Research And Application Of Compressed Sensing Reconstruction

The theory of compressed sensing(CS)breaks through the restriction on the lower limit of sampling frequency in Nyquist's theorem,and has attracted broad attention once it was proposed.CS can effectively solve the problem of high sampling rate.What's more,it also has good anti-noise performance.Thus it has been widely applied in military and civil fields.The problem of high sampling rate caused by the wide bandwidth of frequency hopping(FH)signal and the problem of error code in channel coding can be both solved by CS.This paper mainly focuses on the reconstruction algorithm of CS and its application in FH signals and channel coding.The work of this paper can be summarized as following aspects:(1)The reconstruction algorithm of CS is studied in depth,including the L1 based algorithm and greedy algorithm.The reconstruction performance of multiple algorithms is compared and analyzed.Specifically,the effects of sparsity,compression ratio and SNR on reconstruction accuracy and time complexity are studied.(2)The application of CS in the field of HF communication is studied.On the one hand,the FH signal is block-sparse in the frequency domain.On the other hand,the receiver knows the key information of the FH signal before reconstruction.These two characteristics are not taken into account in the existing reconstruction algorithm of FH signal,which leads to poor performance in terms of accuracy and time complexity.To solve this problem,a new reconstruction algorithm of FH signal is proposed in this paper.In the proposed algorithm,the key information of the FH signal is used to find the central atom.According to the block-sparsity of HF signal in the frequency domain,the corresponding atoms in the main lobe and a few sidelobe are selected into the support set.And then the original FH signal is reconstructed.This method only needs to select the atoms once,which avoids the problem of low precision and high time complexity caused by the multiple iterations.In addition,noise plays an important role in the reconstruction of FH signals.The influence of noise on the reconstruction of HF signal is not taken into account in the existing reconstruction algorithm of FH signal,resulting in the low accuracy.To solve this problem,an adaptive reconstruction algorithm of HF signal is also proposed in this paper.In the proposed algorithm,the noise is judged according to the characteristic that the noise with same energy has different effects on the main and side lobes.Then the number of non-zero values of the reconstructed signal is determined based on the SNR,so that the original FH signal can be reconstructed adaptively with SNR.The proposed algorithm improves the reconstruction accuracy without increasing the time complexity,especially in the case of low SNR.(3)The application of CS in channel coding is studied.Specifically,a method of linear block codec based on compressed sensing is studied.The method completes the decoding by applying reconstruction algorithm,which improving the accuracy under low SNR by taking the advantage of the anti-noise performance of CS.However,the method does not take into account the randomness of the observation matrix,which affects the accuracy.To solve this problem,an improved codec method based on CS is proposed in this paper.The proposed method applies the idea of CS to the encoder,and designs a new coding matrix to ensure the randomness of observation matrix,which improves the accuracy.