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Asymptotic Value of the Probability That the First Order Statistic Is from Null Hypothesis
Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea
Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea
School of Information, Communications, and Electronics Engineering, The Catholic University of Korea, Bucheon, South Korea
College of Information and Communication Engineering, Sungkyunkwan University, Suwon, South Korea
- 1 Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea
- 2 Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea
- 3 School of Information, Communications, and Electronics Engineering, The Catholic University of Korea, Bucheon, South Korea
- 4 College of Information and Communication Engineering, Sungkyunkwan University, Suwon, South Korea
Applied Mathematics·Volume 04 (2013)·Pages 1702–1705·Published 8 November 2013·DOI10.4236/am.2013.412231
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Abstract
When every element of a random vector X =( X 1 , X 2 , ... , X n ) assumes the cumulative distribution function F 0 and F 1 with probability p and 1 - p , respectively, we have shown that the probability S 0 that the first order statistic of X is originally under F 0 can be expressed as . We have also shown that , where and with the support of F i (x) . Applications and implications of the results are discussed in the performance of wideband spectrum sensing schemes.
KeywordsEnergyOrder StatisticProbabilitySpectrum Sensing
- T. Yücek and H. Arslan, “A Survey of Spectrum Sensing Algorithms for Cognitive Radio Applications,” IEEE Communications Surveys and Tutorials, Vol. 11, No. 1, 2009, pp. 116-130.
- Z. Quan, S. Cui, A. H. Sayed and H. V. Poor, “Optimal Multiband Joint Detection for Spectrum Sensing in Cognitive Radio Networks,” IEEE Transactions on Signal Processing, Vol. 57, No. 3, 2009, pp. 1128-1140. http://dx.doi.org/10.1109/TSP.2008.2008540
- A. Taherpour, M. Nasiri-Kenari and S. Gazor, “Multiple Antenna Spectrum Sensing in Cognitive Radios,” IEEE Transactions on Wireless Communications, Vol. 9, No. 2, 2010, pp. 814-823. http://dx.doi.org/10.1109/TWC.2009.02.090385
- P. Paysarvi-Hoseini and N. C. Beaulieu, “Optimal Wideband Spectrum Sensing Framework for Cognitive Radio Systems,” IEEE Transactions on Signal Processing, Vol. 59, No. 3, 2011, pp. 1170-1182. http://dx.doi.org/10.1109/TSP.2010.2096220
- T. An, H.-K. Min, S. Lee and I. Song, “Likelihood Ratio Test for Wideband Spectrum Sensing,” Proceedings of IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, Victoria, 27-29 August 2013.
- H. A. David and H. N. Nagaraja, “Order Statistics,” 3rd edition, John Wiley and Sons, New York, 2003. http://dx.doi.org/10.1002/0471722162
- I. Song, K. S. Kim, S. R. Park and C. H. Park, “Principles of Random Processes,” Kyobo, Seoul, 2009.
- V. K. Rohatgi and A. K. Md. E. Saleh, “An Introduction to Probability and Statistics,” 2nd edition, John Wiley and Sons, New York, 2001.
- I. S. Gradshteyn and I. M. Ryzhik, “Table of Integrals, Series, and Products,” Academic, New York, 1980.
- J. Hajek, Z. Sidak and P. K. Sen, “Theory of Rank Tests,” 2nd edition, Academic, New York, 1999.