Airborne sparse flight array SAR 3D imaging based on compressed sensing in frequency domain

In airborne array synthetic aperture radar(SAR), the three-dimensional(3D) imaging performance and cross-track resolution depends on the length of the equivalent array. In this paper, Barker sequence criterion is used for sparse flight sampling of airborne array SAR, in order to obtain high cross-track resolution in as few times of flights as possible. Under each flight, the imaging algorithm of back projection(BP) and the data extraction method based on modified uniformly redundant arrays(MURAs) are utilized to obtain complex 3D image pairs. To solve the side-lobe noise in images, the interferometry between each image pair is implemented, and compressed sensing(CS) reconstruction is adopted in the frequency domain. Furthermore, to restore the geometrical relationship between each flight, the phase information corresponding to negative MURA is compensated on each single-pass image reconstructed by CS. Finally,by coherent accumulation of each complex image, the high resolution in cross-track direction is obtained. Simulations and experiments in X-band verify the availability.

DOA estimation of high-dimensional signals based on Krylov subspace and weighted l_(1)-norm

With the extensive application of large-scale array antennas,the increasing number of array elements leads to the increasing dimension of received signals,making it difficult to meet the real-time requirement of direction of arrival(DOA)estimation due to the computational complexity of algorithms.Traditional subspace algorithms require estimation of the covariance matrix,which has high computational complexity and is prone to producing spurious peaks.In order to reduce the computational complexity of DOA estimation algorithms and improve their estimation accuracy under large array elements,this paper proposes a DOA estimation method based on Krylov subspace and weighted l_(1)-norm.The method uses the multistage Wiener filter(MSWF)iteration to solve the basis of the Krylov subspace as an estimate of the signal subspace,further uses the measurement matrix to reduce the dimensionality of the signal subspace observation,constructs a weighted matrix,and combines the sparse reconstruction to establish a convex optimization function based on the residual sum of squares and weighted l_(1)-norm to solve the target DOA.Simulation results show that the proposed method has high resolution under large array conditions,effectively suppresses spurious peaks,reduces computational complexity,and has good robustness for low signal to noise ratio(SNR)environment.

Novel imaging methods of stepped frequency radar based on compressed sensing

The theory of compressed sensing （CS） provides a new chance to reduce the data acquisition time and improve the data usage factor of the stepped frequency radar system. In light of the sparsity of radar target reflectivity, two imaging methods based on CS, termed the CS-based 2D joint imaging algorithm and the CS-based 2D decoupled imaging algorithm, are proposed. These methods incorporate the coherent mixing operation into the sparse dictionary, and take random measurements in both range and azimuth directions to get high resolution radar images, thus can remarkably reduce the data rate and simplify the hardware design of the radar system while maintaining imaging quality. Ex- periments from both simulated data and measured data in the anechoic chamber show that the proposed imaging methods can get more focused images than the traditional fast Fourier trans- form method. Wherein the joint algorithm has stronger robustness and can provide clearer inverse synthetic aperture radar images, while the decoupled algorithm is computationally more efficient but has slightly degraded imaging quality, which can be improved by increasing measurements or using a robuster recovery algorithm nevertheless.

Joint 2D DOA and Doppler frequency estimation for L-shaped array using compressive sensing

A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix,three smaller scale matrices with independent azimuth,elevation and Doppler frequency are introduced adopting a separable observation model.Afterwards,the estimation is achieved by L1-norm minimization and the Bayesian CS algorithm.In addition,under the L-shaped array topology,the azimuth and elevation are separated yet coupled to the same radial Doppler frequency.Hence,the pair matching problem is solved with the aid of the radial Doppler frequency.Finally,numerical simulations corroborate the feasibility and validity of the proposed algorithm.

Compressive sensing based multiuser detector for massive MBM MIMO uplink

Media based modulation(MBM)is expected to be a prominent modulation scheme,which has access to the high data rate by using radio frequency(RF)mirrors and fewer transmit antennas.Associated with multiuser multiple input multiple output(MIMO),the MBM scheme achieves better performance than other conventional multiuser MIMO schemes.In this paper,the massive MIMO uplink is considered and a conjunctive MBM transmission scheme for each user is employed.This conjunctive MBM transmission scheme gathers aggregate MBM signals in multiple continuous time slots,which exploits the structured sparsity of these aggregate MBM signals.Under this kind of scenario,a multiuser detector with low complexity based on the compressive sensing(CS)theory to gain better detection performance is proposed.This detector is developed from the greedy sparse recovery technique compressive sampling matching pursuit(CoSaMP)and exploits not only the inherently distributed sparsity of MBM signals but also the structured sparsity of multiple aggregate MBM signals.By exploiting these sparsity,the proposed CoSaMP based multiuser detector achieves reliable detection with low complexity.Simulation results demonstrate that the proposed CoSaMP based multiuser detector achieves better detection performance compared with the conventional methods.

