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.

Efficient Recovery of Structured Sparse Signals via Approximate Message Passing with Structured Spike and Slab Prior

Due to limited volume, weight and power consumption, micro-satellite has to reduce data transmission and storage capacity by image compression when performs earth observation missions. However, the quality of images may be unsatisfied. This paper considers the problem of recovering sparse signals by exploiting their unknown sparsity pattern. To model structured sparsity, the prior correlation of the support is encoded by imposing a transformed Gaussian process on the spike and slab probabilities. Then, an efficient approximate message-passing algorithm with structured spike and slab prior is derived for posterior inference, which, combined with a fast direct method, reduces the computational complexity significantly. Further, a unified scheme is developed to learn the hyperparameters using expectation maximization(EM) and Bethe free energy optimization. Simulation results on both synthetic and real data demonstrate the superiority of the proposed algorithm.

Speech Enhancement Based on Approximate Message Passing

To overcome the limitations of conventional speech enhancement methods, such as inaccurate voice activity detector(VAD) and noise estimation, a novel speech enhancement algorithm based on the approximate message passing(AMP) is adopted. AMP exploits the difference between speech and noise sparsity to remove or mute the noise from the corrupted speech. The AMP algorithm is adopted to reconstruct the clean speech efficiently for speech enhancement. More specifically, the prior probability distribution of speech sparsity coefficient is characterized by Gaussian-model, and the hyper-parameters of the prior model are excellently learned by expectation maximization(EM) algorithm. We utilize the k-nearest neighbor(k-NN) algorithm to learn the sparsity with the fact that the speech coefficients between adjacent frames are correlated. In addition, computational simulations are used to validate the proposed algorithm, which achieves better speech enhancement performance than other four baseline methods-Wiener filtering, subspace pursuit(SP), distributed sparsity adaptive matching pursuit(DSAMP), and expectation-maximization Gaussian-model approximate message passing(EM-GAMP) under different compression ratios and a wide range of signal to noise ratios(SNRs).

Message Passing Based Detection for Orthogonal Time Frequency Space Modulation

The orthogonal time frequency space(OTFS)modulation has emerged as a promis⁃ing modulation scheme for wireless communications in high-mobility scenarios.An efficient detector is of paramount importance to harvesting the time and frequency diversities promised by OTFS.Recently,some message passing based detectors have been developed by exploiting the features of the OTFS channel matrices.In this paper,we provide an overview of some re⁃cent message passing based OTFS detectors,compare their performance,and shed some light on potential research on the design of message passing based OTFS receivers.

Combined UAMP and MF Message Passing Algorithm for Multi-Target Wideband DOA Estimation with Dirichlet Process Prior

When estimating the direction of arrival (DOA) of wideband signals from multiple sources, the performance of sparse Bayesian methods is influenced by the frequency bands occupied by signals in different directions. This is particularly true when multiple signal frequency bands overlap. Message passing algorithms (MPA) with Dirichlet process (DP) prior can be employed in a sparse Bayesian learning (SBL) framework with high precision. However, existing methods suffer from either high complexity or low precision. To address this, we propose a low-complexity DOA estimation algorithm based on a factor graph. This approach introduces two strong constraints via a stretching transformation of the factor graph. The first constraint separates the observation from the DP prior, enabling the application of the unitary approximate message passing (UAMP) algorithm for simplified inference and mitigation of divergence issues. The second constraint compensates for the deviation in estimation angle caused by the grid mismatch problem. Compared to state-of-the-art algorithms, our proposed method offers higher estimation accuracy and lower complexity.

