Joint Multi-Domain Channel Estimation Based on Sparse Bayesian Learning for OTFS System

Since orthogonal time-frequency space(OTFS)can effectively handle the problems caused by Doppler effect in high-mobility environment,it has gradually become a promising candidate for modulation scheme in the next generation of mobile communication.However,the inter-Doppler interference(IDI)problem caused by fractional Doppler poses great challenges to channel estimation.To avoid this problem,this paper proposes a joint time and delayDoppler(DD)domain based on sparse Bayesian learning(SBL)channel estimation algorithm.Firstly,we derive the original channel response(OCR)from the time domain channel impulse response(CIR),which can reflect the channel variation during one OTFS symbol.Compare with the traditional channel model,the OCR can avoid the IDI problem.After that,the dimension of OCR is reduced by using the basis expansion model(BEM)and the relationship between the time and DD domain channel model,so that we have turned the underdetermined problem into an overdetermined problem.Finally,in terms of sparsity of channel in delay domain,SBL algorithm is used to estimate the basis coefficients in the BEM without any priori information of channel.The simulation results show the effectiveness and superiority of the proposed channel estimation algorithm.

Design and implementation of code acquisition using sparse Fourier transform

Code acquisition is the kernel operation for signal synchronization in the spread-spectrum receiver.To reduce the computational complexity and latency of code acquisition,this paper proposes an efficient scheme employing sparse Fourier transform(SFT)and the relevant hardware architecture for field programmable gate array(FPGA)and application-specific integrated circuit(ASIC)implementation.Efforts are made at both the algorithmic level and the implementation level to enable merged searching of code phase and Doppler frequency without incurring massive hardware expenditure.Compared with the existing code acquisition approaches,it is shown from theoretical analysis and experimental results that the proposed design can shorten processing latency and reduce hardware complexity without degrading the acquisition probability.

Sparse underwater acoustic OFDM channel estimation based on superimposed training

A superimposed training （ST） based channel estimation method is presented that provides accurate estimation of a sparse underwater acoustic orthogonal frequency-division multiplexing （OFDM） channel while improving bandwidth transmission efficiency. A periodic low power training sequence is superimposed on the information sequence at the transmitter. The channel parameters can be estimated without consuming any extra system bandwidth, but an unknown information sequence can interfere with the ST channel estimation method, so in this paper, an iterative method was adopted to improve estimation performance. An underwater acoustic channel＇s properties include large channel dimensions and a sparse structure, so a matching pursuit （MP） algorithm was used to estimate the nonzero taps, allowing the performance loss caused by additive white Gaussian noise （AWGN） to be reduced. The results of computer simulations show that the proposed method has good channel estimation performance and can reduce the peak-to-average ratio of the OFDM channel as well.

DOA estimation of coexisted noncoherent and coherent signals via sparse representation of cleaned array covariance matrix

A new direction finding method is presented to deal with coexisted noncoherent and co- herent signals without smoothing operation. First the direction-of-arrival （DOA） estimation task is herein reformulated as a sparse reconstruction problem of the cleaned array covariance matrix, which is processed to eliminate the affection of the noise. Then by using the block of matrices, the information of DOAs which we pursuit are implied in the sparse coefficient matrix. Finally, the sparse reconstruction problem is solved by the improved M-FOCUSS method, which is applied to the situation of block of matrices. This method outperforms its data domain counterpart in terms of noise suppression, and has a better performance in DOA estimation than the customary spatial smoothing technique. Simulation results verify the efficacy of the proposed method.

DOA ESTIMATION USING A SPARSE LINEAR MODEL BASED ON EIGENVECTORS

To reduce high computational cost of existing Direction-Of-Arrival(DOA) estimation techniques within a sparse representation framework,a novel method with low computational com-plexity is proposed.Firstly,a sparse linear model constructed from the eigenvectors of covariance matrix of array received signals is built.Then based on the FOCal Underdetermined System Solver(FOCUSS) algorithm,a sparse solution finding algorithm to solve the model is developed.Compared with other state-of-the-art methods using a sparse representation,our approach also can resolve closely and highly correlated sources without a priori knowledge of the number of sources.However,our method has lower computational complexity and performs better in low Signal-to-Noise Ratio(SNR).Lastly,the performance of the proposed method is illustrated by computer simulations.

