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.

Vector Approximate Message Passing with Sparse Bayesian Learning for Gaussian Mixture Prior

Compressed sensing(CS)aims for seeking appropriate algorithms to recover a sparse vector from noisy linear observations.Currently,various Bayesian-based algorithms such as sparse Bayesian learning(SBL)and approximate message passing(AMP)based algorithms have been proposed.For SBL,it has accurate performance with robustness while its computational complexity is high due to matrix inversion.For AMP,its performance is guaranteed by the severe restriction of the measurement matrix,which limits its application in solving CS problem.To overcome the drawbacks of the above algorithms,in this paper,we present a low complexity algorithm for the single linear model that incorporates the vector AMP(VAMP)into the SBL structure with expectation maximization(EM).Specifically,we apply the variance auto-tuning into the VAMP to implement the E step in SBL,which decrease the iterations that require to converge compared with VAMP-EM algorithm when using a Gaussian mixture(GM)prior.Simulation results show that the proposed algorithm has better performance with high robustness under various cases of difficult measurement matrices.

Probabilistic outlier detection for sparse multivariate geotechnical site investigation data using Bayesian learning

Various uncertainties arising during acquisition process of geoscience data may result in anomalous data instances(i.e.,outliers)that do not conform with the expected pattern of regular data instances.With sparse multivariate data obtained from geotechnical site investigation,it is impossible to identify outliers with certainty due to the distortion of statistics of geotechnical parameters caused by outliers and their associated statistical uncertainty resulted from data sparsity.This paper develops a probabilistic outlier detection method for sparse multivariate data obtained from geotechnical site investigation.The proposed approach quantifies the outlying probability of each data instance based on Mahalanobis distance and determines outliers as those data instances with outlying probabilities greater than 0.5.It tackles the distortion issue of statistics estimated from the dataset with outliers by a re-sampling technique and accounts,rationally,for the statistical uncertainty by Bayesian machine learning.Moreover,the proposed approach also suggests an exclusive method to determine outlying components of each outlier.The proposed approach is illustrated and verified using simulated and real-life dataset.It showed that the proposed approach properly identifies outliers among sparse multivariate data and their corresponding outlying components in a probabilistic manner.It can significantly reduce the masking effect(i.e.,missing some actual outliers due to the distortion of statistics by the outliers and statistical uncertainty).It also found that outliers among sparse multivariate data instances affect significantly the construction of multivariate distribution of geotechnical parameters for uncertainty quantification.This emphasizes the necessity of data cleaning process(e.g.,outlier detection)for uncertainty quantification based on geoscience data.

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.

Sparse Bayesian learning in ISAR tomography imaging

Inverse synthetic aperture radar(ISAR) imaging can be regarded as a narrow-band version of the computer aided tomography(CT). The traditional CT imaging algorithms for ISAR, including the polar format algorithm(PFA) and the convolution back projection algorithm(CBP), usually suffer from the problem of the high sidelobe and the low resolution. The ISAR tomography image reconstruction within a sparse Bayesian framework is concerned. Firstly, the sparse ISAR tomography imaging model is established in light of the CT imaging theory. Then, by using the compressed sensing(CS) principle, a high resolution ISAR image can be achieved with limited number of pulses. Since the performance of existing CS-based ISAR imaging algorithms is sensitive to the user parameter, this makes the existing algorithms inconvenient to be used in practice. It is well known that the Bayesian formalism of recover algorithm named sparse Bayesian learning(SBL) acts as an effective tool in regression and classification,which uses an efficient expectation maximization procedure to estimate the necessary parameters, and retains a preferable property of the l0-norm diversity measure. Motivated by that, a fully automated ISAR tomography imaging algorithm based on SBL is proposed.Experimental results based on simulated and electromagnetic(EM) data illustrate the effectiveness and the superiority of the proposed algorithm over the existing algorithms.

EARLY CATARACT DETECTION BY DYNAMIC LIGHT SCATTERING WITH SPARSE BAYESIAN LEARNING

Dynamic light scattering(DLS)is a promising technique for early cataract detection and for studying cataractogenesis.A novel probabilistic analysis tool,the sparse Bayesian learning(SBL)algorithm,is described for reconstructing the most-probable size distribution ofα-crystallin and their aggregates in an ocular lens from the DLS data.The performance of the algorithm is evaluated by analyzing simulated correlation data from known distributions and DLS data from the ocular lenses of a fetal calf,a Rhesus monkey,and a man,so as to establish the required efficiency of the SBL algorithm for clinical studies.

