Framework And Applications Of Communication Signal Under-sampling Via Low-rank Approximation

In the field of signal processing,it is well-known that sampling rate should be higher or equal to two times of highest frequency of signal by using Nyquist sampling theorem. Such a high-speed sampling rate leads to higher cost and complexity of algorithms.In real communication scenario,the operation of data recovery is necessary when under-sampling is done. Note that signal is usually affected by noise and other factors in transmission channel. Hence, how to extract useful information from the incomplete signal plays an import role in the signal processing. We found that common communication signal usually has an inherent low-rank structure. Although randomly sampled points are limited,they also contains majority of information. Therefore we can utilize compressive sensing and low-rank matrix reconstruction theory to design a novel low-rank signal demodulation method.In this thesis, we mainly studies the low-rank communication signal recovery and demodulation method under the condition of under-sampling. First we analyze the structure of the low rank signal, and verify the communication signal of the low-rank structure which was affected by the interference between the White Gaussian Noise and the ISI with different SNR by using simulation. Secondly, we propose a novel recovery and signal demodulation algorithm based on rank-1 decomposition. Compared with different signal recovery algorithms, it is shown that the proposed method provides the best performance.Last, the recovery algorithm and rank-1 decomposition demodulation algorithm are implemented by self-developed software radio platform to verify the correctness of the algorithm. With the FPGA implement the down-sampling, and the DSP achieve the recovery algorithm of the under-sampling signal and demodulation algorithm of DSSS signal. Then study the recovery performance of many communication signals under difference sample ratio and frequencies and discuss the demodulation capability with different SNR, which verifies the reliability of the algorithm.