Research On Compressive Sampling Techniques Of Sparse Multiband Signals

The radio resources below 3 GHz are becoming increasingly congested, users tend to transmit narrowband signals with high carrier frequencies. In a wide frequency range, it is normal that multi-user signals exist at the same time. When use Nyquist sampling theorem to sample and process the signal, many problems will occur, such as the selection of high sampling rate analog to digital converter (ADC) and the great pressure to the digital storage. It is very important to choose the proper sampling technique to reduce the analog and digital sampling rates in wideband communications, especially in the case of limited digital resources. In this paper, two application scenarios are considered, the main work and contributions are presented as follows:In order to receive, compress, store and recover a single-band RF signal, the local oscillator scanning method is used to determine the center frequency of the signal, and the signal is down-converted near the baseband. The bandpass signal is sampled first and compressed later. In analog terminal, the bandpass signal is sampled with a high sampling rate according to the Nyquist sampling theorem. In digital terminal, a extraction and interpolation program is designed according to the bandpass sampling theorem. The related Verilog program is implemented and the program is tested in FPGA. The results show that the program can realize compressed storage of bandpass signal. With respect to the original sampling rate, the program can reduce 66.7% storage space and realize low distortion recovery.For the detection and recovery of multiband sparse signal, the modulated wideband converter (MWC) structure is employed. The structure is based on the compressive sensing theory and integrate the sampling and compression steps together, which can decrease the high sampling rate of analog terminal. However, the basic structure of MWC has too much channel numbers and the expanded structure of MWC has high single-channel sampling rate with complex digital computation. In order to solve the above problems, a quadrature frequency conversion down-sampling structure based on the MWC is proposed. With this structure, the frequency shift portion of the expanded structure is transferred advanced to the analog front end, which decreases the digital computation complexity and low single-channel sampling rate is maintained. Moreover, the channel numbers comparing to basic structure of MWC are decreased. The proposed structure and the expanded structure of MWC are proved to be equivalent in both mathematical and physical meanings. Simulation results show that, in the absence of noise occasion, the proposed structure performs no worse than the other two structures. In addition, the proposed structure performs even better in white gaussian noise environment.When we use the 1-bit CS algorithm to recover the support set of signal, it requires more observation channel numbers to improve the performance, which increase hardware complexity. In this paper, a group binary iterative hard thresholding lp method solving multiple measurement vector problems (M-GBIHT lP) is proposed. The proposed algorithm utilizes the group sparsity of recovered signal, ties the nonzero locations together and regards it as a group. We find the largest groups instead of finding the largest elements to locate the nonzero supports. Experiments show that the proposed algorithm achieve higher reconstruction probability than the existed simultaneous binary iterative hard thresholding l2 norm (SBIHTl2) algorithm, particularly in low signal to noise ratio (SNR) enviroment.