Property Investigation on the Additive White Gaussian Noise After Sub-Nyquist Sampling

The sub-Nyquist sampling (SNS) has emerged as an appealing technique for wideband signal sampling and has found its applications in many areas, such as, cognitive radios, radar and medical imaging, etc.. However, existing SNS based approaches generally assume that the output noise of SNS (termed as SNS noise) is generated as the additive white Gaussian noise without considering the SNS effect. To give more insights on the noise after SNS, we propose a generalized modulated converter to represent existing prevalent SNS systems and give an analysis on statistics of the SNS noise in terms of the proposed SNS system. The noise folding factor and the uncorrelated and white keeping properties are derived and concluded from the derived statistics, in which the former is used to show the noise enhancement by SNS and the latter describes the SNS noise uncorrelation and equal power intensity in different frequencies, respectively. In the final, simulation results validate the derived results and conclusions.