Detection and estimation of improper complex random signals

P.J. Schreier, L.L. Scharf, C.T. Mullis, IEEE Trans.\ Inform.\ Theory 51 (2005) 306–312.

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Journal Article
Author
Schreier, Peter J.; Scharf, Louis L.; Mullis, Clifford T.
Abstract
Nonstationary complex random signals are in general improper (not circularly symmetric), which means that their complementary covariance is nonzero. Since the Karhunen-Loeve (K-L) 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 improper observable coordinates. We then use the K-L expansion to solve the problems of detection and estimation of improper complex random signals in additive white Gaussian noise. We derive a general result comparing the performance of conventional processing, which ignores complementary covariances, with processing that takes these into account. In particular, for the detection and estimation problems considered, we find that the performance gain, as measured by deflection and mean-squared error (MSE), respectively, can be as large as a factor of 2. In a communications example, we show how this finding generalizes the result that coherent processing enjoys a 3-dB gain over noncoherent processing.
Publishing Year
Journal Title
IEEE Trans.\ Inform.\ Theory
Volume
51
Issue
1
Page
306–312
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Schreier PJ, Scharf LL, Mullis CT. Detection and estimation of improper complex random signals. IEEE Trans\ Inform\ Theory. 2005;51(1):306–312. doi:10.1109/TIT.2004.839538
Schreier, P. J., Scharf, L. L., & Mullis, C. T. (2005). Detection and estimation of improper complex random signals. IEEE Trans.\ Inform.\ Theory, 51(1), 306–312. https://doi.org/10.1109/TIT.2004.839538
@article{Schreier_Scharf_Mullis_2005, title={Detection and estimation of improper complex random signals}, volume={51}, DOI={10.1109/TIT.2004.839538}, number={1}, journal={IEEE Trans.\ Inform.\ Theory}, author={Schreier, Peter J. and Scharf, Louis L. and Mullis, Clifford T.}, year={2005}, pages={306–312} }
Schreier, Peter J., Louis L. Scharf, and Clifford T. Mullis. “Detection and Estimation of Improper Complex Random Signals.” IEEE Trans.\ Inform.\ Theory 51, no. 1 (2005): 306–312. https://doi.org/10.1109/TIT.2004.839538.
P. J. Schreier, L. L. Scharf, and C. T. Mullis, “Detection and estimation of improper complex random signals,” IEEE Trans.\ Inform.\ Theory, vol. 51, no. 1, pp. 306–312, 2005, doi: 10.1109/TIT.2004.839538.
Schreier, Peter J., et al. “Detection and Estimation of Improper Complex Random Signals.” IEEE Trans.\ Inform.\ Theory, vol. 51, no. 1, 2005, pp. 306–312, doi:10.1109/TIT.2004.839538.

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