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A low-complexity iterative algorithm for multiuser millimeter-wave systems

ANNALS OF TELECOMMUNICATIONS 2024年第1-2期79卷 101-110页

作者： Mulla, Mustafa Ulusoy, Ali Hakan Rizaner, Ahmet Amca, Hasan Middle East Tech Univ Dept Elect & Elect Engn Northern Cyprus CampusVia Mersin 10 TR-99738 Guzelyurt North Cyprus Turkiye Eastern Mediterranean Univ Sch Comp & Technol Dept Informat Technol Via Mersin 10 TR-99628 Famagusta North Cyprus Turkiye Eastern Mediterranean Univ Dept Elect & Elect Engn Via Mersin 10 TR-99628 Famagusta North Cyprus Turkiye

In this paper, we design a low-complexity multiuser millimeter-wave massive-multiple-input-multiple-output system with the help of a hybrid analog/digital precoding architecture. Hybrid precoding is used to reduce the hardware cost and power consumption of millimeter-wave large-scale antenna systems. In this manner, we proposed a novel approach to solve the well-known zero-forcing algorithm by using an iterative optimization method called the conjugate gradient method. The problem is transformed into an optimization problem, and the complex matrix inverse operation required in the zero-forcing algorithm is eliminated. Hence, the complexity of the zero-forcing algorithm is reduced while the spectral efficiency is maintained at the same level as that of the reference zero-forcing detector. The simulation results demonstrate that the proposed conjugate gradient-based algorithm achieves better performance than competing methods in terms of complexity and spectral efficiency.

关键词： Multiuser Millimeter wave Massive multiple-input-multiple-output Hybrid precoding Iterative optimization conjugate gradient algorithm

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Numerical Estimation of the Inverse Eigenvalue Problem for a Weighted Helmholtz Equation

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JOURNAL OF SCIENTIFIC COMPUTING 2023年第1期96卷 1-31页

作者： Zhang, Zhengfang Gao, Xiangjing Cheng, Xiaoliang Hangzhou Dianzi Univ Coll Sci Hangzhou 310018 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

The inverse eigenvalue problem for a weighted Helmholtz equation is investigated. Based on the finite spectral data, the density function is estimated. The inverse problem is formulated as a least squared functional with respect to the density function, with a L(2 )regularity term. The continuity of the eigenpairs with respect to the density is proved. Mathematical properties of the continuous and the discrete optimization problems are established. A conjugate gradient algorithm is proposed. Numerical results for 1D and 2D inverse eigenvalue problem of the weighted Helmholtz equation are presented to illustrate the effectiveness and efficiency of the proposed algorithm.

关键词： Inverse eigenvalue problem Weighted Helmholtz equation conjugate gradient algorithm Finite element method

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FOURIER ACCELERATION OF ITERATIVE PROCESSES IN DISORDERED-SYSTEMS

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JOURNAL OF STATISTICAL PHYSICS 1988年第3-4期52卷 747-773页

作者： BATROUNI, GG HANSEN, A ECOLE NORMALE SUPER PHYS SOLIDES GRPF-75231 PARISFRANCE UNIV COLOGNE INST THEORET PHYSD-5000 COLOGNE 41FED REP GER

Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria.

关键词： Fourier acceleration critical slowing down relaxation conjugate gradient algorithm disordered systems

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Spatiotemporal hierarchical Bayesian modeling: Tropical ocean surface winds

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2001年第454期96卷 382-397页

作者： Wikle, CK Milliff, RF Nychka, D Berliner, LM Univ Missouri Dept Stat Columbia MO 65211 USA Colorado Res Associates Boulder CO 80301 USA Natl Ctr Atmospher Res Geophys Stat Project Boulder CO 80307 USA Ohio State Univ Dept Stat Columbus OH 43210 USA

Spatiotemporal processes are ubiquitous in the environmental and physical sciences. This is certainly true of atmospheric and oceanic processes, which typically exhibit many different scales of spatial and temporal variability. The complexity of these processes and the large number of observation/prediction locations preclude the use of traditional covariance-based spatiotemporal statistical methods. Alternatively, we focus on conditionally specified (i.e., hierarchical) spatiotemporal models. These methods offer several advantages over traditional approaches. Primarily, physical and dynamical constraints can be easily incorporated into the conditional formulation, so that the series of relatively simple yet physically realistic conditional models leads to a much more complicated spatiotemporal covariance structure than can be specified directly. Furthermore, by making use of the sparse structure inherent in the hierarchical approach, as well as multiresolution (wavelet) bases, the models can be computed with very large datasets. This modeling approach was necessitated by a scientifically meaningful problem in the geosciences. Satellite-derived wind estimates have high spatial resolution but limited global coverage. In contrast, wind fields provided by the major weather centers provide complete coverage but have low spatial resolution. The god is to combine these data in a manner that incorporates the space-time dynamics inherent in the surface wind field. This is an essential task to enable meteorological research, because no complete high-resolution surface wind datasets exist over the world oceans. High-resolution datasets of this type are crucial for improving our understanding of global air-sea interactions affecting climate and tropical disturbances, and for driving large-scale ocean circulation models.

