CSpace中国科学院数学与系统科学研究院http://ir.amss.ac.cn:802021-10-15T21:36:23Z2021-10-15T21:36:23ZHigh Order PSK Modulation in Massive MIMO Systems With 1-Bit ADCsSun, BuleZhou, YiqingYuan, JinhongLiu, Ya-FengWang, LuLiu, Linghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/585062021-06-01T23:52:02Z2021-06-01T23:52:02ZTitle: High Order PSK Modulation in Massive MIMO Systems With 1-Bit ADCs
Authors: Sun, Bule; Zhou, Yiqing; Yuan, Jinhong; Liu, Ya-Feng; Wang, Lu; Liu, Ling
Description: Massive multiple-input multiple-output (MIMO) systems with 1-bit analog-to-digital converters (ADCs) are promising to reduce the energy consumption. However, the serious quantization error caused by 1-bit ADCs will potentially limit the feasibility of high order modulations. This paper focuses on the analysis of the high order phase-shift keying (PSK) signal transmission in the 1-bit ADC massive MIMO system. Firstly, assuming ideal channel estimation and a single mobile station (MS), we theoretically prove that with an asymptotically large number of antennas at the base station, PSK signals with arbitrary modulation order can be recovered in the 1-bit ADC massive MIMO system. Secondly, we analyze the impact of pilot based channel estimation on the recovery of the high order PSK signals, which leads to a periodic asymptotic detection phase error (ADPE) at high signal to noise ratio (SNR). Furthermore, we also propose to optimize the pilot sequence for minimizing the cumulative absolute ADPE. Finally, the analysis is extended to the multi-MS case and the performance with different pilot patterns is discussed. Simulation results validate our analysis and show that using our proposed optimized pilot sequence can significantly improve the detection performance for both single-MS and multi-MS 1-bit ADC massive MIMO systems.2021-06-01T23:52:02ZNumerical Schemes for Time-Space Fractional Vibration EquationsZhang, JingnaAleroev, Temirkhan S.Tang, YifaHuang, Jianfeihttp://ir.amss.ac.cn:80/handle/2S8OKBNM/585092021-06-01T23:52:02Z2021-06-01T23:52:02ZTitle: Numerical Schemes for Time-Space Fractional Vibration Equations
Authors: Zhang, Jingna; Aleroev, Temirkhan S.; Tang, Yifa; Huang, Jianfei
Description: In this paper, we present a numerical scheme and an alternating direction implicit (ADI) scheme for the one-dimensional and two-dimensional time-space fractional vibration equations (FVEs), respectively. Firstly, the considered time-space FVEs are equivalently transformed into their partial integro-differential forms with the classical first order integrals and the Riemann-Liouville derivative. This transformation can weaken the smoothness requirement in time when discretizing the partial integro-differential problems. Secondly, we use the Crank-Nicolson technique combined with the midpoint formula, the weighted and shifted Grunwald difference formula and the second order convolution quadrature formula to deal with the temporal discretizations. Meanwhile, the classical central difference formula and fractional central difference formula are applied to approximate the second order derivative and the Riesz derivative in spatial direction, respectively. Further, an ADI scheme is constructed for the two-dimensional case. Then, the convergence and unconditional stability of the proposed schemes are proved rigorously. Both of the schemes are convergent with the second order accuracy in time and space. Finally, two numerical examples are given to support the theoretical results.2021-06-01T23:52:02ZImaging of buried obstacles in a two-layered medium with phaseless far-field dataLi, LongYang, JianshengZhang, BoZhang, Haiwenhttp://ir.amss.ac.cn:80/handle/2S8OKBNM/585032021-06-01T23:52:01Z2021-06-01T23:52:01ZTitle: Imaging of buried obstacles in a two-layered medium with phaseless far-field data
Authors: Li, Long; Yang, Jiansheng; Zhang, Bo; Zhang, Haiwen
