The Karhunen-Loève expansion of improper complex random signals with applications in detection
P.J. Schreier, L.L. Scharf, in: Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 2003, pp. 717–720.
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Conference Paper
Author
Schreier, Peter J.;
Scharf, Louis L.
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Abstract
Non-stationary complex random signals are in general improper (not circularly symmetric), which means that their complementary covariance is non-zero. Since the Karhunen-Loeve expansion in its known form is only valid for proper processes, we derive the improper version of this expansion. It produces two sets of eigenvalues and an improper internal description. We use the Karhunen-Loeve expansion to solve the problem of detecting non-stationary improper complex random signals in additive white Gaussian noise. Using the deflection criterion we compare the performance of conventional processing, which ignores complementary covariances, with processing that takes these into account. The performance gain can be as great as a factor of 2.
Publishing Year
Proceedings Title
Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process.
Volume
6
Page
717–720
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Cite this
Schreier PJ, Scharf LL. The Karhunen-Loève expansion of improper complex random signals with applications in detection. In: Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process. Vol 6. ; 2003:717–720. doi:10.1109/ICASSP.2003.1201782
Schreier, P. J., & Scharf, L. L. (2003). The Karhunen-Loève expansion of improper complex random signals with applications in detection. Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 6, 717–720. https://doi.org/10.1109/ICASSP.2003.1201782
@inproceedings{Schreier_Scharf_2003, title={The Karhunen-Loève expansion of improper complex random signals with applications in detection}, volume={6}, DOI={10.1109/ICASSP.2003.1201782}, booktitle={Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process.}, author={Schreier, Peter J. and Scharf, Louis L.}, year={2003}, pages={717–720} }
Schreier, Peter J., and Louis L. Scharf. “The Karhunen-Loève Expansion of Improper Complex Random Signals with Applications in Detection.” In Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 6:717–720, 2003. https://doi.org/10.1109/ICASSP.2003.1201782.
P. J. Schreier and L. L. Scharf, “The Karhunen-Loève expansion of improper complex random signals with applications in detection,” in Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 2003, vol. 6, pp. 717–720, doi: 10.1109/ICASSP.2003.1201782.
Schreier, Peter J., and Louis L. Scharf. “The Karhunen-Loève Expansion of Improper Complex Random Signals with Applications in Detection.” Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., vol. 6, 2003, pp. 717–720, doi:10.1109/ICASSP.2003.1201782.
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