OTFS系统SBL-Turbo压缩感知信道估计算法

针对正交时频空调制(OTFS)系统由多普勒频移引起的信道估计准确度下降的问题,本文提出了一种联合无线信道在时延-多普勒域稀疏特性的SBL-Turbo压缩感知信道估计算法。首先,对时延-多普勒域稀疏信道建模,使其服从以噪声功率为条件的高斯先验分布,利用稀疏贝叶斯学习模块估计得到稀疏信道的均值与方差,并结合期望最大化算法更新高斯先验模型中的参数。其次,引入了LMMSE(线性最小均方误差)估计器模块,该模块对稀疏信道的后验分布进行再估计,提高估计的准确度。通过对每个模块估计得到的信道后验分布进行数据处理,使得模块的输入值与输出值解耦,进而减少模块间的错误传播。最后,两个模块采用Turbo结构迭代估计信道的后验分布,得到信道状态信息。实验结果表明,相较于其他估计方法,该算法能够显著提高信道估计的精度,并且改善系统的误码率性能,能够有效地解决OTFS系统中由多普勒频移引起的信道估计问题。

Learning Bayesian networks by constrained Bayesian estimation

Bayesian networks (BNs) have become increasingly popular in recent years due to their wide-ranging applications in modeling uncertain knowledge. An essential problem about discrete BNs is learning conditional probability table (CPT) parameters. If training data are sparse, purely data-driven methods often fail to learn accurate parameters. Then, expert judgments can be introduced to overcome this challenge. Parameter constraints deduced from expert judgments can cause parameter estimates to be consistent with domain knowledge. In addition, Dirichlet priors contain information that helps improve learning accuracy. This paper proposes a constrained Bayesian estimation approach to learn CPTs by incorporating constraints and Dirichlet priors. First, a posterior distribution of BN parameters is developed over a restricted parameter space based on training data and Dirichlet priors. Then, the expectation of the posterior distribution is taken as a parameter estimation. As it is difficult to directly compute the expectation for a continuous distribution with an irregular feasible domain, we apply the Monte Carlo method to approximate it. In the experiments on learning standard BNs, the proposed method outperforms competing methods. It suggests that the proposed method can facilitate solving real-world problems. Additionally, a case study of Wine data demonstrates that the proposed method achieves the highest classification accuracy.

Synthetic aperture radar imaging based on attributed scatter model using sparse recovery techniques

The sparse recovery algorithms formulate synthetic aperture radar （SAR） imaging problem in terms of sparse representation （SR） of a small number of strong scatters＇ positions among a much large number of potential scatters＇ positions, and provide an effective approach to improve the SAR image resolution. Based on the attributed scatter center model, several experiments were performed with different practical considerations to evaluate the performance of five representative SR techniques, namely, sparse Bayesian learning （SBL）, fast Bayesian matching pursuit （FBMP）, smoothed 10 norm method （SL0）, sparse reconstruction by separable approximation （SpaRSA）, fast iterative shrinkage-thresholding algorithm （FISTA）, and the parameter settings in five SR algorithms were discussed. In different situations, the performances of these algorithms were also discussed. Through the comparison of MSE and failure rate in each algorithm simulation, FBMP and SpaRSA are found suitable for dealing with problems in the SAR imaging based on attributed scattering center model. Although the SBL is time-consuming, it always get better performance when related to failure rate and high SNR.

基于稀疏恢复的快速高精度DOA估计算法

传统的基于稀疏恢复的波达方向(direction of arrival,DOA)估计算法使用密集的采样网格,导致计算量显著增加,且对邻近入射信号的估计精度不高。针对这一问题,提出一种快速高精度DOA估计算法。该算法首先使用网格进化方法降低网格点总数。然后,对噪声方差和信号功率进行二次估计,进而使用离网求根稀疏贝叶斯学习(off-grid root sparse Bayesian learning,OGRSBL)技术来实现入射角的精确估计。仿真表明,相比传统稀疏贝叶斯学习类算法,所提算法计算效率高,同时对紧邻信号有着更好的估计能力。

