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arXiv 2020年

作者： Xie, Hailiang Xu, Jie Liu, Ya-Feng School of Information Engineering Guangdong University of Technology Guangzhou510006 China Shenzhen518172 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

This paper investigates an intelligent reflecting surface (IRS)-aided multi-cell multiple-input single-output (MISO) system with a set of multi-antenna base stations (BSs) each communicating with a single-antenna user, in which an IRS is dedicatedly deployed for assisting the wireless transmission and suppressing the inter-cell interference. Under this setup, we jointly optimize the coordinated transmit beamforming vectors at the BSs and the reflective beamforming vector at the IRS, for the purpose of maximizing the minimum weighted signal-to-interference-plus-noise ratio (SINR) at the users, subject to the individual maximum transmit power constraints at the BSs and the reflection constraints at the IRS. To solve the non-convex min-weighted-SINR maximization problem, we first present an exact-alternating-optimization approach to optimize the transmit and reflective beamforming vectors in an alternating manner, in which the transmit and reflective beamforming optimization subproblems are solved exactly in each iteration by using the techniques of second-order-cone program (SOCP) and semi-definite relaxation (SDR), respectively. However, the exact-alternating-optimization approach has high computational complexity, and may lead to compromised performance due to the uncertainty of randomization in SDR. To avoid these drawbacks, we further propose an inexact-alternating-optimization approach, in which the transmit and reflective beamforming optimization subproblems are solved inexactly in each iteration based on the principle of successive convex approximation (SCA). In addition, to further reduce the computational complexity, we propose a low-complexity inexact-alternating-optimization design, in which the reflective beamforming optimization subproblem is solved more inexactly. Via numerical results, it is shown that the proposed three designs achieve significantly increased min-weighted-SINR values, as compared with benchmark schemes without the IRS or with random re

关键词： Beamforming

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An efficient quadratic programming relaxation based algorithm for large-scale MIMO detection

arXiv

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arXiv 2020年

作者： Zhao, Ping-Fan Li, Qing-Na Chen, Wei-Kun Liu, Ya-Feng School of Mathematics and Statistics Beijing Institute of Technology Beijing China School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Multiple-input multiple-output (MIMO) detection is a fundamental problem in wireless communications and it is strongly NP-hard in general. Massive MIMO has been recognized as a key technology in the fifth generation (5G) and beyond communication networks, which on one hand can significantly improve the communication performance, and on the other hand poses new challenges of solving the corresponding optimization problems due to the large problem size. While various efficient algorithms such as semidefinite relaxation (SDR) based approaches have been proposed for solving the small-scale MIMO detection problem, they are not suitable to solve the large-scale MIMO detection problem due to their high computational complexities. In this paper, we propose an efficient sparse quadratic programming (SQP) relaxation based algorithm for solving the large-scale MIMO detection problem. In particular, we first reformulate the MIMO detection problem as an SQP problem. By dropping the sparse constraint, the resulting relaxation problem shares the same global minimizer with the SQP problem. In sharp contrast to the SDRs for the MIMO detection problem, our relaxation does not contain any (positive semidefinite) matrix variable and the numbers of variables and constraints in our relaxation are significantly less than those in the SDRs, which makes it particularly suitable for the large-scale problem. Then we propose a projected Newton based quadratic penalty method to solve the relaxation problem, which is guaranteed to converge to the vector of transmitted signals under reasonable conditions. By extensive numerical experiments, when applied to solve small-scale problems, the proposed algorithm is demonstrated to be competitive with the state-of-the-art approaches in terms of detection accuracy and solution efficiency;when applied to solve large-scale problems, the proposed algorithm achieves better detection performance than a recently proposed generalized power *** Codes 90C2

关键词： Quadratic programming

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Parallel exponential time differencing methods for geophysical flow simulations

arXiv

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arXiv 2021年

作者： Lan, Rihui Leng, Wei Wang, Zhu Ju, Lili Gunzburger, Max Department of Mathematics University of South Carolina ColumbiaSC29208 United States State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing100190 China Department of Scientific Computing Florida State University TallahasseeFL32306 United States

Two ocean models are considered for geophysical flow simulations: the multi-layer shallow water equations and the multi-layer primitive equations. For the former, we investigate the parallel performance of exponential time differencing (ETD) methods, including exponential Rosenbrock-Euler, ETD2wave, and B-ETD2wave. For the latter, we take advantage of the splitting of barotropic and baroclinic modes and propose a new two-level method in which an ETD method is applied to solve the fast barotropic mode. These methods could improve the computational efficiency of numerical simulations because ETD methods allow for much larger time step sizes than traditional explicit time-stepping techniques that are commonly used in existing computational ocean models. Several standard benchmark tests for ocean modeling are performed and comparison of the numerical results demonstrate a great potential of applying the parallel ETD methods for simulating real-world geophysical flows. © 2021, CC BY-NC-ND.

