Millimeter Wave Channel Estimation via Exploiting Joint Sparse and Low-Rank Structures

We consider the problem of channel estimation for millimeter wave (mmWave) systems, where, to minimize the hardware complexity and power consumption, an analog transmit beamforming and receive combining structure with only one radio frequency (RF) chain at the base station (BS) and mobile station (MS) is employed. Most existing works for mmWave channel estimation exploit sparse scattering characteristics of the channel. In addition to sparsity, mmWave channels may exhibit angular spreads over the angle of arrival (AoA), angle of departure (AoD), and elevation domains. In this paper, we show that angular spreads give rise to a useful low-rank structure that, along with the sparsity, can be simultaneously utilized to reduce the sample complexity, i.e. the number of samples needed to successfully recover the mmWave channel. Specifically, to effectively leverage the joint sparse and low-rank structure, we develop a two-stage compressed sensing method for mmWave channel estimation, where the sparse and low-rank properties are respectively utilized in two consecutive stages, namely, a matrix completion stage and a sparse recovery stage. Our theoretical analysis reveals that the proposed two-stage scheme can achieve a lower sample complexity than a direct compressed sensing method that exploits only the sparse structure of the mmWave channel. Simulation results are provided to corroborate our theoretical results and to show the superiority of the proposed two-stage method

Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signals

We consider the problem of recovering block-sparse signals whose structures are unknown \emph{a priori}. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the knowledge of the block structure is usually unavailable in practice. In this paper, we develop a new sparse Bayesian learning method for recovery of block-sparse signals with unknown cluster patterns. Specifically, a pattern-coupled hierarchical Gaussian prior model is introduced to characterize the statistical dependencies among coefficients, in which a set of hyperparameters are employed to control the sparsity of signal coefficients. Unlike the conventional sparse Bayesian learning framework in which each individual hyperparameter is associated independently with each coefficient, in this paper, the prior for each coefficient not only involves its own hyperparameter, but also the hyperparameters of its immediate neighbors. In doing this way, the sparsity patterns of neighboring coefficients are related to each other and the hierarchical model has the potential to encourage structured-sparse solutions. The hyperparameters, along with the sparse signal, are learned by maximizing their posterior probability via an expectation-maximization (EM) algorithm. Numerical results show that the proposed algorithm presents uniform superiority over other existing methods in a series of experiments

Learning to decompose the modes in few-mode fibers with deep convolutional neural network

We introduce deep learning technique to perform complete mode decomposition for few-mode optical fiber for the first time. Our goal is to learn a fast and accurate mapping from near-field beam profiles to the complete mode coefficients, including both modal amplitudes and phases. We train the convolutional neural network with simulated beam patterns, and evaluate the network on both of the simulated beam data and the real beam data. In simulated beam data testing, the correlation between the reconstructed and the ideal beam profiles can achieve 0.9993 and 0.995 for 3-mode case and 5-mode case respectively. While in the real 3-mode beam data testing, the average correlation is 0.9912 and the mode decomposition can be potentially performed at 33 Hz frequency on Graphic Processing Unit, indicating real-time processing ability. The quantitative evaluations demonstrate the superiority of our deep learning based approach

Weight Normalization based Quantization for Deep Neural Network Compression

With the development of deep neural networks, the size of network models becomes larger and larger. Model compression has become an urgent need for deploying these network models to mobile or embedded devices. Model quantization is a representative model compression technique. Although a lot of quantization methods have been proposed, many of them suffer from a high quantization error caused by a long-tail distribution of network weights. In this paper, we propose a novel quantization method, called weight normalization based quantization (WNQ), for model compression. WNQ adopts weight normalization to avoid the long-tail distribution of network weights and subsequently reduces the quantization error. Experiments on CIFAR-100 and ImageNet show that WNQ can outperform other baselines to achieve state-of-the-art performance.Comment: 10 pages, 5 figure

Deep learning enabled superfast and accurate M^2 evaluation for fiber beams

We introduce deep learning technique to predict the beam propagation factor M^2 of the laser beams emitting from few-mode fiber for the first time, to the best of our knowledge. The deep convolutional neural network (CNN) is trained with paired data of simulated near-field beam patterns and their calculated M^2 value, aiming at learning a fast and accurate mapping from the former to the latter. The trained deep CNN can then be utilized to evaluate M^2 of the fiber beams from single beam patterns. The results of simulated testing samples have shown that our scheme can achieve an averaged prediction error smaller than 2% even when up to 10 eigenmodes are involved in the fiber. The error becomes slightly larger when heavy noises are added into the input beam patterns but still smaller than 2.5%, which further proves the accuracy and robustness of our method. Furthermore, the M^2 estimation takes only about 5 ms for a prepared beam pattern with one forward pass, which can be adopted for real-time M^2 determination with only one supporting Charge-Coupled Device (CCD). The experimental results further prove the feasibility of our scheme. Moreover, the method we proposed can be confidently extended to other kinds of beams provided that adequate training samples are accessible. Deep learning paves the way to superfast and accurate M^2 evaluation with very low experimental efforts.Comment: 12 pages, 10 figure

Solving localized wave solutions of the derivative nonlinear Schrodinger equation using an improved PINN method

