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Optimal Frequency Offset Selection for FDA-MIMO Beampattern Design in the Range-Angle Plane

IEEE SIGNAL PROCESSING LETTERS 2024年 31卷 316-320页

作者： Jia, Wenkai Jakobsson, Andreas Wang, Wen-Qin Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Peoples R China Lund Univ Ctr Math Sci Div Math Stat SE-22100 Lund Sweden

This work investigates the design of beampatterns for frequency diverse arrays-multiple-input multiple-output (FDA-MIMO) in the range-angle plane, in order to improve the approximation of a desired beampattern. Recognizing that the energy radiated by the array cannot be locked at a fixed range and angle, the beampattern is designed for the equivalent beampattern at the receiving end, differing from the traditional emphasis on the transmit beampattern. The proposed scheme formulates the beampattern design as a minimization problem, where the cost function is defined as the squared error between the designed and the given beampatterns. The developed scheme is then implemented through an optimal selection of both the FDA frequency offsets and the receiver steering weights. To this end, an iterative algorithm with monotonic convergence is introduced to solve the resulting non-convex optimization problem involving a fourth-order polynomial objective function as well as multiple non-convex constraints. Numerical simulations verify the performance of the algorithm and show that the proposed scheme can efficiently concentrate the energy of the echo signal on the desired region in the range-angle plane.

关键词： Beampattern design FDA frequency offset selection iterative algorithm

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Analysis of the Convergence of Biased Contribution Index: A Fairness Index

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2024年第3期71卷 1541-1545页

作者： Awasthi, Sateesh Kumar Singh, Yatindra Nath Dr BR Ambedkar Natl Inst Technol Dept Elect & Commun Engn Jalandhar 144011 India Indian Inst Technol Kanpur Dept Elect Engn Kanpur 208016 India

This brief presents the global convergence behavior of an iterative algorithm used in the computation of a fairness index, named Biased Contribution Index (BCI). The BCI is used to maintain fairness in a cooperative computing system. It is expressed as a ratio of the first-order polynomials of the BCI of the other agents in the system. In this brief, first, we generalize the definition of the BCI, by expressing it as a ratio of fractional polynomials, then we prove the global convergence of the iterative method used in its solution. With the help of numerical examples, we explain the impact of the parameters used in the definition of BCI on its convergence.

关键词： iterative algorithm cooperative computing non-negative matrix free-rider eigenvector

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A Modified iterative Method for Solving the Non-symmetric Coupled Algebraic Riccati Equation

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TAIWANESE JOURNAL OF MATHEMATICS 2024年第2期28卷 377-396页

作者： Wang, Li Wang, Yibo Hunan Univ Sci & Technol Sch Math & Computat Sci Xiangtan 411201 Hunan Peoples R China

In this paper, a modified alternately linear implicit (MALI) iteration method is derived for solving the non-symmetric coupled algebraic Riccati equation trix equations are fixed at each iteration step. In addition, the MALI iteration method utilizes a weighted average of the estimates in both the last step and current step to update the estimates in the next iteration step. Further, we give the convergence theory of the modified algorithm. Last, numerical examples demonstrate the effectiveness and feasibility of the derived algorithm.

关键词： non-symmetric couple algebraic Riccati equation non-negative solution iterative algorithm convergence

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An efficient algorithm for areal morphological filtering

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MEASUREMENT TECHNIQUES 2024年第12期66卷 906-912页

作者： Grigoriev, Sergey N. Zakharov, Oleg V. Lysenko, Valery G. Masterenko, Dmitriy A. Moscow State Univ Technol STANKIN Moscow Russia Yuri Gagarin State Tech Univ Saratov Saratov Russia Russian Res Inst Metrol Serv Moscow Russia

