Statistical Properties of SNR for Compressed Measurements

Abstract EN

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.