Fast Reconstruction Of Radar Signals With Compressive Sampling

Compressive sampling or compressed sensing(CS)is a signal representation theory,which represents a sparse signal at a rate much lower than the Nyquist rate.As an application of CS theory,analog-to-information(AIC)efficiently performs sub-Nyquist sampling of sparse analog signals,and thus obtains wide and in-depth research on the sampling of wide-band signals.In radar applications,AIC can implement the sub-Nyquist rate sampling of wideband and ultra-wideband radar signals and thus provides a new strategy for the develop-ment of wideband and ultra-wideband radars.However,in some applications,it is often re-quired to recover the Nyqusit-rate radar echoes from the sub-Nquist rate samples.From the CS theory,this is a large-scale sparse reconstruction problem.It is difficult to perform re-al-time reconstruction by using the current sparse reconstruction algorithms because of huge storage and large computational load.There are different AIC systems according to the signals to be sampled.Currently,the AIC systems can be divided into three categories:lowpass-type AIC,bandpass-type AIC,and mutiband-type AIC.In this dissertation,we develop fast reconstruction schemes of Nyquist-rate radar signals with the radar echoes sampled by the three types of AIC systems.The main works and contributions of this dissertation are as follows:1.Applying the random demodulation(RD)AIC to the sampling of the pulsed radar baseband signals,we propose a segment-sliding reconstruction(SegSR)scheme,which can realize fast recovery of radar baseband echoes.RD is typical of lowpass-type AIC systems.We apply the RD system to perform sub-Nyquist sampling of the radar baseband echoes.Based on the characteristics of RD sys-tem and the sparse representation of the radar baseband echoes,we find that the measurement matrix has a banded structure,and then propose a SegSR scheme.The SegSR scheme divides the compressive measurement data obtained during the observation time into overlapping segments,and then transforms the large-scale sparse reconstruction problem into a series of small-scale sparse reconstruction sub-problems.Finally,the fast reconstruction is realized by solving each sub-problem in a sliding mode.With the anaysis of the effect of the interference introduced from the adjacent segments,we theoretically analyze the reconstruction perfor?mance of the SegSR scheme,and validate the effectiveness by simulations.2.Applying the quadrature compressive sampling(QuadCS)AIC to the sampling of pulsed radar bandpass signal,we propose an approximation scheme to achieve the fast recon-struction of the radar baseband echoes.As a bandpass-type AIC system,QuadCS can perform sub-Nyquist sampling of bandpass analog signals,and acquire the compressive measurements of in-phase and quadrature(I/Q)components.We use the QuadCS system to sample the radar echoes at the intermediate fre-quency.With thorough analyses on the QuadCS system,we find that the QuadCS measure-ment matrix can be approximately transformed into a banded one wllich has a structure simi-lar to the RD measurement matrix.Then we apply the SegSR scheme to the QuadCS samples to realize the fast reconstruction.We theoretically analyze the reasonableness of the approxi-mation scheme,and demonstrate the feasibility and effectiveness by simulations.3.Applying the multiband quadrature compressive sampling(MQCS)AIC to the sam-pling of pulsed radar multiband signals,we propose a block-sparsity-based segment-sliding reconstruction(B SegSR)scheme,which can realize fast recovery of the baseband compo-nents of each subband echo.MQCS is a multiband-type AIC system,which can realize sub-Landau sampling of multiband analog signals,and obtain the compressive I/Q measurements of each subband signal.The multiband radar signals with equal-bandwidth subbands are considered.We apply the MQCS system to sample the multiband radar signals at sub-Landau rate.With the anal-yses on the multiband radar echoes,we reveal the block sparsity of the echo signals and es-tablish a block-sparse reconstruction model to recover all subband echoes.Then we develop a BSegSR scheme for fast reconstruction.The BSegSR scheme decomposes the large-scale block-sparse reconstruction problem into a series of small-scale block-sparse reconstruction sub-problems.As in the SegSR,the BSegSR reconstructs each subband component in a slid-ing mode.Numerical simulations demonstrate the effectiveness of the BSegSR scheme.4.Applying the SegSR scheme to fast reconstruction of moving target echo signals,we propose an orthogonal-projection-based weighted sparse segment-sliding reconstruction(OP-WSegSR)scheme of multiple pulse echoes.Different from a single pulse echo,the moving targets may be across range cells in a co-herent processing interval and thus the echo signals have the property of the time-varying sparsity.We adopt a random model to describe the sparsity and transform the reconstruction of the multiple echoes into a weighted sparse reconstruction problem.With the developed SegSR,we propose an OP-WSegSR scheme for fast reconstruction.As in the SegSR of a sin-gle pulse echo,the adjacent segments will introduce the interference affecting the estimation of the current segments.According to the estimation of sparse positions in the previous pulse,the proposed scheme constructs an orthogonal complement subspace of the interference sub-space,and projects the measurements of the current segment onto the complement subspace.Then the adjacent interference is greatly rejected.Simulations show the effectiveness of the OP-WSegSR scheme.