Research On Compressed Sampling Of Multiband Signal Based On Union Of Shift-invariant Spaces

Multiband signal is a kind of signal that appears frequently in area of UWB communication, Radar detection, Cognitive Radio and spectrum monitoring. Acquiring multiband signals for receivers is always an important issue in application. Traditional methods to acquire multiband signals require carrier frequencies of each band. But in practical work, the bands of multiband signals are distributed in a wide frequency range up to scores of GHz with unknown carrier frequencies. Traditional methods cannot handle these scenarios. Due to the potential of the model of Compressed Sensing in Union of Shift-Invariant spaces(CS-USI) to provide diverse compressed sampling structures for blind multiband signals, we can figure out sampling structures that are easy to implement with practical hardware.Research on the principle of the CS-USI model; illustrate the method of dividing spectrum into slices using USI from the perspective of Shannon theory and present the generators of USI in time domain; define “SNR of amplitude spectrum” to weigh the accuracy of amplitude-frequency characteristic of recovered signal.In order to take Compressed Sampling of Multi-Coset(CSMC) into CS-USI model, we analyze CSMC from the perspective of CS-USI, derive corresponding reconstruction equation and illustrate the physical meaning of the process of CSMC in the frequency domain. Extend the sampling function of CSMC to a wider type, and derive the conditions that the sampling function should meet. To verify the feasibility of CSMC with experiments, we design a prototype of CSMC that can work in a relatively low frequency range, including the development of hardware and software; Analyze the influence of system errors to the performance of CS MC theoretically, and propose a Least Square method to estimate these errors. These errors can be used to calibrate sensing matrix in reconstruction algorithm.For the sake of breaking through the limitation of Full-power Bandwidth in ADCs of CSMC, we propose Compressed Sampling of Modulated Multi-Coset(CSMMC), which is capable of working in a wider frequency range. Derive reconstruction equation of CSMMC and sampling function in time domain theoretically, and prove that CSMMC is also an instance of the CS-USI model. Point out the mathematical conditions of mixing function, which provides some basis of selecting sampling function; Simulation results illustrate that CSMMC is qualified for compres sed sampling blind multiband signals and reconstructing with great probability. Carry out detailed simulations to CSMMC, including the number of channels, specific mix function, parameters of low pass filter and ADCs. Propose a method to simplify the number of channels in CSMMC and simulate its feasibility; Point out the property of “selecting sensing” of CSMMC, and propose a method to extend system performance flexibly with parallel structure of CSMMC. Simulation results shows that this parallel structure is adaptive to the scenario in which the sparsity of multiband signal fluctuates greatly.