vinogradova, Julia ^a   Couillet, Romain ^b   Hachem, Walid ^a  

^a INSTITUT TELECOM   (France)

^b SUPELEC   (France)

Author keywords

Correlated noise; MUSIC algorithm; Power estimation; Random matrix theory; Sensor arrays; Source detection

Indexed keywords

CORRELATED NOISE; MUSIC ALGORITHMS; POWER ESTIMATIONS; RANDOM MATRIX THEORY; SOURCE DETECTION;

ANTENNA ARRAYS; RANDOM VARIABLES; SENSOR ARRAYS; SENSORS; WAVELET ANALYSIS;

WHITE NOISE;

EID: 84886694101     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2013.2280443     Document Type: Article

References (36)

1. H. Urkowitz, "Energy detection of unknown deterministic signals," Proc. IEEE, vol. 55, no. 4, pp. 523-531, 1967.
2. H. Akaike, "A new look at the statistical model identification, " IEEE Trans. Autom. Control, vol. AC-19, no. 6, pp. 716-723, 1974.
3. J. Rissanen, "Modeling by shortest data description," Automatica, vol. 14, pp. 465-471, 1978.
4. M. Wax and T. Kailath, "Detection of signals by information theoretic criteria," IEEE Trans. Acoust., Speech, Signal Process., vol. 33, no. 2, pp. 387-392, 1985.
5. R. O. Schmidt, "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propag., vol. 34, no. 3, pp. 276-280, 1986.
6. R. R. Nadakuditi and A. Edelman, "Sample eigenvalue based detection of high-dimensional signals in white noise using relatively few samples," IEEE Trans. Signal Process. vol. 56, no. 7, pp. 2625-2638, 2008 [Online]. Available: http://dx.doi.org/10.1109/TSP.2008.917356
7. S. Kritchman and B. Nadler, "Non-parametric detection of the number of signals: Hypothesis testing and random matrix theory," IEEE Trans. Signal Process., vol. 57, no. 10, pp. 3930-3941, 2009.
8. S. Kritchman and B. Nadler, "Determining the number of components in a factor model from limited noisy data," Chemometr. Intell. Lab. Syst., vol. 94, no. 1, pp. 19-32, 2008.
9. R. Couillet, J. W. Silverstein, Z. D. Bai, and M. Debbah, "Eigen-inference for energy estimation of multiple sources," IEEE Trans. Inf. Theory, vol. 57, no. 4, pp. 2420-2439, 2011.
10. X. Mestre, "Improved estimation of eigenvalues and eigenvectors of covariance matrices using their sample estimates," IEEE Trans. Inf. Theory, vol. 54, no. 11, pp. 5113-5129, 2008.
11. O. Besson, S. Kraut, and L. L. Scharf, "Detection of an unknown rank-one component in white noise," IEEE Trans. Signal Process., vol. 54, no. 7, pp. 2835-2839, 2006.
12. L. S. Cardoso, M. Debbah, P. Bianchi, and J. Najim, "Cooperative spectrum sensing using random matrix theory," in Proc. IEEE 3rd Int. Symp. Wireless Pervasive Comput. (ISWPC), 2008, pp. 334-338.
13. F. Penna, R. Garello, and M. Spirito, "Cooperative spectrum sensing based on the limiting eigenvalue ratio distribution inWishartmatrices," IEEE Commun. Lett., vol. 13, no. 7, pp. 507-509, 2009.
14. P. Bianchi, M. Debbah, M. Maida, and J. Najim, "Performance of statistical tests for single-source detection using random matrix theory," IEEE Trans. Inf. Theory, vol. 57, no. 4, pp. 2400-2419, 2011.
15. B. Nadler, F. Penna, and R. Garello, "Performance of eigenvalue-based signal detectors with known and unknown noise level," in Proc. IEEE Int. Conf. Commun. (ICC), 2011, pp. 1-5, IEEE.
16. R. R. Nadakuditi and J. W. Silverstein, "Fundamental limit of sample generalized eigenvalue based detection of signals in noise using relatively few signal-bearing and noise-only samples," IEEE J. Sel. Topics Signal Process., vol. 4, no. 3, pp. 468-480, 2010.