Inter-Carrier Interference-Aware Sparse Time-Varying Underwater Acoustic Channel Estimation Based on Fast Reconstruction Algorithm

In this paper,a fast orthogonal matching pursuit(OMP)algorithm based on optimized iterative process is proposed for sparse time-varying underwater acoustic(UWA)channel estimation.The channel estimation consists of calculating amplitude,delay and Doppler scaling factor of each path using the received multi-path signal.This algorithm,called as OIP-FOMP,can reduce the computationally complexity of the traditional OMP algorithm and maintain accuracy in the presence of severe inter-carrier interference that exists in the time-varying UWA channels.In this algorithm,repeated inner product operations used in the OMP algorithm are removed by calculating the candidate path signature Hermitian inner product matrix in advance.Efficient QR decomposition is used to estimate the path amplitude,and the problem of reconstruction failure caused by inaccurate delay selection is avoided by optimizing the Hermitian inner product matrix.Theoretical analysis and simulation results show that the computational complexity of the OIP-FOMP algorithm is reduced by about 1/4 compared with the OMP algorithm,without any loss of accuracy.

Fast Sparse Multipath Channel Estimation with Smooth L0 Algorithm for Broadband Wireless Communication Systems

Broadband wireless channels are often time dispersive and become strongly frequency selective in delay spread domain. Commonly, these channels are composed of a few dominant coefficients and a large part of coefficients are approximately zero or under noise floor. To exploit sparsity of multi-path channels (MPCs), there are various methods have been proposed. They are, namely, greedy algorithms, iterative algorithms, and convex program. The former two algorithms are easy to be implemented but not stable;on the other hand, the last method is stable but difficult to be implemented as practical channel estimation problems be-cause of computational complexity. In this paper, we introduce a novel channel estimation strategy using smooth L0 (SL0) algorithm which combines stable and low complexity. Computer simulations confirm the effectiveness of the introduced algorithm. We also give various simulations to verify the sensing training signal method.

Parameter estimation of maneuvering targets in OTHR based on sparse time-frequency representation

This paper proposes a new method for estimating the parameter of maneuvering targets based on sparse time-frequency transform in over-the-horizon radar（OTHR）. In this method, the sparse time-frequency distribution of the radar echo is obtained by solving a sparse optimization problem based on the short-time Fourier transform. Then Hough transform is employed to estimate the parameter of the targets. The proposed algorithm has the following advantages： Compared with the Wigner-Hough transform method, the computational complexity of the sparse optimization is low due to the application of fast Fourier transform（FFT）. And the computational cost of Hough transform is also greatly reduced because of the sparsity of the time-frequency distribution. Compared with the high order ambiguity function（HAF） method, the proposed method improves in terms of precision and robustness to noise. Simulation results show that compared with the HAF method, the required SNR and relative mean square error are 8 dB lower and 50 dB lower respectively in the proposed method. While processing the field experiment data, the execution time of Hough transform in the proposed method is only 4% of the Wigner-Hough transform method.

DOA estimation based on multi-frequency joint sparse Bayesian learning for passive radar

This paper considers multi-frequency passive radar and develops a multi-frequency joint direction of arrival(DOA)estimation algorithm to improve estimation accuracy and resolution.The developed algorithm exploits the sparsity of targets in the spatial domain.Specifically,we first extract the required frequency channel data and acquire the snapshot data through a series of preprocessing such as clutter suppression,coherent integration,beamforming,and constant false alarm rate(CFAR)detection.Then,based on the framework of sparse Bayesian learning,the target’s DOA is estimated by jointly extracting the multi-frequency data via evidence maximization.Simulation results show that the developed algorithm has better estimation accuracy and resolution than other existing multi-frequency DOA estimation algorithms,especially under the scenarios of low signalto-noise ratio(SNR)and small snapshots.Furthermore,the effectiveness is verified by the field experimental data of a multi-frequency FM-based passive radar.