关键词： Numerical methods

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An efficient global algorithm for single-group multicast beamforming

arXiv

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arXiv 2017年

作者： Lu, Cheng Liu, Ya-Feng School of Economics and Management North China Electric Power University Beijing102206 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

Consider the single-group multicast beamforming problem, where multiple users receive the same data stream simultaneously from a single transmitter. The problem is NPhard and all existing algorithms for the problem either find suboptimal approximate or local stationary solutions. In this paper, we propose an efficient branch-and-bound algorithm for the problem that is guaranteed to find its global solution. To the best of our knowledge, our proposed algorithm is the first tailored global algorithm for the single-group multicast beamforming problem. Simulation results show that our proposed algorithm is computationally efficient (albeit its theoretical worstcase iteration complexity is exponential with respect to the number of receivers) and it significantly outperforms a state-ofthe- art general-purpose global optimization solver called Baron. Our proposed algorithm provides an important benchmark for performance evaluation of existing algorithms for the same problem. By using it as the benchmark, we show that two state-of-theart algorithms, semidefinite relaxation algorithm and successive linear approximation algorithm, work well when the problem dimension (i.e., the number of antennas at the transmitter and the number of receivers) is small but their performance deteriorates quickly as the problem dimension increases. Copyright © 2017, The Authors. All rights reserved.

关键词： Beamforming

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Splitting iteration methods for non-Hermitian positive definite systems of linear equations

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Hokkaido Mathematical Journal 2007年第4期36卷 801-814页

作者： Bai, Zhong-Zhi State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 P.O. Box 2719 China

For large sparse system of linear equations with a non-Hermitian positive definite coefficient matrix, we review the recently developed Hermitian/skew-Hermitian splitting (HSS) iteration, normal/skew-Hermitian splitting (NSS) iteration, positive-definite/ skew-Hermitian splitting (PSS) iteration, and block triangular/skew-Hermitian splitting (BTSS) iteration. These methods converge unconditionally to the exact solution of the linearsystem, with the upper bounds of their convergence factors being only dependent on the spectrum of the Hermitian (or normal, or positive-definite) splitting matrix, but independent of the spectrum of the skew-Hermitian splitting matrix as well as the eigenvectors of all matrices involved. © 2007 by the University of Notre Dame. All rights reserved.

关键词： Block triangular matrix Hermitian and skew-Hermitian splitting Non-Hermitian matrix Normal/Skew-Hermitian splitting Positive definite matrix Positivedefinite/Skew-Hermitian splitting Splitting iteration method

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Efficient CI-Based One-Bit Precoding for Multiuser Downlink Massive MIMO Systems with PSK Modulation

arXiv

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arXiv 2021年

作者： Wu, Zheyu Jiang, Bo Liu, Ya-Feng Shao, Mingjie Dai, Yu-Hong The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Ministry of Education Key Laboratory for NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing210023 China The School of Information Science and Engineering Shandong University Qingdao China

In this paper, we consider the one-bit precoding problem for the multiuser downlink massive multiple-input multiple-output (MIMO) system with phase shift keying (PSK) modulation. We focus on the celebrated constructive interference (CI)-based problem formulation. We first establish the NP-hardness of the problem (even in the single-user case), which reveals the intrinsic difficulty of globally solving the problem. Then, we propose a novel negative 1 penalty model for the considered problem, which penalizes the one-bit constraint into the objective by a negative 1-norm term, and show the equivalence between (global and local) solutions of the original problem and the penalty problem when the penalty parameter is sufficiently large. We further transform the penalty model into an equivalent min-max problem and propose an efficient alternating proximal/projection gradient descent ascent (APGDA) algorithm for solving it, which performs a proximal gradient decent over one block of variables and a projection gradient ascent over the other block of variables alternately. The APGDA algorithm enjoys a low per-iteration complexity and is guaranteed to converge to a stationary point of the min-max problem and a local minimizer of the penalty problem. To further reduce the computational cost, we also propose a low-complexity implementation of the APGDA algorithm, where the values of the variables will be fixed in later iterations once they satisfy the one-bit constraint. Numerical results show that, compared to the state-of-the-art CI-based algorithms, both of the proposed algorithms generally achieve better bit-error-rate (BER) performance with lower computational cost. Copyright © 2021, The Authors. All rights reserved.