The solving of the derivative nonlinear Schrodinger equation (DNLS) has attracted considerable attention in theoretical analysis and physical applications. Based on the physics-informed neural network (PINN) which has been put forward to uncover dynamical behaviors of nonlinear partial different equation from spatiotemporal data directly, an improved PINN method with neuron-wise locally adaptive activation function is presented to derive localized wave solutions of the DNLS in complex space. In order to compare the performance of above two methods, we reveal the dynamical behaviors and error analysis for localized wave solutions which include one-rational soliton solution, genuine rational soliton solutions and rogue wave solution of the DNLS by employing two methods, also exhibit vivid diagrams and detailed analysis. The numerical results demonstrate the improved method has faster convergence and better simulation effect. On the bases of the improved method, the effects for different numbers of initial points sampled, residual collocation points sampled, network layers, neurons per hidden layer on the second order genuine rational soliton solution dynamics of the DNLS are considered, and the relevant analysis when the locally adaptive activation function chooses different initial values of scalable parameters are also exhibited in the simulation of the two-order rogue wave solution

Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics

Artificial neural networks have been successfully incorporated into variational Monte Carlo method (VMC) to study quantum many-body systems. However, there have been few systematic studies of exploring quantum many-body physics using deep neural networks (DNNs), despite of the tremendous success enjoyed by DNNs in many other areas in recent years. One main challenge of implementing DNN in VMC is the inefficiency of optimizing such networks with large number of parameters. We introduce an importance sampling gradient optimization (ISGO) algorithm, which significantly improves the computational speed of training DNN in VMC. We design an efficient convolutional DNN architecture to compute the ground state of a one-dimensional (1D) SU($N$) spin chain. Our numerical results of the ground-state energies with up to 16 layers of DNN show excellent agreement with the Bethe-Ansatz exact solution. Furthermore, we also calculate the loop correlation function using the wave function obtained. Our work demonstrates the feasibility and advantages of applying DNNs to numerical quantum many-body calculations.Comment: 8 pages, 7 figure

High-efficiency terahertz spin-decoupled meta-coupler for spoof surface plasmon excitation and beam steering

Spoof surface plasmon (SSP) meta-couplers that efficiently integrate other diversified functionalities into a single ultrathin device are highly desirable in the modern microwave and terahertz fields. However, the diversified functionalities, to the best of our knowledge, have not been applied to circular polarization meta-couplers because of the spin coupling between the orthogonal incident waves. In this paper, we propose and numerically demonstrate a terahertz spin-decoupled bifunctional meta-coupler for SSP excitation and beam steering. The designed meta-coupler is composed of a coupling metasurface and a propagating metasurface. The former aims at realizing anomalous reflection or converting the incident waves into SSP under the illumination of the left or right circular polarization waves, respectively, and the latter are used to guide out the excited SSP. The respective converting efficiency can reach 82% and 70% at 0.3THz for the right and left circular polarization incident waves. Besides, by appropriately adjusting the reflection phase distribution, many other diversified functionalities can also be integrated into the meta-coupler. Our study may open up new routes for polarization-related SSP couplers, detectors, and other practical terahertz devices

Far-field subwavelength resolution imaging by spatial spectrum sampling

Imaging below the diffraction limit is always a public interest because of the restricted resolution of conventional imaging systems. To beat the limit, evanescent harmonics decaying in space must participate in the imaging process. Here, we introduce the method of spatial spectrum sampling, a novel far-field superresolution imaging method for microwave and terahertz regime. Strong dispersion and momentum conservation allow the spoof surface plasmon polaritons (SSP) structure to become a sensitive probe for spatial harmonics. This enables that the spatial information of the targets including both propagating and evanescent components, can be extracted by tuning and recording SSP in the far field. Then, the subwavelength resolution is constructed by the inversed Fourier transform of the sampled spatial spectrum. Using the modified subwavelength metallic grating as the spoof plasmonic structure, a far-field resolution of 0.17 wavelength is numerically and experimentally verified, and two-dimensional imaging ability is also fully discussed. The imaging ability and flexibility can be further optimizing the SSP structures. We are confident that our working mechanism will have great potentials in the superresolution imaging applications in the microwave and terahertz frequency rangeComment: 7 figures,48 reference,24 page

Theoretical study of kinetics of proton coupled electron transfer in photocatalysis

Photocatalysis induced by sunlight is one of the most promising approach to environmental protection, solar energy conversion and sustainable production of fuels. The computational modeling of photocatalysis is a rapidly expending field which requires to adapt and further develop the available theoretical tools. The coupled transfer of proton and electron is an important reaction during photocatalysis. In this work, we present the first step of our methodology development in which we apply existing kinetic theory of such coupled transfer to a model system, namely, methanol photo-dissociation on rutile TiO$_2$(110) surface, with the help of high-level first-principles calculations. Moreover, we adapt the Stuchebrukhov-Hammes-Schiffer kinetic theory, where we use the Georgievskii-Stuchebrukhova vibronic coupling, to calculate the rate constant of the proton coupled electron transfer reaction for a particular pathway. In particular, we propose a modified expression to calculate the rate constant which enforces the near-resonance condition for the vibrational wavefunction during proton tunneling