Research On Compressive Sampling And Reconstruction Algorithm Of The Non-stationary Signal

The traditional Shannon-Nyquist sampling theorem requires that the sampling rate must be two times greater than the maximum frequency of the signal.When dealing with the ultra-wideband non-stationary signal,the required sampling rate is extremely high which is almost unachievable,thus this theorem is already not applicable.Therefore,the real-time sampling and reconstruction for this kind of signals becomes a problem ur-gently to be solved.Compressive sampling?CS?can realize the ultra-wideband real-time sampling at a low rate by utilizing the sparsity of signals,and can reconstruct the original signal from the incomplete samples by non-linear algorithm,it is an advanced theory of breaking through the limitation of the sampling theorem.This thesis dives deeply into the compressive sampling and reconstruction of ultra-wideband non-stationary signals,presents a compressive sampling method which is based on the modulated wideband converter?MWC?for signals with ultra-wideband,designs a blind reconstruction algo-rithm for signals which are non-stationary,analyses the theoretical constraint condition that guarantees the target signal can be reconstructed,and applies the compressive sam-pling method and reconstruction algorithm to two kinds of ultra-wideband non-stationary signals:frequency hopping signals and linear frequency modulation signals.The main contribution and innovation of the dissertation are as follows:1.To solve the real-time sampling problem of ultra-wideband non-stationary sig-nals,based on the run length limited?RLL?sequence and MWC,this thesis presents a compressive sampling model named RLL-MWC and the corresponding ultra-wideband sampling method.This method utilizes all harmonics of RLL sequence to alias the spec-trum of target signal into baseband,thus,the signal can be sampled at a low rate in the baseband.Since the RLL sequence contains plenty of higher harmonics,the sampling bandwidth of RLL-MWC is wider than that of the original MWC under the same pa-rameter condition,so it is more applicable for acquiring ultra-wideband signals.In this thesis,an empirical equation which is used for choosing parameters of RLL sequence is given,when the RLL-MWC is correctly configured,using this empirical equation to choose parameter guarantees that the sampling wideband of RLL-MWC can be improved by 25%compared with the MWC.2.To solve the problem that iteration halting conditions of existing reconstruction algorithms are related with the prior information of signal,based on the RLL-MWC,this thesis proposes a halting condition adaptive generation method which does not rely on the prior information of target signal.In the course of compressive sampling,RLL-MWC has to use the continuous-to-finite?CTF?block to reduce the dimension of samples,thus sim-plifies the reconstruction flow.This thesis proves that after dimension reduction,CTF will output a residue which is associated with noise,so the halting condition adaptive generation method can use this residue to estimate the7)₂ norm of noise which resides in the samples.Since the7)₂ norm is only related with samples,using it as the halting condition of iteration algorithm can avoid utilizing the prior information during the re-construction flow,such as the occupied band number and the sparsity level,and thereby the blind signal reconstruction can be realized.3.To solve the reconstruction problem of non-stationary signal after block-sparse decomposition,this thesis proposes a greedy iteration algorithm which achieves an out-standing reconstruction probability and is named block matching pursuit?BMP?.Usually,the non-stationary signal has a high sparsity level,which makes it difficult to be recon-structed,therefore,it will be transformed into a block-sparse signal with a low sparsity level.After transformation,all effective information of the original signal can be repre-sented by a few non-zero entries.If the reconstruction algorithm can find out all these non-zero entries,the original signal can be reconstructed.This thesis proves that as long as the sampling matrix satisfies with a restriction condition related with RIP,the BMP is capable of finding all non-zero entries.Furthermore,the BMP differs from the normal algorithm which only calculates one non-entry in one iteration,it is capable of searching non-zero block by utilizing the piecewise continuity property of non-zero entries,so it can greatly improve the reconstruction probability.4.To solve the real-time sampling problem of frequency hopping signal,based on the Short-Time Fourier Transform?STFT?,this thesis proposes the time-frequency two-dimension sparse decomposition method which makes the frequency hopping signal has the sparsity,then based on this method and the RLL-MWC,proposes a compressive sam-pling model which can directly reconstruct the time-frequency spectrum of frequency hopping signal and is named SMWC.SMWC uses a series of window functions to trun-cate the time domain samples,then transforms these compressive samples of time do-main signal into compressive samples of two-dimension sparse matrix by STFT.This thesis transforms the two-dimension sparse matrix reconstruction problem into a one-dimension block-sparse vector reconstruction problem,and designs an algorithm which is derived from BMP and is capable of processing block-sparse signals.Using these transformed samples can reconstruct the two-dimension sparse matrix which represents the time-frequency spectrum of original signal.5.To solve the real-time sampling problem of linear frequency modulation?LFM?signal,based on the SMWC,this thesis proposes a chirp rate estimation algorithm which can reduce the bandwidth of signal,and then proposes a compressive sampling model which is dedicated to LFM signal and is named CEDMWC.The CEDMWC contains the SMWC,and it leverages the frequency variation of signals of different windows to estimate the chirp rate,thus,converts the LFM signal to the stationary signal which has a relatively low sparsity level and is easier to be reconstructed.However,the estimation algorithm may result in deviation,then the de-chirped signal is“approximate”station-ary for which the conventional reconstruction algorithms are not applicable.Therefore,this thesis designs a multiple measurement vectors-BMP algorithm by utilizing the“row block-sparsity”of sparse matrix of“approximate”stationary signal to realize the sig-nal reconstruction.