A multi-channel sub-nyquist sampling method based on spectrum co-prime permutation

Abstract

In this paper, we investigate sub-Nyquist sampling method, which can work at the sampling rate below the Nyquist rate. Nowadays, the sampling rate of the classical sub-Nyquist sampling is higher than discrete Compressed Sensing (CS), since the sparseness of the original signal is always destroyed by basis mismatch. We propose a new multi-channel co-prime sampling system along with Sparse Fourier Transform. The analog signal of each channel is firstly mixed by a series of exponential functions. Then, it is fed into integrators and commercial analog-to-digital converters (ADCs). It is noted that the frequency parameters of each subsystem are co-prime. Chinese remainder theorem (CRT) is utilized for the joint processing of all sets of samples and the reconstruction of original signals. Finally, the effects of the signal sparsity, the sampling rate and the signal to noise ratio are simulated in this system. In addition, the experimental results show that the proposed system can work at the rate lower than Random Demodulation RD), Modulated wideband converter (MWC) and their improved version.