Block Compressed Sensing Image Reconstruction Based on SL0 Algorithm

By applying smoothed l0norm（SL0）algorithm,a block compressive sensing（BCS）algorithm called BCS-SL0 is proposed,which deploys SL0 and smoothing filter for image reconstruction.Furthermore,BCS-ReSL0 algorithm is developed to use regularized SL0（ReSL0）in a reconstruction process to deal with noisy situations.The study shows that the proposed BCS-SL0 takes less execution time than the classical BCS with smoothed projected Landweber（BCS-SPL）algorithm in low measurement ratio,while achieving comparable reconstruction quality,and improving the blocking artifacts especially.The experiment results also verify that the reconstruction performance of BCS-ReSL0 is better than that of the BCSSPL in terms of noise tolerance at low measurement ratio.

COMPRESSED SPEECH SIGNAL SENSING BASED ON THE STRUCTURED BLOCK SPARSITY WITH PARTIAL KNOWLEDGE OF SUPPORT

Structural and statistical characteristics of signals can improve the performance of Compressed Sensing (CS). Two kinds of features of Discrete Cosine Transform (DCT) coefficients of voiced speech signals are discussed in this paper. The first one is the block sparsity of DCT coefficients of voiced speech formulated from two different aspects which are the distribution of the DCT coefficients of voiced speech and the comparison of reconstruction performance between the mixed program and Basis Pursuit (BP). The block sparsity of DCT coefficients of voiced speech means that some algorithms of block-sparse CS can be used to improve the recovery performance of speech signals. It is proved by the simulation results of the mixed program which is an improved version of the mixed program. The second one is the well known large DCT coefficients of voiced speech focus on low frequency. In line with this feature, a special Gaussian and Partial Identity Joint (GPIJ) matrix is constructed as the sensing matrix for voiced speech signals. Simulation results show that the GPIJ matrix outperforms the classical Gaussian matrix for speech signals of male and female adults.

NOVEL METHOD OF MOVING TARGET DETECTION FOR DUAL-CHANNEL WAS RADAR BASED ON COMPRESSED SENSING

We propose a ground moving target detection method for dual-channel Wide Area Surveillance(WAS) radar based on Compressed Sensing(CS).Firstly,the method of moving target detection of the WAS radar is studied.In order to reduce the sample data quantity of the radar,the echo data is randomly sampled in the azimuth direction,then,the matched filter is used to perform the range direction focus.We can use the compressive sensing theory to recover the signal in the Doppler domain.At last,the phase difference between the two channels is compensated to suppress the clutter.The result of the simulated data verifies the effectiveness of the proposed method.

Wavelet-based L_(1/2) regularization for CS-TomoSAR imaging of forested area

Tomographic synthetic aperture radar(TomoSAR)imaging exploits the antenna array measurements taken at different elevation aperture to recover the reflectivity function along the elevation direction.In these years,for the sparse elevation distribution,compressive sensing(CS)is a developed favorable technique for the high-resolution elevation reconstruction in TomoSAR by solving an L_(1) regularization problem.However,because the elevation distribution in the forested area is nonsparse,if we want to use CS in the recovery,some basis,such as wavelet,should be exploited in the sparse L_(1/2) representation of the elevation reflectivity function.This paper presents a novel wavelet-based L_(2) regularization CS-TomoSAR imaging method of the forested area.In the proposed method,we first construct a wavelet basis,which can sparsely represent the elevation reflectivity function of the forested area,and then reconstruct the elevation distribution by using the L_(1/2) regularization technique.Compared to the wavelet-based L_(1) regularization TomoSAR imaging,the proposed method can improve the elevation recovered quality efficiently.

Robust signal recovery algorithm for structured perturbation compressive sensing

It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.

