Gaussian Mixture-Learned Approximate Message Passing(GM-LAMP)Based Hybrid Precoders for mmWave Massive MIMO Systems

Hybrid precoder design is a key technique providing better antenna gain and reduced hardware complexity in millimeter-wave(mmWave)massive multiple-input multiple-output(MIMO)systems.In this paper,Gaussian Mixture learned approximate message passing(GM-LAMP)network is presented for the design of optimal hybrid precoders suitable for mmWave Massive MIMO systems.Optimal hybrid precoder designs using a compressive sensing scheme such as orthogonal matching pursuit(OMP)and its derivatives results in high computational complexity when the dimensionality of the sparse signal is high.This drawback can be addressed using classical iterative algorithms such as approximate message passing(AMP),which has comparatively low computational complexity.The drawbacks of AMP algorithm are fixed shrinkage parameter and non-consideration of prior distribution of the hybrid precoders.In this paper,the fixed shrinkage parameter problem of the AMP algorithm is addressed using learned AMP(LAMP)network,and is further enhanced as GMLAMP network using the concept of Gaussian Mixture distribution of the hybrid precoders.The simula-tion results show that the proposed GM-LAMP network achieves optimal hybrid precoder design with enhanced achievable rates,better accuracy and low computational complexity compared to the existing algorithms.

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.

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.

基于AMP框架的小波域图像压缩重构

针对压缩感知中的图像重构问题,基于近似消息传递(AMP)框架,提出一种新的图像压缩重构算法。该算法推导AMP框架在小波域下的系数迭代公式,证明AMP中滤波函数的操作对象是图像的小波系数,通过小波变换提高处理对象的稀疏度,并引入Wiener函数降低标量函数的求导复杂度。实验结果表明,与基于梯度投影的重构算法和正交匹配追踪算法相比,该算法具有较好的视觉效果和较高的重构精度。

基于SAMP的低复杂度大规模MIMO信号检测算法

在大规模MIMO系统上行链路中,最小均方误差(MMSE)算法能达到近似最优的线性信号检测性能。但是,MMSE算法引入了高计算复杂度的矩阵求逆运算。文中提出了一种基于简化近似信息传递(Simplified Approximate Message Passing,SAMP)的低复杂度迭代阈值算法以替代矩阵求逆,并通过重构准确的有效噪声方差及设置合适的初始值,进一步提高了检测性能。仿真结果表明,在设定的有效噪声方差和合适的初始值条件下,仅通过少数几次迭代,SAMP算法就能够以较低的计算复杂度快速接近MMSE算法的检测性能。

基于方向自适应观测与AMP的小波域图像压缩感知

为了解决现有的基于近似消息传递(AMP)的图像压缩感知(CS)算法通常需要构建大尺寸观测矩阵的问题,研究了基于方向自适应观测与AMP的图像小波域压缩感知方案。针对传统变换域图像压缩感知方案采用的逐列观测、逐列重构方式的缺点,设计了一种基于图像空间相关性的方向自适应小波域压缩观测方法。进而,结合局部自适应维纳滤波,设计了一种基于AMP的小波系数子带压缩感知重构算法,能够在稀疏度未知的情况下以子带为单位实现图像小波系数的重建。仿真实验结果表明,与现有的图像小波域压缩感知方案相比,本文方案的重建图像质量较高;与现有的直接对整幅图像进行观测与重构的AMP方案相比,本文方案能够有效降低图像重建算法的运行时间。

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。

基于CAMP稀疏重建算法的并行实现

高分辨率合成孔径雷达(SAR)数据量大,导致稀疏重建过程计算量大。复数近似信息传递(CAMP)是一种收敛速度快的稀疏重建算法,经常被用于稀疏信号重建。为了解决计算量大的问题,提出了一种基于CAMP的并行算法,在计算统一设备架构(CUDA)上对CAMP算法中Chirp Scaling算子和排序算法进行优化。在Chirp Scaling算子中,主要对矩阵转置、FFT和IFFT进行并行优化,并引入并行版本的双调排序。最后,利用串行的CAMP算法和并行的CAMP算法分别重构点目标图像。实验结果表明,在正确重建的前提下,并行的CAMP算法的比串行CAMP算法快29.55倍。

