| Citation: | Jianxin GAI, Haochen DU, Qi LIU, Ziquan TONG. Sub-Nyquist Sampling Recovery Algorithm Based on Kernel Space of the Random-compression Sampling Value Matrix[J]. Journal of Electronics & Information Technology, 2019, 41(2): 484-491. doi: 10.11999/JEIT180323
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To solve the low performance problem of the existing Modulated Wideband Converter (MWC)-based sub-Nyquist sampling recovery algorithm, this paper proposes a support recovery algorithm based on the kernel space of sampling value and a random compression rank-reduction idea. Combining them, a high-performance sampling recovery algorithm is achieved. Firstly random compression transforms are used to convert the sampling equation into several new multiple-measurement-vector problems, without changing the sparsity of the unknown matrix. Then the orthogonal relationship between the kernel space of sampling value and the support vectors of sampling matrix is utilized to obtain joint sparse support set of the unknown. The final recovery is performed by the pseudo inversion. The proposed method is analyzed and verified by theory and experiment. Numerical experiments show that, compared with the traditional recovery algorithm, the proposal can improve the recovery success rate, and reduce the channel number required for high-probability recovery. Furthermore, in general, the recovery performance improves with the rise of compression times.
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