Asymptotic distribution of circularity coefficients estimate of complex random variables

Signal Processing

Volumn 89, Issue 12, 2009, Pages 2670-2675

  Delmas, Jean Pierre ^a   Abeida, Habti ^a  

^a TELECOM SUDPARIS   (France)

Author keywords

Canonical correlations; Circular noncircular; Circularity coefficients; Circularity spectrum; Coherence matrix; Proper improper; Rectilinear signal

Indexed keywords

CANONICAL CORRELATIONS; CIRCULAR/NONCIRCULAR; CIRCULARITY COEFFICIENTS; CIRCULARITY SPECTRUM; COHERENCE MATRIX; PROPER/IMPROPER; RECTILINEAR SIGNAL;

ASYMPTOTIC ANALYSIS; DISTRIBUTION FUNCTIONS; MAXIMUM LIKELIHOOD ESTIMATION; RANDOM PROCESSES; VISUAL COMMUNICATION;

RANDOM VARIABLES;

EID: 67651124813     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2009.05.013     Document Type: Article

References (21)

1. Picinbono B., and Chevalier P. Widely linear estimation with complex data. IEEE Trans. Signal Process. 43 8 (August 1995) 2030-2033
2. Schreier P.J., Scharf L., and Mullis C.T. Detection and estimation of improper complex random signals. IEEE Trans. Inform. Theory 51 1 (January 2005) 306-312
3. Delmas J.P. Asymptotically minimum variance second-order estimation for non-circular signals with application to DOA estimation. IEEE Trans. Signal Process. 52 5 (May 2004) 1235-1241
4. Schreier P.J., and Scharf L. Second-order analysis of improper complex random vectors and processes. IEEE Trans. Signal Process. 51 3 (March 2003) 714-725
5. Picinbono B. Second-order complex random vectors and normal distributions. IEEE Trans. Signal Process. 44 10 (October 1996) 2637-2640
6. Eriksson J., and Koivunen V. Complex random vectors and ICA models, uniqueness, and separability: identifiability. IEEE Trans. Inform. Theory 52 3 (March 2006) 1017-1029
7. Schreier P.J., Scharf L., and Hanssen A. A generalized likelihood ratio test for impropriety of complex signals. IEEE Signal Process. Lett. 13 7 (July 2006) 433-436
8. Schreier P.J. Bound on the degree of improperty of complex random vectors. IEEE Signal Process. Lett. 15 (2008) 190-193
9. P.J. Schreier, The degree of improperty (noncircularity) of complex random vectors, in: Proceedings of the ICASSP, Las Vegas, April 2008.
10. H. Abeida, J.P. Delmas, On the degree of second-order non-circularity of complex random variables, in: Proceedings of the ICASSP, Las Vegas, April 2008.
11. Chargé P., Wang Y., and Saillard J. A non-circular sources direction finding method using polynomial rooting. Signal Process. 81 (2001) 1765-1770
12. M. Haardt, F. Römer, Enhancements of unitary ESPRIT for non circular sources, in: International Conference on ASSP Montreal, May 2004.
13. Abeida H., and Delmas J.P. MUSIC-like estimation of direction of arrival for non-circular sources. IEEE Trans. Signal Process. 54 7 (July 2006) 2678-2690
14. Abeida H., and Delmas J.P. Statistical performance of MUSIC-like algorithms in resolving noncircular sources. IEEE Trans. Signal Process. 56 9 (September 2008) 4317-4329
15. Neeser F.D., and Massey J.L. Proper complex random processes with applications to information theory. IEEE Trans. Inform. Theory 39 4 (July 1993) 1293-1302
16. Chevalier P., and Pipon F. New insights into optimal widely linear array receivers for the demodulation of BPSK, MSK and GMSK signals corrupted by non circular interferences-application to SAIC. IEEE Trans. Signal Process. 54 3 (March 2006) 870-883
17. Brewer J.W. Kronecker products and matrix calculus in system theory. IEEE Trans. Circuits System CAS-25 (September 1978) 772-781
18. I.T. Jolliffe, Principal Component Analysis, in: Springer Series in Statistics, 2002.
19. Serfling R.J. Approximation Theorems of Mathematical Statistics (1980), Wiley, New York
20. A Horn R., and Johnson C.R. Matrix Analysis (1985), Cambridge University Press, Cambridge
21. J.R. Magnus, H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, in: Wiley Series in Probability And Statistics, revised ed., 1999.