The present article considers the estimation of functional product surface properties using the results of measuring areal surface texture parameters via morphological filtering. Under this method, a form of measurement data representation is proposed to improve the efficiency of an algorithm for iterating over surface coordinates. It is shown that for wide implementation of areal morphological filtering in metrological practice, it is necessary to create an efficient filtering algorithm. In the work, an algorithm was developed relying on a matrix representation of morphological operations on surface coordinates. Different indexing of the primary surface and structuring element points was introduced. A sphere or flat segment was used as the structuring element. The performance of the developed algorithm is higher than that of some other algorithms due to the fact that all computations are performed by iterating over surface coordinates in a single pass without nested loops. The diagrams of algorithms for the morphological operations of dilation and erosion are given;these operations were used to construct closing and opening filters. Simulations performed for different datasets and a comparison with known morphological filtering algorithms confirmed the high efficiency of the developed algorithm. The obtained results can be applied in the analysis of the functional properties of product surfaces.

关键词： Roughness Filtering Morphological filter iterative algorithm 681.2.083

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iterative kernel density estimation from noisy-dependent observations

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BANACH JOURNAL OF MATHEMATICAL ANALYSIS 2024年第1期18卷 1-19页

作者： Li, Yaxu Hangzhou Normal Univ Sch Math Hangzhou 311121 Peoples R China

We consider the nonparametric estimation of the density function of an underlying random variable from a sequence of strongly mixing noisy observations. We develop a two-step estimation procedure to accomplish this task. At the first step, we propose an appropriate nonparametric kernel density estimation based on the observations, which allows a flexible bandwidth matrix. At the second step, we invoke an iterative algorithm to estimate the underlying density function, where the initialization function is constructed using the estimator established at the first step. Under some smoothness conditions on the involved densities, we show that the estimator resulting from the iterative procedure is a consistent estimator of the underlying density. This indicates that deconvolution can be achieved by correcting an appropriate kernel density estimator constructed on the basis of noisy observations. Our analysis is conducted in the real domain.

关键词： Density estimation Random sampling Strongly mixing observations Deconvolution iterative algorithm

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Total asymptotically nonexpansive mappings and generalized variational-like inclusion problems in semi-inner product spaces

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OPTIMIZATION 2024年第3期73卷 741-792页

作者： Balooee, Javad Al-Homidan, Suliman Univ Tehran Coll Sci Sch Math Stat & Comp Sci Tehran Iran King Fahd Univ Petr & Minerals Dept Math Dhahran Saudi Arabia King Fahd Univ Petr & Minerals Interdisciplinary Res Ctr Smart Mobil & Logist Dhahran Saudi Arabia

This paper focuses on investigating the problem of finding a common element of the set of solutions of a generalized nonlinear implicit variational-like inclusion problem involving an (A, eta)-maximal m-relaxed monotone mapping in the sense of L.-G.-s.i.p. and the set of fixed points of a total asymptotically nonexpansive mapping. To achieve such a purpose, a new iterative algorithm is constructed. Applying the concepts of graph convergence and generalized resolvent operator associated with an (A, eta)-maximal m-relaxed monotone mapping in the sense of L.-G.-s.i.p. As an application of the obtained equivalence relationship, the strong convergence of the sequence generated by our proposed iterative algorithm to a point belonging to the intersection of the two sets mentioned above is proved.

关键词： Total asymptotically nonexpansive mapping fixed point problem variational-like inclusions semi-inner product spaces resolvent operator technique graph convergence (A,eta)-maximal m-relaxed monotone mapping iterative algorithm convergence analysis

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Robust estimation method for panel interval-valued data model with fixed effects

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2024年第14期94卷 3230-3251页

作者： Zhang, Jinjin Li, Qingqing Wei, Bowen Ji, Aibing Hebei Univ Coll Math & Informat Sci Baoding 071002 Peoples R China

Panel data model with fixed effects is widely used in economic and administrative applications. However, the presence of factors: measurement errors, data variability and outliers may potentially decrease the accuracy of the model prediction. In this paper, we use panel interval-valued data to represent measurement errors and data volatility of observations. Further, we propose a corresponding panel interval-valued data model with fixed effects, in which both the response and explanatory variables are interval-valued data. To reduce the impact of outliers on our model, we propose a robust estimation method based on the iterative weighted least squares technique. Later, Monte Carlo simulation and empirical application demonstrate that our model is a suitable tool for analyzing the behaviour of panel interval-valued data.