Description: This paper is concerned with the inverse problem of reconstructing the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. Similarly to the homogenous background medium case, for this problem it is also true that the modulus of the far-field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, and thus it is impossible to determine the location of the obstacle from such phaseless far-field data. Based on the idea of using superpositions of two plane waves with different directions as the incident fields, a direct imaging algorithm is developed in this paper to locate the position of small anomalies with the intensity of the far-field pattern measured in the upper half-space. This is a nontrivial extension of our previous work (2018 Inverse Problems 34 104005) from the homogenous background medium case to the two-layered background medium case. Both the limited aperture measurement data and the presence of the two-layered background medium lead to difficulties in the theoretical analysis of the proposed imaging algorithm. To overcome the difficulties we employ the theory of oscillatory integrals. Further, with the aid of the imaging algorithm, a recursive Newton-type iteration algorithm in frequencies is proposed to reconstruct both the location and shape of extended obstacles. Finally, numerical experiments are presented to illustrate the feasibility of our algorithms.2021-06-01T23:52:01ZLong-Time Asymptotics for the Focusing Hirota Equation with Non-Zero Boundary Conditions at Infinity Via the Deift-Zhou ApproachChen, ShuyanYan, ZhenyaGuo, Bolinghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/585002021-06-01T23:52:01Z2021-06-01T23:52:01ZTitle: Long-Time Asymptotics for the Focusing Hirota Equation with Non-Zero Boundary Conditions at Infinity Via the Deift-Zhou Approach
Authors: Chen, Shuyan; Yan, Zhenya; Guo, Boling
Description: We are concerned with the long-time asymptotic behavior of the solution for the focusing Hirota equation (also called third-order nonlinear Schrodinger equation) with symmetric, non-zero boundary conditions (NZBCs) at infinity. Firstly, based on the Lax pair with NZBCs, the direct and inverse scattering problems are used to establish the oscillatory Riemann-Hilbert (RH) problem with distinct jump curves. Secondly, the Deift-Zhou nonlinear steepest-descent method is employed to analyze the oscillatory RH problem such that the long-time asymptotic solutions are proposed in two distinct domains of space-time plane (i.e., the plane-wave and modulated elliptic-wave domains), respectively. Finally, the modulation instability of the considered Hirota equation is also investigated.2021-06-01T23:52:01ZQuantifying Decoherence of Gaussian Noise ChannelsZhang, YueLuo, Shunlonghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/584942021-06-01T23:52:00Z2021-06-01T23:52:00ZTitle: Quantifying Decoherence of Gaussian Noise Channels
Authors: Zhang, Yue; Luo, Shunlong
Description: Gaussian noise channels (also called classical noise channels, bosonic Gaussian channels) arise naturally in continuous variable quantum information and play an important role in both theoretical analysis and experimental investigation of information transmission. After reviewing concisely the basic properties of these channels, we introduce an information-theoretic measure for the decoherence of optical states caused by these channels in terms of averaged Wigner-Yanase skew information, explore its basic features, obtain a scaling law, and derive a complementarity relation between the decoherence and the quantum affinity. As an application of the decoherence measure, we derive a convenient and sufficient criterion for detecting optical nonclassicality. The decoherence on some typical optical states caused by Gaussian noise channels are explicitly evaluated to illustrate the concept.2021-06-01T23:52:00ZDual-density-based reweighted l(1)-algorithms for a class of l(0)-minimization problemsXu, JialiangZhao, Yun-Binhttp://ir.amss.ac.cn:80/handle/2S8OKBNM/584972021-06-01T23:52:00Z2021-06-01T23:52:00ZTitle: Dual-density-based reweighted l(1)-algorithms for a class of l(0)-minimization problems
Authors: Xu, Jialiang; Zhao, Yun-Bin
