Abstract
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.
Highlights
Benefiting from the compressed sensing (CS) theory [1], sub-Nyquist sampling (SNS) has emerged as an appealing technique to break through the bottleneck of traditional sampling techniques for wideband signal sampling [2]
Even though the noise can be generally described as the additive white Gaussian noise (AWGN) in practice, the simple assumption of SNS noise could lead to an inaccurate description of SNS noise statistics without considering the SNS effect introduced to the input noise
The input noise corrupting the received signal is generated as a zero mean AWGN, whose power is determined according to the signal power in order to keep a pre-defined value of signal to noise ratio (SNR)
Summary
Benefiting from the compressed sensing (CS) theory [1], sub-Nyquist sampling (SNS) has emerged as an appealing technique to break through the bottleneck of traditional sampling techniques for wideband signal sampling [2]. Different from previous works, in this paper, we employ a concrete SNS system instead of using a discrete sensing matrix and we investigate the noise property in a continuous manner without any approximation. Statistics of the SNS noise, such as mean, variance, covariance and power spectral density (PSD), are derived based on a continuous manner analysis. These statistics show that the SNS noise follows the UWKPs and is proportional to the variance of the input AWGN by a noise folding factor.
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