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。

基于聚类与稀疏字典学习的近似消息传递

基于传统字典学习的近似消息传递(approximate message passing,AMP)算法对训练样本数量的需求较高,且运算成本较高。本文引入双稀疏模型,构建基于稀疏字典学习的AMP框架,降低迭代过程中字典学习对训练样本数量的需求,提高压缩感知图像重建的质量与效率。进一步,提出基于聚类与稀疏字典学习的AMP算法,在迭代过程中依据图像块特征进行分类,并为各类图像块分别学习稀疏字典,实现自适应去噪。与基于传统字典学习的AMP算法相比,基于聚类与稀疏字典学习的AMP算法能够将重建图像的峰值信噪比提高0.20~1.75 dB,并且能够将运算效率平均提高89%。

天波超视距雷达非均匀采样信号频谱重构

受瞬态干扰影响和空海同时探测的需求,在长相参积累时间条件下,天波超视距雷达(over-the-horizon radar,OTHR)回波信号的有效采样点往往缺损且非均匀,严重影响目标检测性能。针对此问题,提出了一种基于压缩感知的OTHR频谱重构方法。首先,建立了OTHR频域信号的稀疏模型;然后,提出了快速自适应复近似消息传递(fast adaptive complex approximate message passing,FACAMP)频谱重构算法并给出了算法实现步骤;最后,利用FACAMP算法实现了OTHR频谱重构并分析了重构性能。与现有重构算法相比,FACAMP算法具有重构精度高、运算复杂度低、可自适应调整参数和保留背景噪声高斯性的优势。理论分析和仿真实验均验证了所提算法的有效性。

OFDM叠加导频联合信道估计和检测方法

针对现有正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)系统信道估计和迭代检测算法中频谱效率低和鲁棒性差等问题,提出了一种基于酉近似消息传递和叠加导频的信道估计与联合检测方法。首先,在软调制/解调中叠加导频对正交幅度调制的星座点进行预处理,检测时将叠加的导频作为频域符号的先验分布,利用置信传播算法进行调制和解调,实现检测模型的简化。然后,应用因子图-消息传递算法对OFDM传输系统和信道进行建模和全局优化,引入酉变换加强信道估计算法的鲁棒性。最后,建立OFDM仿真环境对现有方法进行仿真分析。仿真结果表明,相对于现有的独立导频类算法,所提算法能够以相同复杂度显著提升OFDM系统的频谱效率和鲁棒性。

基于消息传递的机载雷达组网航迹融合

机载雷达组网航迹融合需要解决目标跟踪、数据关联与航迹管理3个子问题,然而这3个子问题相互耦合,采用开环序贯估计算法会导致性能下降.本文提出了一种基于消息传递的机载雷达组网航迹融合方法,该方法在联合优化框架下解决目标跟踪、数据关联与航迹管理3个子问题.首先,建立机载雷达组网航迹融合的联合概率密度函数,并将其转换为因子图.其次,将因子图分解为置信传播区域与平均场近似区域.目标运动状态的统计模型服从共轭指数模型,因此采用平均场近似以获得简单的消息传递更新公式.数据关联包含一对一约束,因此采用置信传播.目标存在状态同样采用置信传播,以获得更好的近似结果.最后,可以通过闭环迭代框架近似估计后验分布,从而有效处理目标跟踪、数据关联与航迹管理之间的耦合问题.仿真结果表明,所提算法的性能优于多假设跟踪算法和联合概率密度关联算法.

基于GA-MP的低复杂度OTFS检测算法

针对正交时频空(Orthogonal Time Frequency Space,OTFS)通信系统信号检测复杂度高的问题,提出一种改进的高斯近似消息传递(Gaussian Approximate Message Passing,GA-MP)检测算法。依据最大后验概率检测准则,对发送信号及隐变量进行逐符号高斯近似,基于置信传播算法与联合因子图进行消息传递,用边缘后验概率替代GA-MP中的外部信息以减少运算量,结合阻尼因子提升收敛速度,同时引入概率阈值减少后续更新的节点数,从而使运算复杂度得到有效降低。实验结果表明,改进后的GA-MP算法在保证误码率性能的前提下具有更低的复杂度。

UAMP-Based Delay-Doppler Channel Estimation for OTFS Systems

Orthogonal time frequency space(OTFS)technique, which modulates data symbols in the delayDoppler(DD) domain, presents a potential solution for supporting reliable information transmission in highmobility vehicular networks. In this paper, we study the issues of DD channel estimation for OTFS in the presence of fractional Doppler. We first propose a channel estimation algorithm with both low complexity and high accuracy based on the unitary approximate message passing(UAMP), which exploits the structured sparsity of the effective DD domain channel using hidden Markov model(HMM). The empirical state evolution(SE) analysis is then leveraged to predict the performance of our proposed algorithm. To refine the hyperparameters in the proposed algorithm,we derive the update criterion for the hyperparameters through the expectation-maximization(EM) algorithm. Finally, Our simulation results demonstrate that our proposed algorithm can achieve a significant gain over various baseline schemes.