DOA estimation via sparse recovering from the smoothed covariance vector

A direction of arrival（DOA） estimation algorithm is proposed using the concept of sparse representation. In particular, a new sparse signal representation model called the smoothed covariance vector（SCV） is established, which is constructed using the lower left diagonals of the covariance matrix. DOA estimation is then achieved from the SCV by sparse recovering, where two distinguished error limit estimation methods of the constrained optimization are proposed to make the algorithms more robust. The algorithm shows robust performance on DOA estimation in a uniform array, especially for coherent signals. Furthermore, it significantly reduces the computational load compared with those algorithms based on multiple measurement vectors（MMVs）. Simulation results validate the effectiveness and efficiency of the proposed algorithm.

DOA Estimation Method Using Sparse Representation with Orthogonal Projection

In order to reduce the effect of noises on DOA estimation,this paper proposes a direc-tion-of-arrival(DOA)estimation method using sparse representation with orthogonal projection(OPSR).The OPSR method obtains a new covariance matrix by projecting the covariance matrix of the array data to the signal subspace,leading to the elimination of the noise subspace.After-wards,based on the new covariance matrix after the orthogonal projection,a new sparse representa-tion model is established and employed for DOA estimation.Simulation results demonstrate that compared to other methods,the OPSR method has higher angle resolution and better DOA estima-tion performance in the cases of few snapshots and low SNRs.

DOA estimation method for wideband signals by block sparse reconstruction

For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.

An improved sparsity estimation variable step-size matching pursuit algorithm

To improve the reconstruction performance of the greedy algorithm for sparse signals, an improved greedy algorithm, called sparsity estimation variable step-size matching pursuit, is proposed. Compared with state-of-the-art greedy algorithms, the proposed algorithm incorporates the restricted isometry property and variable step-size, which is utilized for sparsity estimation and reduces the reconstruction time, respectively. Based on the sparsity estimation, the initial value including sparsity level and support set is computed at the beginning of the reconstruction, which provides preliminary sparsity information for signal reconstruction. Then, the residual and correlation are calculated according to the initial value and the support set is refined at the next iteration associated with variable step-size and backtracking. Finally, the correct support set is obtained when the halting condition is reached and the original signal is reconstructed accurately. The simulation results demonstrate that the proposed algorithm improves the recovery performance and considerably outperforms the existing algorithm in terms of the running time in sparse signal reconstruction.

Sparsity-Aware Channel Estimation for mmWave Massive MIMO: A Deep CNN-Based Approach

The deep convolutional neural network(CNN)is exploited in this work to conduct the challenging channel estimation for mmWave massive multiple input multiple output(MIMO)systems.The inherent sparse features of the mmWave massive MIMO channels can be extracted and the sparse channel supports can be learnt by the multi-layer CNN-based network through training.Then accurate channel inference can be efficiently implemented using the trained network.The estimation accuracy and spectrum efficiency can be further improved by fully utilizing the spatial correlation among the sparse channel supports of different antennas.It is verified by simulation results that the proposed deep CNN-based scheme significantly outperforms the state-of-the-art benchmarks in both accuracy and spectrum efficiency.

Target parameter estimation for OTFS-integrated radar and communications based on sparse reconstruction preprocessing

Orthogonal time-frequency space(OTFS)is a new modulation technique proposed in recent years for high Doppler wireless scenes.To solve the parameter estimation problem of the OTFS-integrated radar and communications system,we propose a parameter estimation method based on sparse reconstruction preprocessing to reduce the computational effort of the traditional weighted subspace fitting(WSF)algorithm.First,an OTFS-integrated echo signal model is constructed.Then,the echo signal is transformed to the time domain to separate the target angle from the range,and the range and angle of the detected target are coarsely estimated by using the sparse reconstruction algorithm.Finally,the WSF algorithm is used to refine the search with the coarse estimate at the center to obtain an accurate estimate.The simulations demonstrate the effectiveness and superiority of the proposed parameterestimation algorithm.

An efficient channel estimator for OFDM system with sparse multipath fading

A channel estimator used in sparse muhipath fading channel for orthogonal frequency division multiplexing （OFDM） system is proposed. The dimension of signal subspace can be reduced to improve the performance of channel estimation. The simplified version of original subspace fitting algorithm is employed to derive the sparse multipaths. In order to overcome the difficulty of termination condition, we consider it as a model identification problem and the set of nonzero paths is found under the generalized Akaike information criterion （GAIC）. The computational complexity can be kept very low under proper training design. Our proposed method is superior to other related schemes due to combining the procedure of selecting the most probable taps with GAIC model selection. Simulation in hilly terrain （HT） channel shows that the proposed method has an outstanding performance.

