Large deviations for eigenvalues of sample covariance matrices, with applications to mobile communication systems

Advances in Applied Probability

Volumn 40, Issue 4, 2008, Pages 1048-1071

  Fey, Anne ^a   van der Hofstad, Remco ^b   Klok, Marten J ^a,c  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c ORTEC The Netherlands   (Netherlands)

Author keywords

CDMA with soft decision parallel interference cancellation; Eigenvalue; Large deviation; Sample covariance matrix

Indexed keywords

BINARY SEQUENCES; CELLULAR TELEPHONE SYSTEMS; CODE DIVISION MULTIPLE ACCESS; COMMUNICATION SYSTEMS; DECODING; EIGENVALUES AND EIGENFUNCTIONS; MOBILE COMPUTING; MOBILE TELECOMMUNICATION SYSTEMS; NUCLEIC ACIDS; OPTICAL COMMUNICATION; ORGANIC ACIDS; PROBABILITY DENSITY FUNCTION; RADIO BROADCASTING; RADIO INTERFERENCE; RANDOM VARIABLES; SIGNAL INTERFERENCE;

ALMOST SURE; BIT ERRORS; CDMA WITH SOFT-DECISION PARALLEL INTERFERENCE CANCELLATION; CODING SEQUENCES; EIGENVALUE; EQUAL PROBABILITIES; HIGH-DIMENSIONAL; LARGE DEVIATION; LARGE DEVIATION PROPERTIES; LARGEST EIGENVALUES; MOBILE COMMUNICATION SYSTEMS; N MATRIXES; NORMAL RANDOM VARIABLES; RATE FUNCTIONS; SAMPLE COVARIANCE MATRIX; SAMPLE COVARIANCES; STUDY SAMPLES; WISHART MATRICES;

COVARIANCE MATRIX;

EID: 59549091666     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1231340164     Document Type: Article

References (23)

1. BAI, Z. D. AND SILVERSTEIN, J. W. (1998). No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Ann. Prob. 26, 316-345.
2. BAI, Z. D. AND SILVERSTEIN, J. W. (2004). CLT for linear spectral statistics of large-dimensional sample covariance matrices. Ann. Prob. 32, 553-605.
3. BAI, Z. D. AND YIN, Y. Q. (1993). Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix. Ann. Prob. 21, 1275-1294.
4. BAI, Z. D., SILVERSTEIN, J. W. AND YIN, Y. Q. (1988). A note on the largest eigenvalue of a large-dimensional sample covariance matrix. J. Multivariate Anal. 26, 166-168.
5. BUEHRER, R. M., NICOLOSO, S. P. AND GOLLAMUDI, S. (1999). Linear versus non-linear interference cancellation. J. Commun. Networks 1, 118-133.
6. DEMBO, A. AND ZEITOUNI, O. (1998). Large Deviations Techniques and Applications, 2nd edn. Springer, New York.
7. DEN HOLLANDER, F. (2000). Large Deviations (Fields Inst. Monogr. 14). American Mathematical Society, Providence, RI.
8. FEY-DEN BOER, A. C., VAN DER HOFSTAD, R. AND KLOK, M. J. (2003). Linear interference cancellation in CDMA systems and large deviations of the correlation matrix eigenvalues. In Proc. Symp. LEEE Benelux Chapter Commum. Veh. Tech. (Eindhoven, 2003).
9. GRANT, A. AND SCHLEGEL, C. (2001). Convergence of linear interference cancellation multiuser receivers. IEEE Trans. Commun. 49, 1824-1834.
10. GUIONNET, A. (2002). Large deviations asymptotics for spherical integrals. J. Funct. Anal. 188, 461-515.
11. GUO, D., RASMUSSEN, L. K., TUN, S. AND LIM, T. J. (2000). A matrix-algebraic approach to linear parallel interference cancellation in CDMA. IEEE Trans. Commun. 48, 152-161.
12. HIAI, F. AND PETZ, D. (1998). Eigenvalue density of the Wishart matrix and large deviations. Infin. Dimens. Anal. Quantum Prob. 1, 633-646.
13. KLOK, M. J. (2001). Performance analysis of advanced third generation receivers. Doctoral Thesis, Delft University of Technology.
14. MARCHENKO, V. A. AND PASTUR, L. A. (1967). The distribution of eigenvalues in certain sets of random matrices. Mat. Sb. 72, 507-536.
15. OLIVIERI, E. AND VARES, A E. (2005). Large Deviations and Metastability (Encyclopedia Math. Appl. 100). Cambridge University Press.
16. RASMUSSEN, L. K. AND OPPERMANN, I. J. (2003). Ping-pong effects in linear parallel interference cancellation for CDMA. IEEE Trans. Wireless Commun. 2, 357-363.
17. ROGERS, C. A. (1963). Covering a sphere with spheres. Mathematika 10, 157-164.
18. VAN DER HOFSTAD, R. AND KLOK, M. J. (2003). Performance of DS-CDMA systems with optimal hard-decision parallel interference cancellation. IEEE Trans. Inf. Theory 25, 2918-2940.
19. VAN DER HOFSTAD, R. AND KLOK, M. J. (2004). Improving the performance of third-generation wireless communication systems. Adv. Appl. Prob. 36, 1046-1084.
20. VAN DER HOFSTAD, R., HOOGHIEMSTRA, G. AND KLOK, M. J. (2002). Analytical methods for CDMA systems with parallel interference cancellation: the large deviation approach. Wireless Personal Commun. 21, 289-307.
21. VAN DER HOFSTAD, R. HOOGHIEMSTRA, G. AND KLOK, M. J. (2002). Large deviations for code division multiple access systems. SIAM J. Appl. Math. 62, 1044-1065.
22. VAN DER HOFSTAD, R., LÖWE, M. AND VERMET, F. (2006). The effect of system load on the existence of bit errors in CDMA with and without parallel interference cancelation. IEEE Trans. Inf. Theory 52, 4733-4741.
23. YIN, Y. Q., BAI, Z. D, AND KRISHNAIAH, P. R. (1988). On the limit of the largest eigenvalue of the large-dimensional sample covariance matrix. Prob. Theory Relat. Fields 78, 509-521.