凸优化在信号处理与通信中的应用Convex Optimization in Signal Processing and Communications
凸优化理论在信号处理以及通信系统中的应用 比较经典的通信系统凸优化入门教程ContentsList of contributorspage IxPrefaceAutomatic code generation for real- time convex optimizationJacob Mattingley and stephen Boyd1.1 Introduction1.2 Solvers and specification languages61. 3 Examples121. 4 Algorithm considerations1.5 Code generation261.6 CVXMOD: a preliminary implementation281.7 Numerical examples291. 8 Summary, conclusions, and implicationsAcknowledgments35ReferencesGradient-based algorithms with applications to signal-recoveryproblemsAmir beck and marc teboulle2.1 Introduction422.2 The general optimization model432.3 Building gradient-based schemes462. 4 Convergence results for the proximal-gradient method2.5 A fast proximal-gradient method2.6 Algorithms for l1-based regularization problems672.7 TV-based restoration problems2. 8 The source-localization problem772.9 Bibliographic notes83References85ContentsGraphical models of autoregressive processes89Jitkomut Songsiri, Joachim Dahl, and Lieven Vandenberghe3.1 Introduction893.2 Autoregressive processes923.3 Autoregressive graphical models983. 4 Numerical examples1043.5 Conclusion113Acknowledgments114References114SDP relaxation of homogeneous quadratic optimization: approximationbounds and applicationsZhi-Quan Luo and Tsung-Hui Chang4.1 Introduction1174.2 Nonconvex QCQPs and sDP relaxation1184.3 SDP relaxation for separable homogeneous QCQPs1234.4 SDP relaxation for maximization homogeneous QCQPs1374.5 SDP relaxation for fractional QCQPs1434.6 More applications of SDP relaxation1564.7 Summary and discussion161Acknowledgments162References162Probabilistic analysis of semidefinite relaxation detectors for multiple-input,multiple-output systems166Anthony Man-Cho So and Yinyu Ye5.1 Introduction1665.2 Problem formulation1695.3 Analysis of the SDr detector for the MPsK constellations1725.4 Extension to the Qam constellations1795.5 Concluding remarks182Acknowledgments182References189Semidefinite programming matrix decomposition, and radar code design192Yongwei Huang, Antonio De Maio, and Shuzhong Zhang6.1 Introduction and notation1926.2 Matrix rank-1 decomposition1946.3 Semidefinite programming2006.4 Quadratically constrained quadratic programming andts sdp relaxation201Contents6.5 Polynomially solvable QCQP problems2036.6 The radar code-design problem2086.7 Performance measures for code design2116.8 Optimal code design2146.9 Performance analysis2186.10 Conclusions223References226Convex analysis for non-negative blind source separation withapplication in imaging22Wing-Kin Ma, Tsung-Han Chan, Chong-Yung Chi, and Yue Wang7.1 Introduction2297.2 Problem statement2317.3 Review of some concepts in convex analysis2367.4 Non-negative, blind source-Separation criterion via CAMNS2387.5 Systematic linear-programming method for CAMNS2457.6 Alternating volume-maximization heuristics for CAMNS2487.7 Numerical results2527.8 Summary and discussion257Acknowledgments263References263Optimization techniques in modern sampling theory266Tomer Michaeli and yonina c. eldar8.1 Introduction2668.2 Notation and mathematical preliminaries2688.3 Sampling and reconstruction setup2708.4 Optimization methods2788.5 Subspace priors2808.6 Smoothness priors2908.7 Comparison of the various scenarios3008.8 Sampling with noise3028. 