Compressive Sampling And Reconstruction Of Sparse Wideband Signals

With the development of science and technology,the number of radio signals is increasing,and the required spectral spectrum is also expanding.Due to the wide spectral range,sampling based on Nyquist-Shannon sampling theorem causes excessive pressure to the analog-to-digital converter(ADC).In view of the shortcomings of traditional sampling mode,compressed sensing(CS)theory is proposed by some scholars and it has become a new research direction in modern signal processing field.In the aspect of analog signal acquisition,sampling under CS theory effectively reduce the pressure on ADC when collecting broadband signal.In the aspect of signal parameter estimation,if the CS data can be processed directly to estimate signal parameters without the reconstruction of original signal,sampling pressure on ADC can be reduced and resources wasting in the process of reconstruction can be avoided.Therefore,study on analog signal acquisition and parameter estimation based on CS theory is of great application value.This dissertation focuses on the compressive sampling and reconstruction of sparse wideband signals,as well as parameters estimation of wideband linear frequency modulated(LFM)signals based on CS theory.The main contributions are illustrated as follows:(1)An adaptive threshold reconstruction algorithm for joint sparse recovery problem is proposed based on simultaneous orthogonal matching pursuit(SOMP)algorithm.It is suitable for the case that both signal sparsity and signal-to-noise ratio(SNR)are unknown.Based on eigen-decomposition of the autocorrelation matrix of received signal,the noise energy can be roughly estimated from the eigenvalues corresponding to noise subspaces,to determine the optimal threshold value.The proposed algorithm is an iterative algorithm,and it stops when the residual improvement of two consecutive iterations is less than the optimal threshold.Compared with SOMP algorithm with a fixed threshold,the proposed algorithm has better reconstruction performance.(2)A compressive sampling system—modulated wideband converter(MWC)is researched.For the MWC with digital sub-channel separation block,we point out that channel gain mismatch and time delay of the practical system cause the existence of an unknown multiplicative diagonal matrix in the system model,and propose a calibration scheme to estimate the unknown matrix.Sending several training signals into the system,we can estimate the matrix from the outputs by solving a convex optimization problem.Then,the calibrated system model is obtained,and the estimates of channel gains and time delays can be calculated from the estimate of the diagonal matrix.(3)For the multi-coset sampling system,a windowing discrete blind reconstruction method is proposed to recovery a multiband signal from the sampling sequence of infinite length.To avoid the spectrum leakage of original signal,the sampling sequence is segmented into blocks by a window function,and the blocks are stitched together after the reconstruction was conducted on each block.In the process of reconstructing each block,the major operations are performed on the low-rate sequences,and the sequences are interpolated to the Nyquist rate after all nonzero spectrum slices are recovered by CS reconstruction algorithm.Hence,the computational complexity of reconstruction process is reduced compared with that of previous methods.(4)Based on undersampling,a parameter-estimation method for multi-component LFM signal is proposed.The received signal is undersampled by multiple ADCs with identical sampling rate and different sampling start time.The total sampling rate of ADCs is lower than the Nyquist rate of original LFM signal.As the product high-order ambiguity function of an undersampling sequence is single tone,the chirp rate is estimated by peak search.Then dechirp operation is completed for all undersampling sequences,and the initial frequencies of LFM components are estimated by solving the moment-preserving problem and over-determined equations.The proposed method is suitable for mulple LFM components with the same chirp rate and different initial frequencies,and it is easily realized with simple operations.(5)A framework of sub-Nyquist sampling and parameters estimation for single-component LFM signal is proposed based on CS theory.The sub-Nyquist sampling is implemented by a two-channel system,with an undersampling channel and a random demodulation(RD)channel.The chirp rate,as well as information related to center frequency,is estimated from the undersampled sequence by the ambiguity function slice and the proper fractional Fourier transform.Then the center frequency is estimated according to the correlation between the output and the sensing matrix of RD.With the absence of CS reconstruction algorithms,the estimation can be implemented with a low computational complexity.