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One-Bit precoding and constellation range design for massive MIMO with QAM Signaling

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arXiv 2018年

作者： Sohrabi, Foad Liu, Ya-Feng Yu, Wei Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S3G4 Canada State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing100190 China

The use of low-resolution digital-to-analog converters (DACs) for transmit precoding provides crucial energy efficiency advantage for massive multiple-input multiple-output (MIMO) implementation. This paper formulates a quadrature amplitude modulation (QAM) constellation range and one-bit symbol-level precoding design problem for minimizing the average symbol error rate (SER) in downlink massive MIMO transmission. A tight upper-bound for SER with low-resolution DAC precoding is first derived. The derived expression suggests that the performance degradation of one-bit precoding can be interpreted as a decrease in the effective minimum distance of the QAM constellation. Using the obtained SER expression, we propose a QAM constellation range design for the singleuser case. It is shown that in the massive MIMO limit, a reasonable choice for constellation range with one-bit precoding is that of the infinite-resolution precoding with per-symbol power constraint, but reduced by a factor of p 2/π or about 0:8. The corresponding minimum distance reduction translates to about 2dB gap between the performance of one-bit precoding and infinite-resolution precoding. This paper further proposes a low-complexity heuristic algorithm for one-bit precoder design. Finally, the proposed QAM constellation range and precoder design are generalized to the multi-user downlink. We propose to scale the constellation range for infinite-resolution zero-forcing (ZF) precoding with per-symbol power constraint by the same factor of p 2/π for one-bit precoding. The proposed one-bit precoding scheme is shown to be within 2dB of infinite-resolution ZF. In term of number of antennas, one-bit precoding requires about 50% more antennas to achieve the same performance as infinite-resolution precoding. Copyright © 2018, The Authors. All rights reserved.

关键词： Quadrature amplitude modulation

Third-order discrete unified gas kinetic scheme for continuum and rarefied flows: Low-speed isothermal case

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Physical Review E 2018年第2期97卷 023306-023306页

作者： Chen Wu Baochang Shi Chang Shu Zhen Chen State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China Department of Mechanical Engineering National University of Singapore 10 Kent Ridge Crescent Singapore 119260 Singapore

An efficient third-order discrete unified gas kinetic scheme (DUGKS) is presented in this paper for simulating continuum and rarefied flows. By employing a two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation-based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second order (or lower order) of accuracy in the time-splitting scheme as in the conventional high-order Runge-Kutta-based kinetic methods, the present method solves the original Boltzmann equation, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows.

关键词： Boltzmann theory

Lattice Boltzmann model for high-order nonlinear partial differential equations

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Physical Review E 2018年第1期97卷 013304-013304页

作者： Zhenhua Chai Nanzhong He Zhaoli Guo Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Computer Wuhan Textile University Wuhan 430200 China

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ+∑k=1mαk∂xkΠk(ϕ)=0 (1≤k≤m≤6), αk are constant coefficients, Πk(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009); H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)] for high-order nonlinear partial differential equations.

关键词： Lattice-Boltzmann methods

Optimized base-station cache allocation for cloud radio access network with multicast backhaul

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arXiv 2018年

作者： Dai, Binbin Liu, Ya-Feng Yu, Wei Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S 3G4 Canada 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 performance of cloud radio access network (C-RAN) is limited by the finite capacities of the backhaul links connecting the centralized processor (CP) with the base-stations (BSs), especially when the backhaul is implemented in a wireless medium. This paper proposes the use of wireless multicast together with BS caching, where the BSs pre-store contents of popular files, to augment the backhaul of C-RAN. For a downlink C-RAN consisting of a single cluster of BSs and wireless backhaul, this paper studies the optimal cache size allocation strategy among the BSs and the optimal multicast beamforming transmission strategy at the CP such that the user’s requested messages are delivered from the CP to the BSs in the most efficient way. We first state a multicast backhaul rate expression based on a joint cache-channel coding scheme, which implies that larger cache sizes should be allocated to the BSs with weaker channels. We then formulate a two-timescale joint cache size allocation and beamforming design problem, where the cache is optimized offline based on the long-term channel statistical information, while the beamformer is designed during the file delivery phase based on the instantaneous channel state information. By leveraging the sample approximation method and the alternating direction method of multipliers (ADMM), we develop efficient algorithms for optimizing cache size allocation among the BSs, and quantify how much more cache should be allocated to the weaker BSs. We further consider the case with multiple files having different popularities and show that it is in general not optimal to entirely cache the most popular files first. Numerical results show considerable performance improvement of the optimized cache size allocation scheme over the uniform allocation and other heuristic schemes. Copyright © 2018, The Authors. All rights reserved.