关键词： Panel interval-valued data robust estimation iterative algorithm panel interval Box-Cox transformation

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Enmsp: an elastic-net multi-step screening procedure for high-dimensional regression

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STATISTICS AND COMPUTING 2024年第2期34卷 79-79页

作者： Xue, Yushan Ren, Jie Yang, Bin Cent Univ Finance & Econ Sch Stat & Math Beijing Peoples R China HollySys Grp Co Ltd Beijing Peoples R China Res Ctr Int Inspection & Quarantine Stand & Tech R Beijing Peoples R China

To improve the estimation efficiency of high-dimensional regression problems, penalized regularization is routinely used. However, accurately estimating the model remains challenging, particularly in the presence of correlated effects, wherein irrelevant covariates exhibit strong correlation with relevant ones. This situation, referred to as correlated data, poses additional complexities for model estimation. In this paper, we propose the elastic-net multi-step screening procedure (EnMSP), an iterative algorithm designed to recover sparse linear models in the context of correlated data. EnMSP uses a small repeated penalty strategy to identify truly relevant covariates in a few iterations. Specifically, in each iteration, EnMSP enhances the adaptive lasso method by adding a weighted l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_2$$\end{document} penalty, which improves the selection of relevant covariates. The method is shown to select the true model and achieve the l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_2$$\end{document}-norm error bound under certain conditions. The effectiveness of EnMSP is demonstrated through numerical comparisons and applications in financial data.

关键词： High-dimensional data Correlated effects Elastic-net iterative algorithm EnMSP

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GENERALIZED CAYLEY OPERATOR WITH APPLICATIONS TO CAYLEY INCLUSIONS IN UNIFORMLY SMOOTH BANACH SPACES

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MATHEMATICAL FOUNDATIONS OF COMPUTING 2024年第1期7卷 20-37页

作者： Ram, Tirth Iqbal, Mohd Univ Jammu Dept Math Jammu 180006 India

In this paper, we present a generalized Cayley operator and a generalized Cayley inclusion problem (GCIP). A fixed point formulation of (GCIP) is established and using this an iterative algorithm is developed to show the existence and convergence of the solutions of (GCIP). We also establish the equivalence of the (GCIP) and generalized resolvent equation problem (GREP), and develop an iterative algorithm and some of its equivalent forms to approximate the solution of (GREP). To support our results, we construct a numerical example and convergence graphs using MATLAB programming.

关键词： Cayley operator Cayley inclusion iterative algorithm resolvent op-erator uniformly smooth Banach space

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On the new Hadamard fractional optimal control problems

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JOURNAL OF VIBRATION AND CONTROL 2023年第19-20期29卷 4413-4421页

作者： Zguaid, Khalid Tajani, Asmae Jajarmi, Amin Baleanu, Dumitru Moulay Ismail Univ Fac Sci Dept Math Zitoune 11201 Meknes Morocco Univ Bojnord Dept Elect Engn Bojnord Iran Cankaya Univ Fac Arts & Sci Dept Math Ankara Turkey Inst Space Sci Bucharest Romania

The main goal of this manuscript is to investigate a fractional optimal control problem subject to a dynamical system involving Hadamard fractional derivatives. Necessary conditions for the optimality of the considered problem are derived in terms of the corresponding Euler-Lagrange equations. An iterative method is also proposed to numerically solve the obtained equations from the necessary optimality conditions. Two illustrative examples are considered and simulated in order to show the applicability and efficiency of the proposed method. Numerical simulations show that the used method presents some satisfying results regarding the absolute error values.

关键词： optimal control Hadamard fractional derivative optimality conditions iterative algorithm fractional calculus

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