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Mathematical Problems in Engineering
Volume 2016, Article ID 3406731, 6 pages
Research Article

Statistical Properties of SNR for Compressed Measurements

1Department of Communication Engineering, Harbin Institute of Technology, Harbin 150080, China
2School of Computer and Information Engineering, Harbin University of Commerce, Harbin 150028, China

Received 14 April 2016; Accepted 5 September 2016

Academic Editor: Haipeng Peng

Copyright © 2016 Yulong Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Some basic statistical properties of the compressed measurements are investigated. It is well known that the statistical properties are a foundation for analyzing the performance of signal detection and the applications of compressed sensing in communication signal processing. Firstly, we discuss the statistical properties of the compressed signal, the compressed noise, and their corresponding energy. And then, the statistical characteristics of SNR of the compressed measurements are calculated, including the mean and the variance. Finally, probability density function and cumulative distribution function of SNR are derived for the cases of the Gamma distribution and the Gaussian distribution. Numerical simulation results demonstrate the correctness of the theoretical analysis.