A CLASS OF DETERMINISTIC CONSTRUCTION OF BINARY COMPRESSED SENSING MATRICES

Compressed Sensing (CS) is an emerging technology in the field of signal processing, which can recover a sparse signal by taking very few samples and solving a linear programming problem. In this paper, we study the application of Low-Density Parity-Check (LDPC) Codes in CS. Firstly, we find a sufficient condition for a binary matrix to satisfy the Restricted Isometric Property (RIP). Then, by employing the LDPC codes based on Berlekamp-Justesen (B-J) codes, we construct two classes of binary structured matrices and show that these matrices satisfy RIP. Thus, the proposed matrices could be used as sensing matrices for CS. Finally, simulation results show that the performance of the proposed matrices can be comparable with the widely used random sensing matrices.

AN ADAPTIVE MEASUREMENT SCHEME BASED ON COMPRESSED SENSING FOR WIDEBAND SPECTRUM DETECTION IN COGNITIVE WSN

An Adaptive Measurement Scheme (AMS) is investigated with Compressed Sensing (CS) theory in Cognitive Wireless Sensor Network (C-WSN). Local sensing information is collected via energy detection with Analog-to-Information Converter (AIC) at massive cognitive sensors, and sparse representation is considered with the exploration of spatial temporal correlation structure of detected signals. Adaptive measurement matrix is designed in AMS, which is based on maximum energy subset selection. Energy subset is calculated with sparse transformation of sensing information, and maximum energy subset is selected as the row vector of adaptive measurement matrix. In addition, the measurement matrix is constructed by orthogonalization of those selected row vectors, which also satisfies the Restricted Isometry Property (RIP) in CS theory. Orthogonal Matching Pursuit (OMP) reconstruction algorithm is implemented at sink node to recover original information. Simulation results are performed with the comparison of Random Measurement Scheme (RMS). It is revealed that, signal reconstruction effect based on AMS is superior to conventional RMS Gaussian measurement. Moreover, AMS has better detection performance than RMS at lower compression rate region, and it is suitable for large-scale C-WSN wideband spectrum sensing.

Reconstruction and transmission of astronomical image based on compressed sensing

In the process of image transmission, the famous JPEG and JPEG-2000 compression methods need more transmission time as it is difficult for them to compress the image with a low compression rate. Recently the compressed sensing（CS） theory was proposed, which has earned great concern as it can compress an image with a low compression rate, meanwhile the original image can be perfectly reconstructed from only a few compressed data. The CS theory is used to transmit the high resolution astronomical image and build the simulation environment where there is communication between the satellite and the Earth. Number experimental results show that the CS theory can effectively reduce the image transmission and reconstruction time. Even with a very low compression rate, it still can recover a higher quality astronomical image than JPEG and JPEG-2000 compression methods.

Imaging algorithm of multi-ship motion target based on compressed sensing

An imaging algorithm based on compressed sensing（CS） for the multi-ship motion target is presented. In order to reduce the quantity of data transmission in searching the ships on a large sea area, both range and azimuth of the moving ship targets are converted into sparse representation under certain signal basis. The signal reconstruction algorithm based on CS at a distant calculation station, and the Keystone and fractional Fourier transform（FRFT） algorithm are used to compensate range migration and obtain Doppler frequency. When the sea ships satisfy the sparsity, the algorithm can obtain higher resolution in both range and azimuth than the conventional imaging algorithm. Some simulations are performed to verify the reliability and stability.

Construction of deterministic sensing matrix and its application to DOA estimation

Compressive sensing（CS） has emerged as a novel sampling framework which enables sparse signal acquisition and reconstruction with fewer measurements below the Nyquist rate.An important issue for CS is the construction of measurement matrix or sensing matrix.A new deterministic sensing matrix,named as OOC-B,is proposed by exploiting optical orthogonal codes（OOCs）,Bernoulli matrix and Singer structure,which has the entries of 0,＋1 and-1 before normalization.We have proven that the designed deterministic matrix is asymptotically optimal.In addition,the proposed deterministic sensing matrix is applied to direction of arrival（DOA） estimation of narrowband signals by CS arrays（CSA）processing and CS recovery.Theoretical analysis and simulation results show that the proposed sensing matrix has good performance for DOA estimation.It is very effective for simplifying hardware structure and decreasing computational complexity in DOA estimation by CSA processing.Besides,lower root mean square error（RMSE） and bias are obtained in DOA estimation by CS recovery.