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。

基于深度学习LDAMP网络的量子状态估计

设计出一种基于学习去噪的近似消息传递(Learned denoising-based approximate message passing,LDAMP)的深度学习网络,将其应用于量子状态的估计.该网络将去噪卷积神经网络与基于去噪的近似消息传递算法相结合,利用量子系统输出的测量值作为网络输入,通过设计出的带有去噪卷积神经网络的LDAMP网络重构出原始密度矩阵,从大量的训练样本中提取各种不同类型密度矩阵的结构特征,来实现对量子本征态、叠加态以及混合态的估计.在对4个量子位的量子态估计的具体实例中,分别在无和有测量噪声干扰情况下,对基于LDAMP网络的量子态估计进行了仿真实验性能研究,并与基于压缩感知的交替方向乘子法和三维块匹配近似消息传递等算法进行估计性能对比研究.数值仿真实验结果表明,所设计的LDAMP网络可以在较少的测量的采样率下,同时完成对4种量子态的更高精度估计.

Deep Learning-Based AMP for Massive MIMO Detection

Low-complexity detectors play an essential role in massive multiple-input multiple-output (MIMO) transmissions. In this work, we discuss the perspectives of utilizing approximate message passing (AMP) algorithm to the detection of massive MIMO transmission. To this end, we need to efficiently reduce the divergence occurrence in AMP iterations and bridge the performance gap that AMP has from the optimum detector while making use of its advantage of low computational load. Our solution is to build a neural network to learn and optimize AMP detection with four groups of specifically designed learnable coefficients such that divergence rate and detection mean squared error (MSE) can be significantly reduced. Moreover, the proposed deep learning-based AMP has a much faster converging rate, and thus a much lower computational complexity than conventional AMP, providing an alternative solution for the massive MIMO detection. Extensive simulation experiments are provided to validate the advantages of the proposed deep learning-based AMP.

UAMP-Based Delay-Doppler Channel Estimation for OTFS Systems

Orthogonal time frequency space(OTFS)technique,which modulates data symbols in the delay-Doppler(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.

AMP Dual-Turbo Iterative Detection and Decoding for LDPC Coded Multibeam MSC Uplink

The uplink of mobile satellite communication(MSC) system with hundreds of spot beams is essentially a multiple-input multiple-output(MIMO) channel. Dual-turbo iterative detection and decoding as a kind of MIMO receiver, which exchanges soft extrinsic information between a soft-in soft-out(SISO) detector and an SISO decoder in an iterative fashion, is an efficient method to reduce the uplink inter-beam-interference(IBI),and so the receiving bit error rate(BER).We propose to replace the linear SISO detector of traditional dual-turbo iterative detection and decoding with the AMP detector for the low-density parity-check(LDPC) coded multibeam MSC uplink. This improvement can reduce the computational complexity and achieve much lower BER.

基于AMP算法的视频在线压缩感知重构

设计出了一个基于AMP算法的在线视频压缩感知重构方案。该方案通过对视频帧应用快速傅里叶变换的伪随机向下取样实现快速简洁的在线编码。线下解码部分,使用AMP算法作为重构算法,结合三维双树复小波变换,逐步迭代更新得到重构数据。实验结果表明,该方案能在快速编码采样数据的基础上获得较好的视频恢复效果。

MBM中基于AMP的多用户检测

针对媒介调制(MBM)系统中低复杂度高精度的多用户检测需求,提出了一种基于近似消息传递(AMP)的多用户检测算法.由于MBM自身具有稀疏性,可利用压缩感知的稀疏信号重构方法进行多用户检测.在检测过程中,当观测矩阵满足独立同分布条件时,采用近似消息传递算法进行多用户检测可在保证高精度检测性能的同时进一步降低检测复杂度.同时,针对噪声方差未知的情况,所提出的算法中设计了利用期望最大方法进行估计噪声方差的步骤,从而更加契合实际场景.经仿真测试表明,所提出的基于AMP的多用户检测算法与传统多用户检测方法以及其他具有相似复杂度的多用户检测方法相比具有最佳的多用户检测性能.