9 Conclusions310Acknowledgments311References311Robust broadband adaptive beamforming using convex optimizationMichael Rubsamen, Amr El-Keyi, Alex B Gershman, and Thia Kirubarajan9.1 Introduction3159.2 Background3179.3 Robust broadband beamformers3219.4 Simulations330Contents9.5 Conclusions337Acknowledgments337References337Cooperative distributed multi-agent optimization340Angelia Nedic and asuman ozdaglar10.1 Introduction and motivation34010.2 Distributed-optimization methods using dual decomposition34310.3 Distributed-optimization methods using consensus algorithms35810.4 Extensions37210.5 Future work37810.6 Conclusions38010.7 Problems381References384Competitive optimization of cognitive radio MIMO systems via game theory387Gesualso Scutari, Daniel P Palomar, and Sergio Barbarossa11.1 Introduction and motivation38711.2 Strategic non-cooperative games: basic solution concepts and algorithms 39311.3 Opportunistic communications over unlicensed bands411.4 Opportunistic communications under individual-interferenceconstraints4151.5 Opportunistic communications under global-interference constraints43111.6 Conclusions438Ackgment439References43912Nash equilibria: the variational approach443Francisco Facchinei and Jong-Shi Pang12.1 Introduction44312.2 The Nash-equilibrium problem4412. 3 EXI45512.4 Uniqueness theory46612.5 Sensitivity analysis47212.6 Iterative algorithms47812.7 A communication game483Acknowledgments490References491Afterword494Index49ContributorsSergio BarbarossaYonina c, eldarUniversity of rome-La SapienzaTechnion-Israel Institute of TechnologyHaifaIsraelAmir beckTechnion-Israel instituteAmr El-Keyiof TechnologyAlexandra universityHaifEgyptIsraelFrancisco facchiniStephen boydUniversity of rome La sapienzaStanford UniversityRomeCaliforniaItalyUSAAlex b, gershmanTsung-Han ChanDarmstadt University of TechnologyNational Tsing Hua UniversityDarmstadtHsinchuGermanyTaiwanYongwei HuangTsung-Hui ChangHong Kong university of scienceNational Tsing Hua Universityand TechnologyHsinchuHong KongTaiwanThia KirubarajanChong-Yung chiMcMaster UniversityNational Tsing Hua UniversityHamilton ontarioHsinchuCanadaTaiwanZhi-Quan LuoJoachim dahlUniversity of minnesotaanybody Technology A/sMinneapolisDenmarkUSAList of contributorsWing-Kin MaMichael rebsamenChinese University of Hong KongDarmstadt UniversityHong KonTechnologyDarmstadtAntonio de maioGermanyUniversita degli studi di napoliFederico iiGesualdo scutariNaplesHong Kong University of Sciencealyand TechnologyHong KongJacob MattingleyAnthony Man-Cho SoStanford UniversityChinese University of Hong KongCaliforniaHong KongUSAJitkomut songsinTomer michaeliUniversity of californiaTechnion-Israel instituteLoS Angeles. CaliforniaogyUSAHaifaMarc teboulleTel-Aviv UniversityAngelia NedicTel-AvUniversity of Illinois atIsraelUrbana-ChampaignInoSLieven VandenbergheUSAUniversity of CaliforniaLos Angeles, CaliforniaUSAAsuman OzdaglarMassachusetts Institute of TechnologyYue WangBoston massachusettsVirginia Polytechnic InstituteUSAand State UniversityArlingtonDaniel p palomarUSAHong Kong University ofScience and TechnologyYinyu YeHong KongStanford UniversityCaliforniaong-Shi PangUSAUniversity of illinoisat Urbana-ChampaignShuzhong zhangIllinoisChinese university of Hong KongUSAHong KongPrefaceThe past two decades have witnessed the onset of a surge of research in optimization.This includes theoretical aspects, as well as algorithmic developments such as generalizations of interior-point methods to a rich class of convex-optimization