Compensated methods for networked control system with packet drops based on compressed sensing

Due to unreliable and bandwidth-limited characteristics of communication link in networked control systems,the realtime compensated methods for single-output systems and multioutput systems are proposed in this paper based on the compressed sensing(CS)theory and sliding window technique,by which the estimates of dropping data packets in the feedback channel are obtained and the performance degradation induced by packet drops is reduced.Specifically,in order to reduce the cumulative error caused by the algorithm,the compensated estimates for single-output systems are corrected via the regularization term;considering the process of single-packet transmission,a new sequential CS framework of sensor data streams is introduced to effectively compensate the dropping packet on single-channel of multi-output systems;in presence of the medium access constraints on multi-channel,the communication sequence for scheduling is coupled to the algorithm and the estimates of the multiple sensors for multi-output systems are obtained via the regularization term.Simulation results illustrate that the proposed methods perform well and receive satisfactory performance.

Adaptive block greedy algorithms for receiving multi-narrowband signal in compressive sensing radar reconnaissance receiver

This paper extends the application of compressive sensing(CS) to the radar reconnaissance receiver for receiving the multi-narrowband signal. By combining the concept of the block sparsity, the self-adaption methods, the binary tree search,and the residual monitoring mechanism, two adaptive block greedy algorithms are proposed to achieve a high probability adaptive reconstruction. The use of the block sparsity can greatly improve the efficiency of the support selection and reduce the lower boundary of the sub-sampling rate. Furthermore, the addition of binary tree search and monitoring mechanism with two different supports self-adaption methods overcome the instability caused by the fixed block length while optimizing the recovery of the unknown signal.The simulations and analysis of the adaptive reconstruction ability and theoretical computational complexity are given. Also, we verify the feasibility and effectiveness of the two algorithms by the experiments of receiving multi-narrowband signals on an analogto-information converter(AIC). Finally, an optimum reconstruction characteristic of two algorithms is found to facilitate efficient reception in practical applications.

Degradation algorithm of compressive sensing

The compressive sensing （CS） theory allows people to obtain signal in the frequency much lower than the requested one of sampling theorem. Because the theory is based on the assumption of that the location of sparse values is unknown, it has many constraints in practical applications. In fact, in many cases such as image processing, the location of sparse values is knowable, and CS can degrade to a linear process. In order to take full advantage of the visual information of images, this paper proposes the concept of dimensionality reduction transform matrix and then se- lects sparse values by constructing an accuracy control matrix, so on this basis, a degradation algorithm is designed that the signal can be obtained by the measurements as many as sparse values and reconstructed through a linear process. In comparison with similar methods, the degradation algorithm is effective in reducing the number of sensors and improving operational efficiency. The algorithm is also used to achieve the CS process with the same amount of data as joint photographic exports group （JPEG） compression and acquires the same display effect.

EFFECT OF MULTIPATH CHANNEL MODELS TO THE RECOVERY ALGORITHMS ON COMPRESSED SENSING IN UWB CHANNEL ESTIMATION

Multipath arrivals in an Ultra-WideBand (UWB) channel have a long time intervals between clusters and rays where the signal takes on zero or negligible values. It is precisely the signal sparsity of the impulse response of the UWB channel that is exploited in this work aiming at UWB channel estimation based on Compressed Sensing (CS). However, these multipath arrivals mainly depend on the channel environments that generate different sparse levels (low-sparse or high-sparse) of the UWB channels. According to this basis, we have analyzed the two most basic recovery algorithms, one based on linear programming Basis Pursuit (BP), another using greedy method Orthogonal Matching Pursuit (OMP), and chosen the best recovery algorithm which are suitable to the sparse level for each type of channel environment. Besides, the results of this work is an open topic for further research aimed at creating a optimal algorithm specially for application of CS based UWB systems.

THE HIGH RESOLUTION MIMO RADAR SYSTEM BASED ON MINIMIZING THE STATISTICAL COHERENCE OF COMPRESSED SENSING MATRIX

Compressed Sensing (CS) theory is a great breakthrough of the traditional Nyquist sampling theory. It can accomplish compressive sampling and signal recovery based on the sparsity of interested signal, the randomness of measurement matrix and nonlinear optimization method of signal recovery. Firstly, the CS principle is reviewed. Then the ambiguity function of Multiple-Input Multiple-Output (MIMO) radar is deduced. After that, combined with CS theory, the ambiguity function of MIMO radar is analyzed and simulated in detail. At last, the resolutions of coherent and non-coherent MIMO radars on the CS theory are discussed. Simulation results show that the coherent MIMO radar has better resolution performance than the non-coherent. But the coherent ambiguity function has higher side lobes, which caused a deterioration in radar target detection performances. The stochastic embattling method of sparse array based on minimizing the statistical coherence of sensing matrix is proposed. And simulation results show that it could effectively suppress side lobes of the ambiguity function and improve the capability of weak target detection.