关键词： Base stations

Capacity optimality of AMP in coded systems

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arXiv 2019年

作者： Liu, Lei Liang, Chulong Ma, Junjie Ping, Li Hong Kong SAR China Nomi 923-1292 Japan Department of Electrical Engineering City University of Hong Kong Hong Kong SAR China Algorithm Department ZTE Corporation Shenzhen 518057 China State Key Laboratory of Mobile Network Mobile Multimedia Technology ZTE Corporation Shenzhen 518057 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Science Beijing China Department of Electronic Engineering City University of Hong Kong Hong Kong SAR China

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. As a byproduct, we provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. We discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. We show that the optimized codes demonstrate significantly better performance over un-matched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed. © 2019, CC BY-NC-SA.

关键词： Message passing

Adaptive low-nonnegative-rank approximation for state aggregation of Markov chains

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arXiv 2018年

作者： Duan, Yaqi Wang, Mengdi Wen, Zaiwen Yuan, Yaxiang Department of Operations Research and Financial Engineering Princeton University United States Beijing International Center for Mathematical Research Peking University China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

This paper develops a low-nonnegative-rank approximation method to identify the state aggregation structure of a finite-state Markov chain under an assumption that the state space can be mapped into a handful of meta-states. The number of meta-states is characterized by the nonnegative rank of the Markov transition matrix. Motivated by the success of the nuclear norm relaxation in low rank minimization problems, we propose an atomic regularizer as a convex surrogate for the nonnegative rank and formulate a convex optimization problem. Because the atomic regularizer itself is not computationally tractable, we instead solve a sequence of problems involving a nonnegative factorization of the Markov transition matrices by using the proximal alternating linearized minimization method. Two methods for adjusting the rank of factorization are developed so that local minima are escaped. One is to append an additional column to the factorized matrices, which can be interpreted as an approximation of a negative subgradient step. The other is to reduce redundant dimensions by means of linear combinations. Overall, the proposed algorithm very likely converges to the global solution. The efficiency and statistical properties of our approach are illustrated on synthetic data. We also apply our state aggregation algorithm on a Manhattan transportation data set and make extensive comparisons with an existing method. Copyright © 2018, The Authors. All rights reserved.

关键词： Linearization

Make 1 regularization effective in training sparse CNN

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arXiv 2018年

作者： He, Juncai Jia, Xiaodong Xu, Jinchao Zhang, Lian Zhao, Liang Department of Mathematics Pennsylvania State University University ParkPA16802 United States Department of Computer Science and Engineering Pennsylvania State University University ParkPA16802 United States State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing100190 China

Compressed Sensing using 1 regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network (CNN)? This paper is aimed to provide an answer to this question and to show how to make it work. Following Xiao (2010), We first demonstrate that the commonly used stochastic gradient decent (SGD) and variants training algorithm is not an appropriate match with 1 regularization and then replace it with a different training algorithm based on a regularized dual averaging (RDA) method. The RDA method of Xiao (2010) was originally designed specifically for convex problem, but with new theoretical insight and algorithmic modifications (using proper initialization and adaptivity), we have made it an effective match with 1 regularization to achieve a state-of-the-art sparsity for the highly non-convex CNN compared to other weight pruning methods without compromising accuracy (achieving 95% sparsity for ResNet-18 on CIFAR-10, for example). Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

Improvements in continuum modeling for biomolecular systems

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Chinese Physics B 2016年第1期25卷 333-338页

作者：乔瑜卢本卓 State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences

Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann （PB）/Poisson-Nernst-Planck （PNP） equations has made great contributions towards simulation of these pro- cesses. However, the model has shortcomings in its commonly used form and cannot capture （or cannot accurately capture） some important physical properties of the biological systems. Considerable efforts have been made to improve the con- tinuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecu- lar systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress.

关键词： Poisson-Boltzmann equation Poisson-Nernst-Planck equations ionic size effects density func-tional theory

A New Fully Polynomial Time Approximation Scheme for the Interval Subset Sum Problem

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arXiv 2017年

作者： Diao, Rui Liu, Ya-Feng Dai, Yu-Hong 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 interval subset sum problem (ISSP) is a generalization of the well-known subset sum problem. Given a set of intervals {[ai,1, ai,2]}ni=1 and a target integer T, the ISSP is to find a set of integers, at most one from each interval, such that their sum best approximates the target T but cannot exceed it. In this paper, we first study the computational complexity of the ISSP. We show that the ISSP is relatively easy to solve compared to the 0-1 Knapsack problem (KP). We also identify several subclasses of the ISSP which are polynomial time solvable (with high probability), albeit the problem is generally NP-hard. Then, we propose a new fully polynomial time approximation scheme (FPTAS) for solving the general ISSP problem. The time and space complexities of the proposed scheme are O (n max {1/ǫ, log n}) and O (n + 1/ǫ), respectively, where ǫ is the relative approximation error. To the best of our knowledge, the proposed scheme has almost the same time complexity but a significantly lower space complexity compared to the best known scheme. Both the correctness and efficiency of the proposed scheme are validated by numerical simulations. In particular, the proposed scheme successfully solves ISSP instances with n = 100, 000 and ǫ = 0.1% within one second. Copyright © 2017, The Authors. All rights reserved.

关键词： Computational complexity