problemsThe development of general-purpose software tools together with insight generated bythe underlying theory have substantially enlarged the set of engineering-design problemsthat can be reliably solved in an efficient manner. The engineering community has greatlybenefited from these recent advances to the point where convex optimization has nowemerged as a major signal-processing technique on the other hand, innovative applica-tions of convex optimization in signal processing combined with the need for robust andefficient methods that can operate in real time have motivated the optimization commu-nity to develop additional needed results and methods. The combined efforts in both theoptimization and signal-processing communities have led to technical breakthroughs ina wide variety of topics due to the use of convex optimization This includes solutions tonumerous problems previously considered intractable; recognizing and solving convex-optimization problems that arise in applications of interest; utilizing the theory of convexoptimization to characterize and gain insight into the optimal-solution structure and toderive performance bounds; formulating convex relaxations of difficult problems; anddeveloping general purpose or application-driven specific algorithms, including thosethat enable large-scale optimization by exploiting the problem structureThis book aims at providing the reader with a series of tutorials on a wide varietyof convex-optimization applications in signal processing and communications, writtenby worldwide leading experts, and contributing to the diffusion of these new developments within the signal-processing community. The goal is to introduce convexoptimization to a broad signal-processing community, provide insights into how convexoptimization can be used in a variety of different contexts, and showcase some notablesuccesses. The topics included are automatic code generation for real-time solvers, graphical models for autoregressive processes, gradient-based algorithms for signal-recoveryapplications, semidefinite programming(SDP)relaxation with worst-case approximationperformance, radar waveform design via SDP, blind non-negative source separation forimage processing, modern sampling theory, robust broadband beamforming techniquesdistributed multiagent optimization for networked systems, cognitive radio systems viagame theory, and the variational-inequality approach for Nash-equilibrium solutionsPrefaceThere are excellent textbooks that introduce nonlinear and convex optimization, providing the reader with all the basics on convex analysis, reformulation of optimizationproblems, algorithms, and a number of insightful engineering applications. This book istargeted at advanced graduate students, or advanced researchers that are already familiarwith the basics of convex optimization. It can be used as a textbook for an advanced graduate course emphasizing applications, or as a complement to an introductory textbookthat provides up-to-date applications in engineering. It can also be used for self-study tobecome acquainted with the state of-the-art in a wide variety of engineering topicsThis book contains 12 diverse chapters written by recognized leading experts worldwide, covering a large variety of topics. Due to the diverse nature of the book chaptersit is not possible to organize the book into thematic areas and each chapter