Description: The optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based reweighted l(1)-algorithms for a class of l(0)-minimization models which can be used to model a wide range of practical problems. This class of algorithms is based on certain convex relaxations of the reformulation of the underlying l(0)-minimization model. Such a reformulation is a special bilevel optimization problem which, in theory, is equivalent to the underlying l(0)-minimization problem under the assumption of strict complementarity. Some basic properties of these algorithms are discussed, and numerical experiments have been carried out to demonstrate the efficiency of the proposed algorithms. Comparison of numerical performances of the proposed methods and the classic reweighted l(1)-algorithms has also been made in this paper.2021-06-01T23:52:00ZLearning nonlinear operators via DeepONet based on the universal approximation theorem of operatorsLu, LuJin, PengzhanPang, GuofeiZhang, ZhongqiangKarniadakis, George Emhttp://ir.amss.ac.cn:80/handle/2S8OKBNM/584882021-06-01T23:51:59Z2021-06-01T23:51:59ZTitle: Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Authors: Lu, Lu; Jin, Pengzhan; Pang, Guofei; Zhang, Zhongqiang; Karniadakis, George Em
Description: It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications.2021-06-01T23:51:59ZAttitude synchronization and rigid formation of multiple rigid bodies over proximity networksDeng, JuanWang, LinLiu, Zhixinhttp://ir.amss.ac.cn:80/handle/2S8OKBNM/584912021-06-01T23:51:59Z2021-06-01T23:51:59ZTitle: Attitude synchronization and rigid formation of multiple rigid bodies over proximity networks
Authors: Deng, Juan; Wang, Lin; Liu, Zhixin
Description: In this paper, the combination of the attitude synchronization and rigid formation problem of multiple moving rigid bodies are considered. The moving rigid bodies communicate with each other via a distance-dependent interaction network, yielding the dynamical neighbor relations and the coupling relationship between positions and attitudes of all rigid bodies. The finite-time control and potential function techniques are combined in the design of distributed control laws for the torques and forces of rigid bodies. We construct the admissible set on the initial states, in which the theoretical results on the attitude synchronization, rigidity maintenance and collision avoidance are established simultaneously without relying on the dynamical connectivity of the neighbor graphs. Furthermore, by transforming the stability of rigid formations into the stability of the parameterized systems, we show that the local asymptotic stability of rigid formations can be achieved. A simulation example is given to illustrate the theoretical results. (C) 2020 Elsevier Ltd. All rights reserved.2021-06-01T23:51:59ZHilbert Expansion of the Boltzmann Equation with Specular Boundary Condition in Half-SpaceGuo, YanHuang, FeiminWang, Yonghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/584852021-06-01T23:51:59Z2021-06-01T23:51:59ZTitle: Hilbert Expansion of the Boltzmann Equation with Specular Boundary Condition in Half-Space
Authors: Guo, Yan; Huang, Feimin; Wang, Yong
Description: Boundary effects play an important role in the study of hydrodynamic limits in the Boltzmann theory. Based on a systematic study of the viscous layer equations and the L-2 to L-infinity framework, we establish the validity of the Hilbert expansion for the Boltzmann equation with specular reflection boundary conditions, which leads to derivations of compressible Euler equations and acoustic equations in half-space.2021-06-01T23:51:59ZGlobal Existence and the Decay of Solutions to the Prandtl System with Small Analytic DataPaicu, MariusZhang, Pinghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/584792021-06-01T23:51:58Z2021-06-01T23:51:58ZTitle: Global Existence and the Decay of Solutions to the Prandtl System with Small Analytic Data
Authors: Paicu, Marius; Zhang, Ping
Description: In this paper, we prove the global existence and the large time decay estimate of solutions to Prandtl system with small initial data, which is analytical in the tangential variable. The key ingredient used in the proof is to derive a sufficiently fast decay-in-time estimate of some weighted analytic energy estimate to a quantity, which consists of a linear combination of the tangential velocity with its primitive one, and which basically controls the evolution of the analytical radius to the solutions. Our result can be viewed as a global-in-time Cauchy-Kowalevsakya result for the Prandtl system with small analytical data, which in particular improves the previous result in Ignatova and Vicol (Arch Ration Mech Anal 220:809-848, 2016) concerning the almost global well-posedness of a two-dimensional Prandtl system.2021-06-01T23:51:58Z