一种基于稀疏贝叶斯学习的离网DOA估计算法

本文提出一种基于稀疏贝叶斯学习的改进离网DOA估计算法,以提升非理想测向环境下在低信噪比、低快拍数时的DOA估计性能,称之为MOGSBL算法。本算法将信号源方位区间进行离散化,得到方位离散网格。为阵列接收信号建立稀疏贝叶斯模型,将网格节点修正量设为模型超参数。采用期望最大化算法迭代更新网格节点修正量,使更新后的网格节点更接近真实源信号方位。为了检验MOGSBL算法的性能,本文进行了大量的数值实验,并将MOGSBL算法的DOA估计结果与RSBL算法、OGSBL算法和L1-SVD算法进行对比。在不同信噪比和不同快拍数时,MOGSBL算法均能清晰分辨方位很接近的两个信号源,角度分辨率明显高于RSBL算法、OGSBL算法和L1-SVD算法。随着信噪比和快拍数的增加,4种算法的RMSE均逐渐减小。但MOGSBL算法的RMSE明显低于RSBL算法、OGSBL算法和L1-SVD算法,且RSBL算法、OGSBL算法优于L1-SVD算法。实验还分析了方向测试范围的离散网格节点数对DOA估计的影响,发现细密的离散网格可以提高DOA估计精度,但DOA估计的计算量会增加。且在任意网格节点数时,相比于RSBL算法、OGSBL算法和L1-SVD算法,本文的MOGSBL算法均具有最低的RMSE和最短的计算时间。

基于近似消息传递的NOMA系统信道和脉冲噪声联合估计方法

针对非高斯脉冲噪声背景下的非正交多址接入(non-orthogonal multiple access,NOMA)系统的信道估计问题,利用信道和脉冲噪声的稀疏特性,提出一种基于近似消息传递的信道和脉冲噪声联合估计方法。首先构建全子载波的压缩感知方程,然后基于稀疏贝叶斯学习理论提出一种信道、脉冲噪声和数据符号的联合估计优化问题。为解决这一超参量非线性非凸问题,设计了一种基于高斯广义近似消息传递和稀疏贝叶斯学习理论的期望最大化实现算法。仿真结果表明,与基于期望最大化的稀疏贝叶斯学习方法相比,所提算法在信道和脉冲噪声估计的均方误差、误码率等方面性能虽略有下降,但算法复杂度降低了1个数量级。

一种低复杂度的正交时频空系统接收机设计

正交时频空(OTFS)调制可以将时间和频率选择性信道转换为时延-多普勒(DD)域的非选择性信道,这为高速移动场景建立可靠的无线通信提供了解决方案。然而,在车联网等复杂的多散射场景下,信道存在严重的多普勒间干扰(IDI),这给OTFS接收机信号的准确解调带来了极大的挑战。针对上述问题,该文提出一种联合稀疏贝叶斯学习(SBL)和阻尼最小二乘最小残差(d-LSMR)的OTFS接收机设计。首先,根据OTFS时域和DD域的关系,采用基扩展模型(BEM)将信道估计问题转换为基系数恢复问题,精准估计包括多普勒采样点在内的DD域信道。然后,提出一种高效的转换算法将基系数转换为信道等效矩阵。其次,将信道估计中估计得到的噪声,用于d-LSMR均衡器中进行信道均衡,并利用DD域信道矩阵的稀疏性实现快速收敛。系统仿真结果表明,与目前代表性的OTFS接收机相比,该文所提方案实现了更好的误码率性能,同时降低了计算复杂度。

基于稀疏贝叶斯学习的GFDM系统联合迭代信道估计与符号检测

针对当前广义频分复用(Generalized Frequency Division Multiplexing,GFDM)系统时变信道估计精度低的问题,提出基于稀疏贝叶斯学习的GFDM系统联合信道估计与符号检测算法.具体地,采用无干扰导频插入的GFDM多重响应信号模型,在稀疏贝叶斯学习框架下,结合期望最大化算法(Expectation-Maximization,EM)和卡尔曼滤波与平滑算法实现块时变信道的最大似然估计;基于信道状态信息的估计值进行GFDM符号检测,并通过信道估计与符号检测的迭代处理逐步提高信道估计与符号检测的精度.仿真结果表明,所提算法能够获得接近完美信道状态信息条件下的误码率性能,且具有收敛速度快、对多普勒频移鲁棒性高等优点.

Online identification of time-varying dynamical systems for industrial robots based on sparse Bayesian learning

Nowadays, industrial robots have been widely used in manufacturing, healthcare, packaging, and more. Choosing robots in these applications mainly attributes to their repeatability and precision. However, prolonged and loaded operations can deteriorate the accuracy and efficiency of industrial robots due to the unavoidable accumulated kinematical and dynamical errors. This paper resolves these aforementioned issues by proposing an online time-varying sparse Bayesian learning(SBL) method to identify dynamical systems of robots in real-time. The identification of dynamical systems for industrial robots is cast as a sparse linear regression problem. By constructing the dictionary matrix, the parameters of the robot dynamics are effectively estimated via a re-weighted1-minimization algorithm. Online recursive methods are integrated into SBL to achieve real-time system identification. By including sparsity and promoting online learning, the proposed method can handle time-varying dynamical systems and therefore improve operational stability and accuracy. Experimental results on both simulated and real selective compliance assembly robot arm(SCARA) robots have demonstrated the effectiveness of the proposed method for industrial robots.