关键词： Gradient methods

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A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems

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Chinese Physics B 2007年第3期16卷 599-604页

作者：刘鸿基傅景礼唐贻发 Institute of Mathematical Physics Shangqiu Teacher's College Shangqiu 476000 China Department of Physics Zhejiang Sci-Tech University Hangzhou 310018 China State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing 100080 China Shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

In this paper Mei symmetry is introduced for a nonconservative system. The necessary and sufficient condition for a Mei symmetry to be also a Lie symmetry is derived. It is proved that the Mei symmetry leads to a non-Noether conservative quantity via a Lie symmetry, and deduces a Lutzky conservative quantity via a Lie point symmetry.

关键词： Mei symmetry non-Noether conservative quantity Lutzky conservative quantity nonconservative system

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Max-min fairness user scheduling and power allocation in full-duplex OFDMA systems

arXiv

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arXiv 2018年

作者： Zhang, Xiaozhou Chang, Tsung-Hui Liu, Ya-Feng Shen, Chao Zhu, Gang State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing China School of Science and Engineering Chinese University of Hong Kong Shenzhen China Shenzhen Research Institute of Big Data Shenzhen China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In a full-duplex (FD) multi-user network, the system performance is not only limited by the self-interference but also by the co-channel interference due to the simultaneous uplink and downlink transmissions. Joint design of the uplink/downlink transmission direction of users and the power allocation is crucial for achieving high system performance in the FD multi-user network. In this paper, we investigate the joint uplink/downlink transmission direction assignment (TDA), user paring (UP) and power allocation problem for maximizing the system max-min fairness (MMF) rate in a FD multi-user orthogonal frequency division multiple access (OFDMA) system. The problem is formulated with a two-time-scale structure where the TDA and the UP variables are for optimizing a long-term MMF rate while the power allocation is for optimizing an instantaneous MMF rate during each channel coherence interval. We show that the studied joint MMF rate maximization problem is NP-hard in general. To obtain high-quality suboptimal solutions, we propose efficient methods based on simple relaxation and greedy rounding techniques. Simulation results are presented to show that the proposed algorithms are effective and achieve higher MMF rates than the existing heuristic methods. Copyright © 2018, The Authors. All rights reserved.

关键词： Optimization

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A class of numerical methods with one parameter for backward stochastic differential equations

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AIP Conference Proceedings 2012年第1期1479卷 1765-1768页

作者： Dongsheng Xu Peng Wang Xiuling Yin State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences 100080 Beijing China College of Mathematics Jilin University 130012 Jilin People's China Department of Mathematics Dezhou University 352023 Shandong People's China

In this paper, we investigate backward stochastic differential equations (BSDEs) driven by Brownian motion. We propose a class of Euler type numerical methods with one parameter based on random walk framework for one-...

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Efficient Estimation of Sensor Biases for the 3-Dimensional Asynchronous Multi-Sensor System

arXiv

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arXiv 2021年

作者： Pu, Wenqiang Liu, Ya-Feng Luo, Zhi-Quan Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

An important preliminary procedure in multi-sensor data fusion is sensor registration, and the key step in this procedure is to estimate sensor biases from their noisy measurements. There are generally two difficulties in this bias estimation problem: one is the unknown target states which serve as the nuisance variables in the estimation problem, and the other is the highly nonlinear coordinate transformation between the local and global coordinate systems of the sensors. In this paper, we focus on the 3-dimensional asynchronous multi-sensor scenario and propose a weighted nonlinear least squares (NLS) formulation by assuming that there is a target moving with a nearly constant velocity. We propose two possible choices of the weighting matrix in the NLS formulation, which correspond to classical and weighted NLS estimation and maximum likelihood (ML) estimation, respectively. To address the intrinsic nonlinearity, we propose a block coordinate descent (BCD) algorithm for solving the formulated problem, which alternately updates different kinds of bias estimates. Specifically, the proposed BCD algorithm involves solving linear LS problems and nonconvex quadratically constrained quadratic program (QCQP) problems with special structures. Instead of adopting the semidefinite relaxation technique, we develop a much more computationally efficient algorithm based on the alternating direction method of multipliers (ADMM) to solve the nonconvex QCQP subproblems. The convergence of the ADMM to the global solution of the QCQP subproblems is established under mild conditions. The effectiveness and efficiency of the proposed BCD algorithm are demonstrated via numerical simulations. Copyright © 2021, The Authors. All rights reserved.

关键词： Maximum likelihood estimation

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