should betreated independently of the others. a brief account of each chapter is given nextIn Chapter 1, Mattingley and Boyd elaborate on the concept of convex optimizationin real-time embedded systems and automatic code generation. As opposed to genericsolvers that work for general classes of problems, in real-time embedded optimization thesame optimization problem is solved many times, with different data, often with a hardreal-time deadline. Within this setup the authors propose an automatic code-generationsystem that can then be compiled to yield an extremely efficient custom solver for theproblem familyIn Chapter 2, Beck and Teboulle provide a unified view of gradient-based algorithmsfor possibly nonconvex and non-differentiable problems, with applications to signalrecovery. They start by rederiving the gradient method from several different perspectives and suggest a modification that overcomes the slow convergence of the algorithmThey then apply the developed framework to different image-processing problems suchas e1-based regularization, TV-based denoising, and Tv-based deblurring, as well ascommunication applications like source localizationIn Chapter 3, Songsiri, Dahl, and Vandenberghe consider graphical models for autore-gressive processes. They take a parametric approach for maximum-likelihood andmaximum-entropy estimation of autoregressive models with conditional independenceconstraints, which translates into a sparsity pattern on the inverse of the spectral-densitymatrix. These constraints turn out to be nonconvex. To treat them the authors proposea relaxation which in some cases is an exact reformulation of the original problem. Theproposed methodology allows the selection of graphical models by fitting autoregressiveprocesses to different topologies and is illustrated in different applicationsThe following three chapters deal with optimization problems closely related to SDPand relaxation techniquesIn Chapter 4, Luo and Chang consider the SDP relaxation for several classes ofquadratic-optimization problems such as separable quadratically constrained quadraticprograms(QCQPs)and fractional QCQPs, with applications in communications and signal processing. They identify cases for which the relaxation is tight as well as classes ofquadratic-optimization problems whose relaxation provides a guaranteed, finite worstcase approximation performance. Numerical simulations are carried out to assess theefficacy of the SDP-relaxation approach
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NTC热敏电阻温度采集方案
NTC温度采集方案，有详细的算法，包括一些程序，硬件设计等SUNPLUS用热敏电阻做朵用温度月录页系统概要系统说明热敏电阻器1.2.1电阻一温度关系1.3数值处理线性插值软件说明软件说明2档案构成2.3程序说明程序范例DEMO程序使件原理佟使用资源硬件使用资源说明参考文献SUNPLUS用热敏电阻做朵用温度修订记录版本日期编写及修订者编写及惨订说明初版错误校SUNPLUS用热敏电阻做朵用温度系统概要系统说明木应用例实现ⅳrC热敏电阻器对温度的测量。热敏电阻器把温度的变化转换为电阻阻值的变化,再应用相应的测量电路把阻佶的变化转换为电压的变化;SPMC75F2413A内建8路ADC可以把模拟的电压值转换为数字信号,对数值信号进行处理可以得到相应的温度值。热敏电阻器热敏电陧有电阻值随温度升高而升高的正温度系数(3 ositive Tcmpcraturc Coefficient简称PC)热敏电阻和电阻值随温度升高而降低的负温度系数( Negative TemperatureCoefficient简称NTC)热敏电阻。NT~热敏电阻器,是·种以过渡金属氧化物为主要原材料,采用电了陶瓷⊥艺制成的热敏半导体陶瓷组件ε这种组件的电阻值随温度升髙而降低,利用这一特性可制成测温、温度补偿和控温组件,又可以制成功率型组件,抑制电路的浪涌电流。电阻温度特性可以近似地用下式来表示:式中:Rη、R分别表示NTC在温度T(K)和额定额定温度T(K)卜的电阻值,单位2,T、T为温度,单位K(Ts(k)-273.15+T(℃))。B,称作B值,NTc热敏电阻特定的材料常数(Beta)。由于B值同样是随温度而变化的,因此NT热敏电阻的实际特性,只能粗略地用指数关系来描述,所以这种方法只能以一定的精度来描述额定温度或电阻值附近的有限的范围。但是在实际应用中,要求有比较精桷的R-T曲线。要用比较复杂的方法(例如用thesteinhart-Hart方程),或者用表格的形式来给定电阻/温度关系应用例选用NC热敏电阻器CwF2-502F3950,基于精确的R-T曲线,来对温度进行精确的测量。