The Sampling And Reconstruction Technology Of Ultra-wideband Sparse Signal

With the increasing complexity of electromagnetic environment,the processing bandwidth of signal of modern electronic warfare in various fields increases significantly.The demand for signal reception,transmission and storage is improving constantly,and the traditional sampling theorem has become the bottleneck of the development of Ultra-wideband signal.As a revolutionary technology,the Compressed Sensing theory(Compressive Sensing,CS)only depends on whether the signal itself is sparse.Not only the sampling frequency is much lower than the Nyquist sampling frequency,but also the sampling and compression can be carried out simultaneously.However,the object of CS theory is discrete signal.In the process of electronic reconnaissance,most of the signals are analog signals,which can be directly compressed and sampled by using an Analog-to-Information-converter(AIC).Non-uniform sampling structure(Non-uniform Sampling,NUS)is a special structure of AIC,which is characterized by simple structure and strong engineering feasibility.In this paper,the CS theory is combined to compress the ultra-wideband sparse signal directly.The nonuniform sampling signal is reconstructed by using OMP algorithm,LASSO algorithm and BCS algorithm respectively.In order to reduce the computational complexity and improve the reconfiguration efficiency,the EM algorithm,TD algorithm and ATD algorithm are used to reconstruct the power spectral density(PSD)directly to obtain spectrum information.The main contents of this paper are as follows:1.First,we introduce the CS theory and a non-uniform sampling structure(NUS).We use three different algorithms to recover the non-uniform sampling signal.According to the simulation results,the conclusions are as follows: OMP algorithm needs the shortest computing time with high reconstruction efficiency.But the reconstruction accuracy is low,the computational complexity is high,a large number of observations are needed,and the obtained solution is usually sub optimal.LASSO algorithm can recover the original signal very well under the condition that the number of observations is small.The amount of calculation is small,the reconstruction accuracy is higher and it is easier to obtain the optimal solution,but the computing time is longer,it does not meet the real-time requirements.With the increase of the number of observations,BSC algorithm has the advantages of little change in time consumption,at the same time it has good robustness.And it has better reconstruction performance when the number of observations is low and the noise is high.2.Reconstruction algorithm not only has high computational complexity,but also may cause loss of signal information.Therefore,we propose to estimate the PSD of the non-uniform sampling signal directly,which can reduce the computational complexity and improve the reconstruction efficiency.Based on the autocorrelation of the signal in the time domain.We use a non-uniform sampling model based on the predetermined pattern,and estimate the missing signal by EM algorithm.Since the EM algorithm does not change the PSD edge,and the edge vector is approximate sparse in the frequency domain,we can combine the CS theory to reconstruct PSD through the estimating edge position of the PSD.3.Last we introduce a non-uniform sampling structure based on Minimal Sparse Ruler(MSR),we obtain the relationship between autocorrelation vector of the original signal and autocorrelation vector of the measurement vector by using TD and ATD two kinds of algorithm,then reconstruct the autocorrelation vector of the original signal by using the least square method and obtain the PSD,finally the spectrum of the original signal can be recovered directly,which reduce the amount of calculation and hardware pressure.