Approximate condition number distribution of complex non-central correlated wishart matrices

IEEE International Conference on Communications

Volumn , Issue , 2011, Pages

  Wei, Lu ^a   Tirkkonen, Olav ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

condition number distribution; MIMO systems; moment based approximation; spatially correlated Ricean MIMO channel

Indexed keywords

ARBITRARY MATRICES; CHANNEL CONDITIONS; COGNITIVE RADIO; CONDITION NUMBER DISTRIBUTION; DETECTION PERFORMANCE; FINITE DIMENSIONAL; MIMO CHANNEL; MOMENT BASED APPROXIMATION; PERFORMANCE ANALYSIS; SPATIALLY CORRELATED RICEAN MIMO CHANNEL; STATISTICAL PROPERTIES; WISHART MATRICES;

COGNITIVE SYSTEMS; COMMUNICATION SYSTEMS; COMPUTATIONAL COMPLEXITY; MIMO SYSTEMS; NUMBER THEORY;

MATRIX ALGEBRA;

EID: 80052168459     PISSN: 05361486     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/icc.2011.5962954     Document Type: Conference Paper

References (22)

1. I. E. Telatar, "Capacity of multi-antenna Gaussian channels," Europ. Trans. Telecommun., vol. 10, no. 6, pp. 585-595, Nov./Dec. 1999.
2. M. Chiani, M. Z. Win, and A. Zanella, "On the capacity of spatially correlated MIMO Rayleigh-fading channels," IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2363-2371, Oct. 2003.
3. M. Kang and M. S. Alouini, "Capacity of MIMO Rician channels,"IEEE Trans. Wirel. Commun., vol. 5, no. 1, pp. 112-122, Jan. 2006.
4. P. A. Dighe, R. K. Mallik, and S. R. Jamuar, "Analysis of trasmitreceive diversity in Rayleigh fading," IEEE Tran. Commun., vol. 51, no. 4, pp.694-703, Apr. 2003.
5. M. Kang and M. S. Alouini, "Largest eigenvalue of complex wishart matrices and performance analysis of MIMO MRC systems," IEEE J. Selec. Areas Commun., vol. 21, no. 3, pp. 418-426, Apr. 2003.
6. A. Forenza, A. Pandharipande, H. Kim, and R. W. Heath, Jr, "Adaptive MIMO transmission scheme: exploiting the spatial selectivity of wireless channels," proc. IEEE VTC, 2005-Spring.
7. J. Maurer, G. Matz, and D. Seethaler, "Low-complexity and full diversity MIMO detection based on condition number thresholding," in Proc. IEEE Int. Conf. Acoustics Speech Signal Process. (ICASSP), vol. 3, Honolulu, HI, pp. 61-64, Apr. 2007.
8. Y. Zeng and Y. C. Liang, "Eigenvalue based spectrum sensing algorithms for cognitive radio," IEEE Tran. Commun., vol. 57, no. 6, pp. 1784-1793, Jun. 2009.
9. F. Penna, R. Garello, and M. A. Spirito, "Cooperative spectrum sensing based on the limiting eigenvalue ratio distribution in Wishart matrices,"IEEE Comm. Letters, vol. 13, issue 7, pp. 507-509, Jul. 2009.
10. A. Edelman, "Eigenvalues and condition numbers of random maltrices,"Ph.D. thesis, Massachusetts Institute of Technology, Cambridge (MA), 1989.
11. M. Matthaiou, D. I. Laurenson, and C. X. Wang, "On analytical derivations of the condition number distributions of dual non-central Wishart matrices," IEEE Tran. Wireless Commun., vol. 8, no. 3, pp. 1212-1217, Mar. 2009.
12. M. Matthaiou, M. R. McKay, P. J. Smith, and J. A. Nossek, "On the condition number distribution of complex Wishart matrices," IEEE Tran. Commun., vol. 58, no. 6, pp. 1705-1711, Jun. 2010.
13. T. Rathnarajah, "Topics in complex random matrices and information theory," Ph.D. dissertation, University of Ottawa, 2003.
14. C. G. Khatri, "Non-central distribution of i-th largest characteristic roots of three matrices concerning complex multivariate multivariate normal populations," J. Institute of Ann. Statistical Math., vol. 21, pp. 23-32, 1969.
15. A. Zanella and M. Chiani, "The pdf of the l-th largest eigenvalue of central Wishart matrices and its application to the performance analysis of MIMO systems," IEEE Global Telecommunications Conference (Globecom), New Orleans, USA, Nov. 2008.
16. Z. D. Bai, and J. F. Yao, "Central limit theorems for eigenvalues in a spiked population model," Ann. Inst. H. Poincaré, vol. 44, no. 3, pp. 447-474, 2008.
17. M. Kiessling and J. Speidel, "Statistical prefilter design for MIMO ZF and MMSE receivers based on majorization theory," IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Montreal, Canada, May 2004.
18. M. A. Golberg, "The derivative of a determinant," American Math. Monthly, vol. 79, pp. 1124-1126, Dec. 1972.
19. P. Bianchi, M. Debbah, and J. Najim, "Asymptotic independence in the spectrum of the gaussian unitary ensemble," arXiv: 0811.0979.
20. L. Wei and O. Tirkkonen, "Approximation to the condition number distribution of almost square matrices," IEEE International Workshop on Random Matrix Theory for Wireless Communications (RMTfWC), Oct. 2009.
21. D. V. Hinkley, "On the ratio of two correlated normal random variables,"Biometrika, vol. 56, no. 3, Dec. 1969.
22. D.-S. Shiu, G. J. Foschini, M. J. Gans, and J. M. Kahn, "Fading correlation and its effect on the capacity of multielement antenna systems," IEEE Trans. Commun., vol. 48, no. 3, pp. 502-513, Mar. 2000.