电阻一温度关系如表1-1所示,NC热敏电阻器CwE2-502F3950各温度点的电阻值,即电阻一温度关系表。从提供的电阻一温度关系表中可以看出NTC热敏电阳器CWE2-502E3950的测温范围为[-55℃,125℃],其电阻值的变化范围为[25006292,242.6492]。表1-1电阻一温度关系衣温度℃电阻值Ω温度℃电阻值Q温度℃电阻值Q55250062542374045322523952213575120241219175C4918158018171895-471626844615393345l∠56384∠1377534313029342123231-4111655CSUNPLUS用热敏电阻做朵用温度4010232391042613898621.793295.53688267.43583521.83479043.93374819.23270833.93167074.730635292960184.6-2857030.22754054.72651247.9-25486002446101.6234374422415192139418.82037435.9-1935563.51833795-1732124.463C545.829053.827643.3-1326309.525047.91123854.2-1022724,621655.320642.719683.618774.917913.6417097.116332.915588.4111891.5014230113601.913005.412438.7l1900.111388.210901.310438.39997.74578.41109181113799128436.83133091.73147762.787449.16167150.C4176864.7592.4196332.49206C34.32215847.31225620.89235404,53245197.72255000264810.9274630.014456.93294291.283C4132.69313980.83323835.383696.03343562.193434.53194.1383C81.22392972.92402869412769.24422673.47432581.5442493.17452408.3462326.76472248.38482173.04492100.6502032511963.92521899.441837.4541777,6已1720.2561664.85571611.541560.2591510.746C1463.08611417,14621372.87631330.18641289.C21249.321211.03671174.C91138.44691104.04701070.83711C38.78721007.8273977.9374949,0675921.1776894.22868.1878843.027980795.1781772.4382750.4483729.1784708.685688.786669.4487650.88632.76SUNPLUS用热敏电阻做朵用温度89615.39C91582.0292566.179550.8194535.9495521.5396507.5797∠94.0598480.9499468.23100453.301443.9710243210321.15104410.26105399.69106389.4407379.5103369.85109360.48101,411112.57112334.01325.69114317.62115309.7716302.16117294.76118287.5719280.59120273.8121267.21122260.8123254.512L248.52125242.64数值处理通过表1-1电阻一温度关系表可以很直观的看到电阻的变化范围从242.649到2500629,在-55℃的时候其表现出的电阻值是125℃时所表现的电阻值的1030倍,这幺大的变化范围也为ADC测量带来了困难。测量电路如图1-1所示。如图1-1测量电路如上图所示NTC热敏电阻Rⅴ和测量电阻Rm(精密电阻)组成一个简单的串联分压电路,参考电压VCC Ref经过分压可以得到一个电压值随着温度值变化而变化的数值,这个电压的大小将反映出NTC电阻的人小,从而也就是相应温度值的反映。通过欧姆定律可以得到输出电压值Vadc和NTc电阻值的一个关系表达式:vadVre上+Rm/(Rv+Rm)那幺接下来的数据处理将基于式(1)展开:sPMC75F2413A的ADC为10-Bit的精度,其参考电SUNPLUS用热敏电阻做朵用温度压为5V,因此这里可以选择Vre￡=5V。各温度点对应的ADC转换后的数字量可以计算。Dadc = 1024*Adc/5V(2)式(1)、(2)结合可以得到:Dadc 1024*Rm/(Rv+Rm)(3)如果这里取测量电阻Rm选择4.7K9,那幺可以计算出在-55℃时所对应的Dadc=1024*1000/(250062+100C)=4;在125℃时所对应的Dadc=1024*1000/(242.64+10C0)824。根据这样的对应关系对数据进行预处理,得到如下处理结果如表1-2所示:表1tatic const Int16 NTCTAB2[18119,20;21,22,23,24,26,27,29,30,32;34,36,38,40,42,44,47,49,52,55,57,61;64,67,71,74,78,82,86,90,95,99,104,109114120,150,156,161,168,172,180,187,194,201,208,215,22,230,238,247255,264,272,280,291,302,310;319328,338;347,357367,376,384;395,4C5,414r424;434444,453,464,47448,494,502;512,522,531,540,551,560,569,579,586;595,604,613,624,633,642,650;658,666,673,680,688:696,704,712,719,726,733,741;749,755,760,767,774,780,785,791,798,804,811,816,8827,832,837,842;847,851,856;862,868,873,856;860,64,868,872,376;879,883,886;890,893,896,899;902,905,908,911,914;917,919,922;924,927,929,931;934,936,938,940,942,94,946,947,949,951,953,954,956,958,959,961,962;964,965,966,968,969,970,971,973,974};//4.7K当然这也是应用例中所需要的一个很重要的转换表,这一部分是事先制作好的表格,将为接下来的处理提供参考依据。测量电阻Rm的选取是有一定的规律的,在实际的应用中不一定都需要测量全程温度,可以估算岀大致的温度范围。木着提高测量精度的宗旨:如果是应用在测量低温的系统中建议Rπ选择较大的电阻(10KΩ),如果在测量较高温的系统中建议Rn选择较小的电阻(1κΩ)等。线性插值在AEC进行数据采集的过程中不可能每个数值都在整温度所对应的AD数值上,所以如果在两个数据的中间一段就要对其进行进一步的精确定位。这样就必须知道采集到的数据在表1-2中的具体位置,因此要对数据表进行搜索、查找。线性表的查找(也称枍索),可以有比较常见的顺序查找、折半查找及分块查找等方法,分析线性表1-2可以得到折半查找的算法是比较高效的。Eg如果ADC采样的数值为Dade=360,即357
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