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Energy-Efficient Beamforming Design for Integrated Sensing and Communications Systems

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arXiv 2023年

作者： Zou, Jiaqi Sun, Songlin Masouros, Christos Cui, Yuanhao Liu, Ya-Feng Ng, Derrick Wing Kwan Beijing100876 China The Department of Electrical and Electronic Engineering University College London LondonWC1E 7JE United Kingdom Beijing China The Department of Electrical and Electronic Engineering University College London WC1E 7JE United Kingdom 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 School of Electrical Engineering and Telecommunications University of New South Wales SydneyNSW2052 Australia

In this paper, we investigate the design of energy-efficient beamforming for an ISAC system, where the transmitted waveform is optimized for joint multi-user communication and target estimation simultaneously. We aim to maximize the system energy efficiency (EE), taking into account the constraints of a maximum transmit power budget, a minimum required signal-to-interference-plus-noise ratio (SINR) for communication, and a maximum tolerable Cramér-Rao bound (CRB) for target estimation. We first consider communication-centric EE maximization. To handle the non-convex fractional objective function, we propose an iterative quadratic-transform-Dinkelbach method, where Schur complement and semi-definite relaxation (SDR) techniques are leveraged to solve the subproblem in each iteration. For the scenarios where sensing is critical, we propose a novel performance metric for characterizing the sensing-centric EE and optimize the metric adopted in the scenario of sensing a point-like target and an extended target. To handle the nonconvexity, we employ the successive convex approximation (SCA) technique to develop an efficient algorithm for approximating the nonconvex problem as a sequence of convex ones. Furthermore, we adopt a Pareto optimization mechanism to articulate the tradeoff between the communication-centric EE and sensing-centric EE. We formulate the search of the Pareto boundary as a constrained optimization problem and propose a computationally efficient algorithm to handle it. Numerical results validate the effectiveness of our proposed algorithms compared with the baseline schemes and the obtained approximate Pareto boundary shows that there is a non-trivial tradeoff between communication-centric EE and sensing-centric EE, where the number of communication users and EE requirements have serious effects on the achievable tradeoff. © 2023, CC BY-NC-ND.

关键词： Energy efficiency

Force-based gradient descent method for ab initio atomic structure relaxation

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Physical Review B 2022年第10期106卷 104101-104101页

作者： Yukuan Hu Xingyu Gao Yafan Zhao Xin Liu Haifeng Song State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China University of Chinese Academy of Sciences Beijing 100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China CAEP Software Center for High Performance Numerical Simulation Beijing 100088 China

Force-based algorithms for ab initio atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive ab initio calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method, WANBB, that circumvents the deficiency. At each iteration, WANBB enters the line minimization process with a trial step size capturing the local curvature of the energy surface. The exit is controlled by a nonrestrictive criterion that tends to accept early trials. These two ingredients streamline the line minimization process in WANBB. The numerical simulations on nearly 80 systems with good universality demonstrate the considerable compression of WANBB on the cost for the unaccepted trials compared with conjugate gradient methods. We also observe across the board significant and universal speedups as well as the superior robustness of WANBB over several widely used methods. The latter point is theoretically established. The implementation of WANBB is pretty simple, in that no a priori physical knowledge is required and only three parameters are present without tuning.

关键词： Crystal structure Structural properties Density functional theory development

Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function

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arXiv 2021年

作者： Wang, Lei Liu, Xin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China

In this paper, we focus on the decentralized optimization problem over the Stiefel manifold, which is defined on a connected network of d agents. The objective is an average of d local functions, and each function is privately held by an agent and encodes its data. The agents can only communicate with their neighbors in a collaborative effort to solve this problem. In existing methods, multiple rounds of communications are required to guarantee the convergence, giving rise to high communication costs. In contrast, this paper proposes a decentralized algorithm, called DESTINY, which only invokes a single round of communications per iteration. DESTINY combines gradient tracking techniques with a novel approximate augmented Lagrangian function. The global convergence to stationary points is rigorously established. Comprehensive numerical experiments demonstrate that DESTINY has a strong potential to deliver a cutting-edge performance in solving a variety of testing problems. Copyright © 2021, The Authors. All rights reserved.

关键词： Iterative methods

Sensing With Communication Signals: From Information Theory to Signal Processing

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arXiv 2025年

作者： Liu, Fan Liu, Ya-Feng Cui, Yuanhao Masouros, Christos Xu, Jie Han, Tony Xiao Buzzi, Stefano Eldar, Yonina C. Jin, Shi National Mobile Communications Research Laboratory School of Information Science and Engineering Southeast University Nanjing210096 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematicsand Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Communication Engineering Beijing University of Posts and Telecommunications Beijing100876 China Department of Electronic and Electrical Engineering University College London LondonWC1E 7JE United Kingdom Guangdong518172 China Huawei Technologies Co. Ltd China Department of Electrical and Information Engineering University of Cassino and Southern Lazio CassinoI-03043 Italy Department of Electronics Information and Bioengineering Politecnico di Milano MilanoI-20133 Italy ParmaI-43124 Italy Faculty of Mathematics and Computer Science Weizmann Institute of Science Rehovot Israel