On fast estimation of direction of arrival for underwater acoustic target based on sparse Bayesian learning

The Direction of Arrival （DOA） estimation methods for underwater acoustic target using Temporally Multiple Sparse Bayesian Learning （TMSBL） as the reconstructing algorithm have the disadvantage of slow computing speed. To solve this problem, a fast underwater acoustic target direction of arrival estimation was proposed. Analyzing the model characteristics of block-sparse Bayesian learning framework for DOA estimation, an algorithm was proposed to obtain the value of core hyper-parameter through MacKay＇s fixed-point method to estimate the DOA. By this process, it will spend less time for computation and provide more superior recovery performance than TMSBL algorithm. Simulation results verified the feasibility and effectiveness of the proposed algorithm.

脉冲干扰下基于变分贝叶斯推断的水声正交频分复用联合估计方法

脉冲干扰环境下水声正交频分复用通信性能严重下降,为此提出了基于变分贝叶斯推断的信道估计方法。该方法利用水声信道和脉冲干扰的稀疏特性,基于平均场变分贝叶斯推断,将信道向量和脉冲干扰向量的后验概率分布分别分解为简单概率分布进行拟合,基于导频子载波迭代直至收敛,得到信道和脉冲干扰的最大后验估计。所提方法改进了基于稀疏贝叶斯学习的干扰、信道联合估计方法中信道和干扰构成的联合向量无法分离二者稀疏度的问题,并且显著降低了计算复杂度。在此基础上,进一步提出了基于变分贝叶斯推断的干扰、信道和符号联合估计方法,将未知符号融入变分贝叶斯推断框架,与干扰和信道一起迭代,最终得到更精确的符号估计。仿真和试验结果验证了所提算法的有效性,与现有方法相比,本文所提方法具有更低的误码率和复杂度。

基于稀疏贝叶斯学习的混合mMIMO系统波达方向估计

波达方向估计是混合mMIMO系统波束成形得以应用的前提,基于协方差矩阵重构的子空间方法在相干信号和有限快拍数条件下性能损失较大。为了应对上述挑战,提出了一种基于稀疏贝叶斯学习的混合mMIMO系统波达方向估计方法,主要创新之处在于:将混合mMIMO系统的波达方向估计问题转化为稀疏信号恢复问题,从而绕过空间协方差矩阵重构,避免了其带来的性能损失。为了便于进行贝叶斯推断,进一步利用变分贝叶斯近似思想,在恢复稀疏信号的同时,自适应估计出未知参数,显著改善了对噪声和相干信号的鲁棒性,提升了有限快拍数情况下的波达方向估计性能。数值模拟结果验证了所提方法的优越性。

基于频率着色的稀疏贝叶斯宽带波达角估计方法

为了提升稀疏贝叶斯(Sparse Bayesian Learning,SBL)算法在干扰环境下对目标信号的检测能力,提出将频率着色技术(Frequency Coloring,FC)推广至SBL算法中。在SBL-FC算法中,首先将阵列接收信号通过傅里叶变换转换至各个子带,在各子带内利用SBL算法进行波达角估计,输出功率谱。不同于常规的SBL算法仅将各子带的功率谱进行简单地叠加,算法考虑干扰和目标频谱结构的差异性,对各子带进行不同的着色,使得干扰和目标轨迹在方位时间历程图上对应于不同的颜色,从而使得目标轨迹更易被提取。数值仿真和实验数据分析表明,利用目标和干扰频谱结构的差异性可有效提升SBL算法在干扰环境下对目标信号的检测能力。

存在幅相误差时二维稳健超分辨测角算法

针对4D车载毫米波雷达在俯仰与方位维角度分辨力较低、阵列存在幅相误差时测角有偏的问题,提出一种基于快速稀疏贝叶斯学习的稳健二维超分辨测角方法。首先,利用空域稀疏性特点,对角度域空间进行栅格划分,构建了存在幅相误差时的二维超分辨测角信号模型;然后,通过固定点更新的MacKay SBL重构算法实现了多个邻近目标二维角度估计,并利用基于向量点乘的自校正算法对相位误差进行估计,以对有偏的角度估计进行修正;最后,给出了多输入多输出虚拟阵列下的二维角度估计的克拉美-罗界,并分析了所提算法的计算复杂度。仿真结果表明,在大陆ARS548雷达实际12发16收天线布局下,通过对比6种超分辨测角算法,所提方法在低信噪比、少量快拍下和幅相误差较小时,具有较高的角度分辨力与较低的均方根误差。