Compressive Sensing Based On Sparse Fourier Transform

Compressive Sensing(CS) is one of the most popular topics in signal processing. In recent years, CS has made great improvement in both theory and application. Various signal acquisition frameworks based on CS have been proposed, and some representative frameworks are Analog-to-Information Converter (AIC), Mudulated Wideband Converter (MWC)and Sparse Fourier Transform (SFT) based framework. Due to their dependence on mixers of Nyquist Rate, AIC and MWC have disadvantages in complexity and energy coconsumption. The SFT based framework does not need high speed mixers. It can be implemented on commodity radios,so it has promising prospect in applications.Studies the theory and its application in wideband spectrum sensing of SFT based CS, focusing on its reconstruction algorithm. With the purpose of promoting robustness, designs a streaming signals acquisition framework and proposes a simultaneous reconstruction algorithm. Finally,studies and analyzes the hardware implementation system based on SFT.The main contributions of this paper are described as follows:1) Focusing on the reconstruction algorithm, Peeling Decoder. Analyzes the impact of additive noise mathematically. Studies the bottle neck of Peeling Decoder, and indicates some possible approaches to improve its capability. Studies the setting principle of key system parameters,like time delay and down-sampling rate. Calculates the theoretical optimum time delay. Deduces the mathematical relationship between down-sampling rate and the failure probability when the occupancy of the spectrum is fixed.2) Designs a streaming signals acquisition framework based on sliding window. On this basis, proposes a simultaneous reconstruction algorithm based on jointly sparse. However, signals in the real world are dynamic. Their supports are changing over time, so the jointly sparse property cannot be guaranteed. To solve this, designs an adaptive mechanism, which makes the proposed simultaneous reconstruction algorithm can perform equally well even when the signals are dynamic.3) Designs a USRP hardware implementation system based on the previous work. Since in implementation system, the fluctuation of the frequency response of different devices should be taken into account,this paper modifies the sampling model and reconstruction algorithm.Some key parameters of the system, like time delay and frequency response, are unknown and need to be estimated. First analyzes the impact that the estimation deviation might bring to the system, then deduces the maximum permissible deviation. Finally, proposes a parameters estimation schema, which is easy to operate and has high acccuracy.