The Integrated Sensing and Communications (ISAC) paradigm is anticipated to be a cornerstone of the upcoming 6G networks. In order to optimize the use of wireless resources, 6G ISAC systems need to harness the communication data payload signals, which are inherently random, for both sensing and communication (S&C) purposes. This tutorial paper provides a comprehensive technical overview of the fundamental theory and signal processing methodologies for ISAC transmission with random communication signals. We begin by introducing the deterministic-random tradeoff (DRT) between S&C from an information-theoretic perspective, emphasizing the need for specialized signal processing techniques tailored to random ISAC signals. Building on this foundation, we review the core signal models and processing pipelines for communication-centric ISAC systems, and analyze the average squared auto-correlation function (ACF) of random ISAC signals, which serves as a fundamental performance metric for multi-target ranging tasks. Drawing insights from these theoretical results, we outline the design principles for the three key components of communication-centric ISAC systems: modulation schemes, constellation design, and pulse shaping filters. The goal is to either enhance sensing performance without compromising communication efficiency or to establish a scalable tradeoff between the two. We then extend our analysis from a single-antenna ISAC system to its multi-antenna counterpart, discussing recent advancements in multiinput multi-output (MIMO) precoding techniques specifically designed for random ISAC signals. We conclude by highlighting several open challenges and future research directions in the field of sensing with communication signals. Copyright © 2025, The Authors. All rights reserved.

关键词： Signal modulation

An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling

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arXiv 2022年

作者： Shi, Bin Sun, Guodong State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing100029 China University of Chinese Academy of Sciences Beijing100049 China

In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (deterministic) optimization methods.1 Specifically, the traditional approach is unavailable in practice, which requires numerically computing the gradient (first-order information) such that the computation cost is expensive since it needs a large number of times to run numerical models. However, the sampling approach directly reduces the gradient to the objective function value (zeroth-order information), which also avoids using the adjoint technique that is unusable for many atmosphere and ocean models and requires large amounts of storage. We show an intuitive analysis for the sampling algorithm from the law of large numbers and further present a Chernoff-type concentration inequality to rigorously characterize the degree to which the sample average probabilistically approximates the exact gradient. The experiments are implemented to obtain the CNOPs for two numerical models, the Burgers equation with small viscosity and the Lorenz-96 model. We demonstrate the CNOPs obtained with their spatial patterns, objective values, computation times and nonlinear error growth. Compared with the performance of the three approaches, all the characters for quantifying the CNOPs are nearly consistent, while the computation time using the sampling approach with fewer samples is extremely shorter. In other words, the new sampling algorithm shortens the computation time to the utmost at the cost of losing little accuracy. © 2022, CC BY-NC-SA.

关键词： Numerical models

Sampling-Based Methods for Multi-Block Optimization Problems over Transport Polytopes

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arXiv 2023年

作者： Hu, Yukuan Li, Mengyu Liu, Xin Meng, Cheng State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing China Institute of Statistics and Big Data Renmin University of China Beijing China Center for Applied Statistics Institute of Statistics and Big Data Renmin University of China Beijing China

This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for the general multi-block problems store and operate on the matrix variables directly, resulting in formidable expenditure for large-scale settings. On the other hand, optimal transport problems, as a special case, have attracted extensive attention and numerical techniques that waive the use of the full matrices have recently emerged. However, it remains nontrivial to apply these techniques to the multi-block, possibly nonconvex problems with theoretical guarantees. In this work, we leverage the benefits of both sides and develop novel sampling-based block coordinate descent-type methods, which are equipped with either entropy regularization or Kullback-Leibler divergence. Each iteration of these methods solves subproblems restricted on the sampled degrees of freedom. Consequently, they involve only sparse matrices, which amounts to considerable complexity reductions. We explicitly characterize the sampling-induced errors and establish convergence and asymptotic properties for the methods equipped with the entropy regularization. Numerical experiments on typical strongly correlated electron systems corroborate their superior scalability over the methods utilizing full matrices. The advantage also enables the first visualization of approximate optimal transport maps between electron positions in three-dimensional *** Codes 52-08, 65C05, 65F50, 81V05, 90C30 © 2023, CC BY.

关键词： Entropy

A Brief Introduction to Manifold Optimization

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Journal of the Operations Research Society of China 2020年第2期8卷 199-248页

作者： Jiang Hu Xin Liu Zai-Wen Wen Ya-Xiang Yuan Beijing International Center for Mathematical Research Peking UniversityBeijing 100871China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100190China

Manifold optimization is ubiquitous in computational and appliedmathematics,statistics,engineering,machine learning,physics,chemistry,*** of the main challenges usually is the non-convexity of the manifold *** utilizing the geometry of manifold,a large class of constrained optimization problems can be viewed as unconstrained optimization problems on *** this perspective,intrinsic structures,optimality conditions and numerical algorithms for manifold optimization are *** recent progress on the theoretical results of manifold optimization is also presented.

关键词： Convergence First-order-type algorithms Manifold optimization Retraction Second-order-type algorithms

Convergence of physics-informed neural networks applied to linear second-order elliptic interface problems

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arXiv 2022年

作者： Wu, Sidi Zhu, Aiqing Tang, Yifa Lu, Benzhuo State Key Laboratory of Scientific and Engineering Computing National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

With the remarkable empirical success of neural networks across diverse scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. However, there has been little theoretical work focusing on neural networks in solving interface problems. In this paper, we perform a convergence analysis of physics-informed neural networks (PINNs) for solving second-order elliptic interface problems. Specifically, we consider PINNs with domain decomposition technologies and introduce gradient-enhanced strategies on the interfaces to deal with boundary and interface jump conditions. It is shown that the neural network sequence obtained by minimizing a Lipschitz regularized loss function converges to the unique solution to the interface problem in H2 as the number of samples increases. Numerical experiments are provided to demonstrate our theoretical analysis. Copyright © 2022, The Authors. All rights reserved.

关键词： Domain decomposition methods

Parallel exponential time differencing methods for geophysical flow simulations

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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