The Locally Most Powerful Invariant Test for Detecting a rank-$P$ Gaussian Signal in White Noise
D. Ramírez, J. Iscar, J. Vía, I. Santamaría, L.L. Scharf, in: Proc.\ IEEE Sensor Array and Multichannel Signal Process. Work., Hoboken, NJ, USA, 2012.
Download
No fulltext has been uploaded.
Conference Paper
Author
Ramírez, D.;
Iscar, J.;
Vía, J.;
Santamaría, I.;
Scharf, L. L.
Department
Abstract
Spectrum sensing has become one of the main components of a cognitive transmitter. Conventional detectors suffer from noise power uncertainties and multiantenna detectors have been proposed to overcome this difficulty, and to improve the detection performance. However, most of the proposed multiantenna detectors are based on non-optimal techniques, such as the generalized likelihood ratio test (GLRT), or even heuristic approaches that are not based on first principles. In this work, we derive the locally most powerful invariant test (LMPIT), that is, the optimal invariant detector for close hypotheses, or equivalently, for a low signal-to-noise ratio (SNR). The traditional approach, based on the distributions of the maximal invariant statistic, is avoided thanks to Wijsman’s theorem, which does not need these distributions. Our findings show that, in the low SNR regime, and in contrast to the GLRT, the additional spatial structure imposed by the signal model is irrelevant for optimal detection. Finally, we use Monte Carlo simulations to illustrate the good performance of the LMPIT.
Publishing Year
Proceedings Title
Proc.\ IEEE Sensor Array and Multichannel Signal Process. Work.
LibreCat-ID
Cite this
Ramírez D, Iscar J, Vía J, Santamaría I, Scharf LL. The Locally Most Powerful Invariant Test for Detecting a rank-$P$ Gaussian Signal in White Noise. In: Proc.\ IEEE Sensor Array and Multichannel Signal Process. Work. ; 2012. doi:10.1109/SAM.2012.6250547
Ramírez, D., Iscar, J., Vía, J., Santamaría, I., & Scharf, L. L. (2012). The Locally Most Powerful Invariant Test for Detecting a rank-$P$ Gaussian Signal in White Noise. Proc.\ IEEE Sensor Array and Multichannel Signal Process. Work. https://doi.org/10.1109/SAM.2012.6250547
@inproceedings{Ramírez_Iscar_Vía_Santamaría_Scharf_2012, place={Hoboken, NJ, USA}, title={The Locally Most Powerful Invariant Test for Detecting a rank-$P$ Gaussian Signal in White Noise}, DOI={10.1109/SAM.2012.6250547}, booktitle={Proc.\ IEEE Sensor Array and Multichannel Signal Process. Work.}, author={Ramírez, D. and Iscar, J. and Vía, J. and Santamaría, I. and Scharf, L. L.}, year={2012} }
Ramírez, D., J. Iscar, J. Vía, I. Santamaría, and L. L. Scharf. “The Locally Most Powerful Invariant Test for Detecting a Rank-$P$ Gaussian Signal in White Noise.” In Proc.\ IEEE Sensor Array and Multichannel Signal Process. Work. Hoboken, NJ, USA, 2012. https://doi.org/10.1109/SAM.2012.6250547.
D. Ramírez, J. Iscar, J. Vía, I. Santamaría, and L. L. Scharf, “The Locally Most Powerful Invariant Test for Detecting a rank-$P$ Gaussian Signal in White Noise,” 2012, doi: 10.1109/SAM.2012.6250547.
Ramírez, D., et al. “The Locally Most Powerful Invariant Test for Detecting a Rank-$P$ Gaussian Signal in White Noise.” Proc.\ IEEE Sensor Array and Multichannel Signal Process. Work., 2012, doi:10.1109/SAM.2012.6250547.
Google Scholar