融合模型求解与深度学习的可见光通信非线性均衡器

沃尔特拉非线性后均衡器(Volterra Series Nonlinear Post-Equalizer,VS-NPE)可以补偿可见光通信(Visible Light Communication,VLC)的非线性失真和多径效应,但其结构复杂且均衡精度有限。在VS-NPE内核求解基础上,提出一种基于阈值自学习近似消息传递(Learned Threshold Approximate Message Passing,LTAMP)网络的非线性均衡器。修正样本观测矩阵以克服其列高度相关的缺陷;在改进近似消息传递(Approximate Message Passing,AMP)算法迭代的基础上,将算法每一次迭代的计算过程映射为一层特殊的神经网络,经逐层展开后构建出完整的LTAMP均衡器。所提方法融合了模型求解和深度学习的优势,可从样本中学习最佳的AMP参数,以克服其对噪声敏感且输出不稳定的缺陷,进而提升内核求解稳定性与计算精度。仿真结果表明,与稳固阈值AMP算法相比,所提方法在误码率为1×10^(-3)时能取得2 dB的信噪比增益,且对样本噪声具有较强的自适应性,展现出优异的非线性失真补偿能力。

压缩感知重构算法的两步深度展开策略研究

针对压缩感知中重构算法的深度展开问题,提出了一种两步深度展开策略(two-step deep unfolding,TwDU)。已有深度展开重构算法通常依赖前一步估计值估计当前值,TwDU对已有深度展开重构算法增加估计深度,依赖于前两步估计值估计当前展开值。TwDU对已有深度展开算法前两步估计值增加了两个训练权重。训练权重优化利用了信号估计值之间的相关特性,可以随着数据的特性自我学习和调整,所提TwDU策略应用于可学习迭代软阈值算法(learned iterative soft thresholding algorithm,LISTA)、可训练迭代软阈值算法(trainable iterative soft thresholding algorithm,TISTA)、可学习近似消息传递算法(learned approximate message passing,LAMP)等已有深度展开算法。通过在一维和二维稀疏信号的仿真验证,TwDU策略在重构精度和收敛速度上都更具有明显优势。

复杂地形环境下基于GAMP-STAP的低空风切变风速估计方法

针对机载气象雷达在复杂的地形环境下探测低空风切变时,地杂波呈现非均匀特征和难以获取足够的独立同分布(IID)样本,导致空时自适应处理(STAP)杂波抑制性能变差,使得风切变风速估计不准的问题。该文基于杂波信号稀疏特性,提出一种广义近似消息传递(GAMP)STAP方法,GAMP-STAP仅利用少量的样本在复杂地形环境下实现了风速较准确的估计。该方法首先利用杂波脊的先验信息构造稀疏字典,然后在贝叶斯框架下利用GAMP算法估计杂波幅度,恢复杂波功率谱,进而计算杂波协方差矩阵,最后构造STAP滤波器实现杂波抑制以及风切变风速估计。后续实验仿真结果证明了该方法的有效性。

基于OAMP算法辅助稀疏连接神经网络的MIMO信号检测

最大似然检测(Maximum likelihood detection,ML)是传统多输入多输出(Multi-input Multi-output,MIMO)信号检测中的最优算法,但是受到天线数量、收发天线比例以及调制信号的约束,致使其仅适用于天线数量少、天线比例较低且调制信号阶数较低的场景。作为一种新型的解决方案,目前基于深度学习(DL)的信号检测算法得到了广泛关注,但同样存在收发天线规模相近时检测性能恶化问题。该文将正交近似消息传递(OAMP)算法与稀疏连接神经网络(ScNet)结合成为可训练的网络结构,提出一种新的适用于MIMO系统上行链路的信号检测算法,称作ScNet-OAMP。该算法通过神经网络提供精确的信号传输参数初始解,改善OAMP过程的线性估计和非线性估计,由此增强其降噪能力,达到提高检测精度的目的,相比于ScNet和OAMP,其能够在同等实验参数下获得最佳检测性能。实验结果表明,此算法适用于QPSK、4QAM及16QAM等不同调制信号,能够处理不同比例收发天线及数量规模的系统配置,尤其是在收发天线数量相近的情况下亦能表现出较好的性能,并且在10-3误码率上有至少0.5 dB,甚至2.2 dB以上的性能增益。