关键词： climate combining information conjugate gradient algorithm dynamical model fractal process Gibbs sampling numerical model ocean model satellite data turbulence wavelets

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A Numerical Method for Cavity Identification in Beams on an Elastic Foundation

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Tsinghua Science and Technology 2007年第5期12卷 540-545页

作者：葛洪海许金余 School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University

An analytical solution for the natural frequencies of a beam containing a cavity on an elastic foundation is presented. Based on the analytical solution, a numerical method for identifying cavities in the foundation is developed. The position and size of the cavities are identified by minimizing an objective function, which is formulated according to the difference between the computed and measured natural frequencies of the system. The conjugate gradient algorithm is adopted for minimizing the objective function. Some numerical examples are presented to demonstrate the applicability of the presented cavity determination method. The results show that the presented method can be used to identify the cavity position and size conveniently and efficiently.

关键词： pavement-subgrade system beam on an elastic foundation cavity identification natural frequency conjugate gradient algorithm

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Fast approximate likelihood evaluation for stable VARFIMA processes

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STATISTICS & PROBABILITY LETTERS 2015年 103卷 160-168页

作者： Pai, Jeffrey Ravishanker, Nalini Univ Manitoba Warren Ctr Actuarial Studies & Res Winnipeg MB R3T 5V4 Canada Univ Connecticut Dept Stat Storrs CT 06269 USA

For VARFIMA models with sub-Gaussian stable errors, we present fast approximate likelihood computation by using a multivariate preconditioned conjugate gradient (MPCG) algorithm, and Monte Carlo integration over unobserved variables. We illustrate our approach on daily average temperatures measured at several US cities. (C) 2015 Elsevier B.V. All rights reserved.

关键词： conjugate gradient algorithm Fast Fourier transform Long memory Preconditioning Sub-Gaussian stable errors

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Numerical Solution of Bratu's Problem Using Multilayer Perceptron Neural Network Method

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NATIONAL ACADEMY SCIENCE LETTERS-INDIA 2015年第5期38卷 425-428页

作者： Kumar, Manoj Yadav, Neha Motilal Nehru Natl Inst Technol Dept Math Allahabad 211004 Uttar Pradesh India ITM Univ Dept Appl Sci Gurgaon 122017 Haryana India

In this article, an artificial neural network (ANN) method is presented to obtain the closed analytic form of the one dimensional Bratu type equations, which are widely applicable in fuel ignition of the combustion theory and heat transfer. Our goal is to provide optimal solution of Bratu type equations with reduced calculus effort using ANN method in comparison to the other existing methods. Various test cases have been simulated using proposed neural network model and the accuracy has been substantiated by considering a large number of simulation data for each model with enough independent runs. Numerical results show that this method has potentiality to become an efficient approach for solving Bratu's problems with less computing time and memory space.

关键词： Artificial neural network Back propagation algorithm Bratu's equations Levenberg-Marquardt algorithm conjugate gradient algorithm

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Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第6期234卷 1904-1911页

作者： Monkola, Sanna Univ Jyvaskyla Dept Math Informat Technol FI-40014 Jyvaskyla Finland

The classical way of solving the time-harmonic linear acousto-elastic wave problem is to discretize the equations with finite elements or finite differences. This approach leads to large-scale indefinite complex-valued linear systems. For these kinds of systems, it is difficult to construct efficient iterative solution methods. That is why we use an alternative approach and solve the time-harmonic problem by controlling the solution of the corresponding time dependent wave equation. In this paper, we use an unsymmetric formulation, where fluid-structure interaction is modeled as a coupling between pressure and displacement. The coupled problem is discretized in space domain with spectral elements and in time domain with central finite differences. After discretization, exact controllability problem is reformulated as a least-squares problem, which is solved by the conjugate gradient method. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Fluid-structure interaction Acoustic waves Elastic waves Coupled problem Time-harmonic solution Spectral element method Controllability conjugate gradient algorithm

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LANGEVIN SIMULATIONS OF LATTICE FIELD-THEORIES USING FOURIER ACCELERATION

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JOURNAL OF STATISTICAL PHYSICS 1986年第5-6期43卷 1073-1075页

作者： DAVIES, C BATROUNI, G KATZ, G KRONFELD, A LEPAGE, P ROSSI, P SVETITSKY, B WILSON, K MIT CAMBRIDGEMA 02139 DESY HAMBURGFED REP GER

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RESPONSE IMPROVEMENTS IN INDUSTRIAL DC DRIVES DERIVED FROM OPTIMAL ANALYSIS

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IEE PROCEEDINGS-B ELECTRIC POWER APPLICATIONS 1985年第3期132卷 171-173页

作者： JONES, DI UNIV COLL N WALES SCH ELECTR ENGN SCIBANGOR LL57 1UTGWYNEDDWALES

Reference is made to a recent paper by B. J. Cardwell and C. J. Goodman (published in IEE Proc. B, Electr. Power Appl. , 1984, 131, (3), pp. 91-98) who calculate the optimal controls for a dc machine executing transient changes in speed. Their computational method is capable of dealing with armature current saturation but, unfortunately, encounters convergence difficulties in the presence of control limits. In this correspondence, the conjugate gradient algorithm is shown to overcome this difficulty. A reply by the original authors is included.

关键词： optimal control armature current saturation electric drives optimal analysis computational method optimal controls Optimal control Drives industrial DC drives DC motors conjugate gradient algorithm transient changes in speed d.c. machines convergence difficulties Control of electric power systems

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