Research On The Reconstruction Of Spatio-temporal Undersampled Signals Based On Compressed Sensing

The traditional signal frequency and direction of arrival(DOA)estimation algorithm requires that the sampling process in the time domain and the spatial domain must satisfy the Nyquist sampling theorem.However,in some specific scenarios,such as the array receiving signals with high frequency,adopting Nyquist sampling will mean higher requirements for the signal sampling and processing units of the system,which will increase the system cost and the difficulty for hardware implementation.However,under-sampling will inevitably lead to ambiguous problems in signal parameters estimation.The proposed compressed sensing theory provides a solution to the problem for under-sampling signal reconstruction.In this paper,the signal reconstruction and solving the ambiguous problem under undersampling is fucused on.A spatio-temporal under-sampled signal reconstruction and parameter estimation algorithm based on compressed sensing is proposed.In this paper,the array signal model and the compressed sensing theory are first briefly introduced.The feasibility of the signal reconstruction algorithm based on compressed sensing is verified,and the ambiguous problem of frequency or DOA estimation caused by under-sampling in time domain or spatial domain is analyzed.It is pointed out that under the uniform undersampling strategy,the ambiguous problem of signal reconstruction and parameter estimation cannot be solved by interpolation.Aiming at the problem of frequency estimation ambiguity caused by undersampling in time domain,this paper proposes a multi-channel under-sampling signal reconstruction algorithm based on compressed sensing.In terms of frequency estimation,compared with the current frequency estimation algorithm based on Chinese remainder theorem(CRT),the performance of the estimation in various signal scenarios is simulated and analyzed.Subsequently,for the multi-channel signal reconstruction algorithm,which requires more signal sampling and processing units and higher cost,a single-channel under-sampling signal reconstruction algorithm based on compressed sensing is proposed,which reconstructs the signal with high precision under a single signal sampling channel.In view of the problem that the under-sampling in the space domain leads to the grating lobes and DOA estimation ambiguity,this paper extend the two time-domain under-sampling strategies proposed before to the space-domain,and proposed two sparse array configurations.Combining the theory of compressed sensing with DOA estimation and beamforming,the signal reconstruction of the sparse array with less sensors is successfully done and then the ambiguous problem in DOA estimation and beamforming is solved.Finally,combining the time domain undersampling signal reconstruction technology with the spatial undersampling signal reconstruction technique,two implementation schemes for joint estimation of signal frequency and DOA under spatio-temperal undersampling are proposed,compared with the single temperal undersampling or spatio undersampling.The effectiveness of the joint estimation scheme of the above two parameters was verified by simulation experiments.