Minimum MSE Weighted Estimator to Make Inferences for a Common Risk Ratio across Sparse Meta-Analysis Data

The paper aims to discuss three interesting issues of statistical inferences for a common risk ratio (RR) in sparse meta-analysis data. Firstly, the conventional log-risk ratio estimator encounters a number of problems when the number of events in the experimental or control group is zero in sparse data of a 2 × 2 table. The adjusted log-risk ratio estimator with the continuity correction points based upon the minimum Bayes risk with respect to the uniform prior density over (0, 1) and the Euclidean loss function is proposed. Secondly, the interest is to find the optimal weights of the pooled estimate that minimize the mean square error (MSE) of subject to the constraint on where , , . Finally, the performance of this minimum MSE weighted estimator adjusted with various values of points is investigated to compare with other popular estimators, such as the Mantel-Haenszel (MH) estimator and the weighted least squares (WLS) estimator (also equivalently known as the inverse-variance weighted estimator) in senses of point estimation and hypothesis testing via simulation studies. The results of estimation illustrate that regardless of the true values of RR, the MH estimator achieves the best performance with the smallest MSE when the study size is rather large and the sample sizes within each study are small. The MSE of WLS estimator and the proposed-weight estimator adjusted by , or , or are close together and they are the best when the sample sizes are moderate to large (and) while the study size is rather small.

Multiple Emitters Localization by UAV with Nested Linear Array:System Scheme and 2D-DOA Estimation Algorithm

Unmanned Aerial Vehicle(UAV)equipped with uniform linear array has been applied to multiple emitters localization.Meanwhile,nested linear array enables to enhance localization resolution and achieve under-determined Direction of Arrival(DOA)estimation.In this paper,we propose a new system structure for emitters localization that combines the UAV with nested linear array,which is capable of significantly increasing the positioning accuracy of interested targets.Specifically,a localization scheme is designed to obtain the paired two-dimensional DOA(2D-DOA,i.e.azimuth and elevation angles)estimates of emitters by nested linear array with UAV.Furthermore,we propose an improved DOA estimation algorithm for emitters localization that utilizes Discrete Fourier Transform(DFT)method to obtain coarse DOA estimates,subsequently,achieve the fine DOA estimates by sparse representation.The proposed algorithm has lower computational complexity because the coarse DOA estimates enable to shrink the range of over-complete dictionary of sparse representation.In addition,compared to traditional uniform linear array,improved 2D-DOA estimation performance of emitters can be obtained with a nested linear array.Extensive simulation results testify the effectiveness of the proposed method.

Compressed sensing based channel estimation for fast fading OFDM systems

A compressed sensing（CS） based channel estimation algorithm is proposed by using the delay-Doppler sparsity of the fast fading channel.A compressive basis expansion channel model with sparsity in both time and frequency domains is given.The pilots in accordance with a novel random pilot matrix in both time and frequency domains are sent to measure the delay-Doppler sparsity channel.The relatively nonzero channel coefficients are tracked by random pilots at a sampling rate significantly below the Nyquist rate.The sparsity channels are estimated from a very limited number of channel measurements by the basis pursuit algorithm.The proposed algorithm can effectively improve the channel estimation performance when the number of pilot symbols is reduced with improvement of throughput efficiency.

Single frame super-resolution reconstruction based on sparse representation

In order to effectively improve the quality of recovered images, a single frame super-resolution reconstruction method based on sparse representation is proposed. The combination method of local orientation estimation-based image patch clustering and principal component analysis is used to obtain a series of geometric dictionaries of different orientations in the dictionary learning process. Subsequently, the dictionary of the nearest orientation is adaptively assigned to each of the input patches that need to be represented in the sparse coding process. Moreover, the consistency of gradients is further incorporated into the basic framework to make more substantial progress in preserving more fine edges and producing sharper results. Two groups of experiments on different types of natural images indicate that the proposed method outperforms some state-of- the-art counterparts in terms of both numerical indicators and visual quality.