17. B.Nadler and I.M. Johnstone, "Detection performance of Roy's largest root test when the noise covariance matrix is arbitrary," in Proc. IEEE Statist. Signal Process. Workshop (SSP), 2011, pp. 681-684.
18. V. A. Marčenko and L. A. Pastur, "Distribution of eigenvalues for some sets of random matrices," Math. USSR-Sbornik, vol. 1, no. 4, pp. 457-483, 1967 [Online]. Available: http://dx.doi.org/10.1070/ SM1967v001n04ABEH001994
19. J.W. Silverstein and Z. D. Bai, "On the empirical distribution of eigenvalues of a class of large-dimensional random matrices," J. Multivar. Anal., vol. 54, no. 2, pp. 175-192, 1995.
20. J. W. Silverstein and S. Choi, "Analysis of the limiting spectral distribution of large-dimensional random matrices," J. Multivar. Anal., vol. 54, no. 2, pp. 295-309, 1995 [Online]. Available: http://dx.doi.org/10. 1006/jmva.1995.1058
21. Z. D. Bai and J. W. Silverstein, "No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices," Ann. Probab., vol. 26, no. 1, pp. 316-345, 1998. (Pubitemid 128073876)
22. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1990.
23. F. Chapon, R. Couillet, W. Hachem, and X. Mestre, "The outliers among the singular values of large rectangular random matrices with additive fixed rank deformation," Markov Process. Related Fields, 2013 [Online]. Available: http://arxiv.org/abs/1207.0471
24. W. Hachem, P. Loubaton, X. Mestre, J. Najim, and P. Vallet, "A subspace estimator for fixed rank perturbations of large random matrices," J. Multivar. Anal., 2012, arXiv/1106.1497, accepted for publication.
25. L. Pastur and M. Ŝerbina, Eigenvalue Distribution of Large Random Matrices. New York, NY, USA: Amer. Math. Soc., 2011, vol. 171.
26. R. M. Gray, Toeplitz and Circulant Matrices: A Review. NewYork, NY, USA: Now, 2006.
27. U. Grenander and G. Szego, Toeplitz Forms and Their Applications, 2nd ed. New York, NY, USA: Chelsea, 1984.
28. N. El Karoui, "Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices," Ann. Probab., vol. 35, no. 2, pp. 663-714, 2007 [Online]. Available: http://dx.doi.org/10.1214/ 009117906000000917
29. A. W. Van der Vaart, Asymptotic Statistics. NewYork,NY,USA: Cambridge Univ. Press, 2000.
30. P. J. Bickel and E. Levina, "Regularized estimation of large covariance matrices," Ann. Statist., vol. 36, no. 1, pp. 199-227, 2008.
31. Z. D. Bai and J. W. Silverstein, "CLT for linear spectral statistics of large-dimensional sample covariance matrices," Ann. Probab., vol. 32, no. 1A, pp. 553-605, 2004 [Online]. Available: http://dx.doi.org/10. 1214/aop/1078415845 (Pubitemid 38545346)
32. P. J. Brockwell and R. A. Davis, Time Series: Theory andMethods, ser. Springer Series in Statistics. New York, NY, USA: Springer, 2006, reprint of 2nd (1991) ed.
33. R. J. Bhansali, L. Giraitis, and P. S. Kokoszka, "Convergence of quadratic forms with nonvanishing diagonal," Statist. Probab. Lett., vol. 77, no. 7, pp. 726-734, 2007 [Online]. Available: http://dx.doi.org/10.1016/j. spl.2006.11.007
34. A. Kammoun, M. Kharouf, W. Hachem, and J. Najim, "A Central Limit Theorem for the SINR at the LMMSE estimator output for largedimensional signals," IEEE Trans. Inf. Theory, vol. 55, no. 11, pp. 5048-5063, 2009.
35. P. Billingsley, Probability and Measure, ser. Wiley Series in Probability and Mathematical Statistics, 3rd ed. New York, NY, USA: Wiley, 1995.
36. N. K. Nikolski, Operators, Functions, and Systems: An Easy Reading. Vol. 2, ser. Mathematical Surveys and Monographs. Providence, RI, USA: Amer. Math. Soc., 2002, vol. 93.