RIS辅助卫星物联网中基于压缩感知的SCMA信号重构

卫星物联网是未来6G网络重要组成部分,在地面部署可重构智能反射面(Reconfigurable Intelligence Surface,RIS)则能进一步增强天地之间信号的传输能力;然而海量设备的接入和检测,以及RIS的引入带来的较高复杂度,给系统设计与实现带来挑战。针对卫星物联网设备和业务稀疏特性,本文提出了一种基于压缩感知的信号重构算法,旨在提高系统的接入用户数和检测成功率,同时降低检测的复杂度。首先,介绍了RIS辅助的卫星物联网系统架构,构建了天地信道模型和星上接收信号模型。然后考虑到卫星物联网地面终端的稀疏性和业务的稀疏性,结合稀疏码分多址(Sparse Code Multiple Access,SCMA)和压缩感知的信号处理方法,通过合理设计SCMA中的稀疏码字,将多用户检测转化为压缩感知理论中的信号重构。最后提出了一种演进的近似消息传播算法(Evolved Approximate Message-Passing,EAMP)来实现压缩感知中的信号重构。仿真结果表明,RIS辅助的SCMA系统与功率域的非正交多址接入技术相比可以提高系统的吞吐量性能,同时EAMP算法相比传统的SIC算法具有更高的正确检测概率和更低的算法复杂度。

矩形窗正交时频空检测算法

针对正交时频空(Orthogonal Time Frequency Space,OTFS)调制系统采用矩形窗函数时,信道矩阵结构复杂导致的鲁棒性差的问题,提出了一种基于时域处理和酉近似消息传递的检测算法。该算法首先添加循环前缀,将时域信道转换为分块对角矩阵;然后应用酉变换和近似消息传递建立迭代检测算法。仿真结果表明,所提检测算法能够在不增加复杂度的条件下有效提升检测精度和鲁棒性,特别是存在信道编码的条件下表现出2 dB的性能增益,使得该算法更适用于杂散多径、高速移动等环境,具有较高的应用价值。

OTFS调制系统的低复杂度GAMP算法实现

针对正交时频空(Orthogonal Time Frequealy Space,OTFS)调制技术信号检测算法复杂度高的问题,结合OTFS信道矩阵特性构建匹配滤波器,在广义近似消息传递(Generalized Approximate Message Passing,GAMP)算法的基础上,提出了基于期望最大化(Empectation Maxinization,EM)的阻尼广义消息传递算法。相较于传统的消息传递(Message Passing,MP)、近似消息传递(Approximate Message Passing,AMP)和GAMP等检测方式,所提算法有更低复杂度。在500 km/h的高动态场景中对该算法进行仿真,其误码率性能优于最小均方差(Minimum Mean Squared Error,MMSE)和传统的GAMP检测算法,并且具有更好的收敛性。

面向星座概率成形的向量近似消息传递软频域均衡算法

在发送端通过能量扩展变换来改善向量近似消息传递软频域均衡算法收敛特性,均衡器迭代输出可近似认为无符号间干扰,均衡器输出符号与发送符号之间可用加性高斯白噪声信道来建模。在带宽受限的加性高斯白噪声信道下,均匀分布的调制方式距离香农容量限有一定差距。为缩小这个差距,发送端可通过星座概率成形设计,获得成形增益。接收端可利用非等概符号的先验信息改进均衡器结构,提升接收性能。理论分析和仿真结果表明,在经典的Proakis B和Proakis C多径信道下,所提算法能够大幅度提升收敛速度以及均衡性能。相比均匀分布的信号,约有0.5 dB的性能增益。