An asymptotic GLRT for the detection of cyclostationary signals
D. Ramírez, L.L. Scharf, J. Vía, I. Santamaría, P.J. Schreier, in: Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., Florence, Italy, 2014.
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Author
Ramírez, D.;
Scharf, L. L.;
Vía, J.;
Santamaría, I.;
Schreier, P. J.
Department
Abstract
We derive the generalized likelihood ratio test (GLRT) for detecting cyclostationarity in scalar-valued time series. The main idea behind our approach is Gladyshev’s relationship, which states that when the scalar-valued cyclostationary sig- nal is blocked at the known cycle period it produces a vector- valued wide-sense stationary process. This result amounts to saying that the covariance matrix of the vector obtained by stacking all observations of the time series is block-Toeplitz if the signal is cyclostationary, and Toeplitz if the signal is wide- sense stationary. The derivation of the GLRT requires the maximum likelihood estimates of Toeplitz and block-Toeplitz matrices. This can be managed asymptotically (for large num- berofsamples)exploitingSzego ̈’stheoremanditsgeneraliza- tion for vector-valued processes. Simulation results show the good performance of the proposed GLRT.
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Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process.
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Ramírez D, Scharf LL, Vía J, Santamaría I, Schreier PJ. An asymptotic GLRT for the detection of cyclostationary signals. In: Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process. ; 2014. doi:10.1109/ICASSP.2014.6854234
Ramírez, D., Scharf, L. L., Vía, J., Santamaría, I., & Schreier, P. J. (2014). An asymptotic GLRT for the detection of cyclostationary signals. Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process. https://doi.org/10.1109/ICASSP.2014.6854234
@inproceedings{Ramírez_Scharf_Vía_Santamaría_Schreier_2014, place={Florence, Italy}, title={An asymptotic GLRT for the detection of cyclostationary signals}, DOI={10.1109/ICASSP.2014.6854234}, booktitle={Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process.}, author={Ramírez, D. and Scharf, L. L. and Vía, J. and Santamaría, I. and Schreier, P. J.}, year={2014} }
Ramírez, D., L. L. Scharf, J. Vía, I. Santamaría, and P. J. Schreier. “An Asymptotic GLRT for the Detection of Cyclostationary Signals.” In Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process. Florence, Italy, 2014. https://doi.org/10.1109/ICASSP.2014.6854234.
D. Ramírez, L. L. Scharf, J. Vía, I. Santamaría, and P. J. Schreier, “An asymptotic GLRT for the detection of cyclostationary signals,” 2014, doi: 10.1109/ICASSP.2014.6854234.
Ramírez, D., et al. “An Asymptotic GLRT for the Detection of Cyclostationary Signals.” Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 2014, doi:10.1109/ICASSP.2014.6854234.
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