1、无线通信发展面临的基础理论问题和数学问题,李建东 ,内容简介,博弈论和遗传算法在无线认知电及网络中的应用（杨春刚、姜健、刘鑫一） 优化分解:网络结构的数学理论（张琰） 基于网络编码的无线协议(杨辉) 干扰信道的自由度(马延军) 多址接入信道和广播信道（陈睿） 复对称矩阵的奇异值分解问题（姚俊良）,博弈论和遗传算法在无线认知电及网络中的应用（杨春刚、姜健、刘鑫一）,认知无线电及网络,目前，对无线服务的需求的增加以及新技术的发展使得无线电频谱成为非常稀有和珍贵的资源，然而现在所使用的需要授权的频谱接入技术被证明是低效的，FCC指出只有平均15-85%的授权频谱被使用。,认知无线电及网络,1999年
2、Mitola在他的文章中提出认知无线电（CR）的概念，认知无线电网络是一个能够感知周围频谱环境的智能无线通信系统。它使用空闲频谱进行通信，并根据环境的变化自适应地调整传输参数（传输能量、传输频率、调制方式、编码策略等）以提高性能，同时避免对其它系统的干扰，可以有效的识别和利用这些空闲频谱，满足日益增长的无线通信服务需求。因此认知无线电网络中动态资源分配的问题可以看做一个多目标优化的问题进行求解。,认知无线电及网络,认知无线电的潜在应用是频谱的租用和第二方无线接入市场，利用无线电和信号处理技术以及新型的频谱分配策略，来使新的用户在拥挤的频谱环境下工作，而不降低原授权用户的性能。,认知无线电及网络
3、,认知无线网络的基本特征是能够根据认知结果，通过自主的决策来调整网络，以适应环境的变化，而端到端效能是认知无线网络调整的依据，也是衡量网络性能的标准，因此如何充分利用认知所获取的多域环境信息，针对资源共享、环境适变和异构网络融合等需求，建立自主管理与控制模型，实现资源的智能、动态、优化管理，显著提升认知无线网络端到端效能,是认知无线网络必须解决的关键问题。,无线认知网络的博弈论,传统的数学工具，例如凸优化以及随机过程理论等在无线通信若干问题的分析上遇到前所未有的障碍。这些是由于越来越高的传输速率要求的业务，时变的无线环境以及紧缺的无线资源造成的。 幸运的是，博弈论（Game Thoery）的出
4、现为进一步改善系统性能以及更好的适应环境的变化的网络提供了一种切实可行的途径。,Basics of CC,认知网络(资源分配和容量)-杨春刚,where,目标函数：,竞争与合作描述,博弈论建模的问题,Overall performance is denoted asMultiple constraint conditions,(A),(B),(C),(D),学者简介,K. J. Ray Liu， Professor Dept. of Electrical and Computer Engineering University of Maryland College Park, USA Jeff
5、rey H. Reed，ProfessorBradley Department of Electrical and Computer Engineering， Virginia Tech , USA,经典文章,1 Cognitive radio and networking research at Virginia Tech, MacKenzie, Allen B.; Reed, Jeffrey H., Proceedings of the IEEE, v 97, n 4, p 660-686, April 2009.2 Game theory in signal processing and
6、 communications, Jorswieck, Eduard A.; Larsson, Erik G.; Luise, Marco; Poor, H. Vincent, IEEE Signal Processing Magazine, v 26, n 5, p 17+132, 2009. 3 Coalitional game theory for communication networks Saad, Walid; Han, Zhu; Debbah, Mrouane; Hjrungnes, Are; Basar, Tamer, IEEE Signal Processing Magaz
7、ine, v 26, n 5, p 77-97, 2009. 4 Game theory for wireless engineers MacKenzie, Allen B. , Dasilva, Luiz A. Source: Synthesis Lectures on Communications, v 1, p 1-86, December 1, 2005,博弈模型 -姜健,博弈的基本模型为：G=，其中N=1,2,.,N表示网络中的用户集；S=1,2,.,S表示网络状态；A是笛卡尔乘积空间，表示用户在不同状态下的行为集；P表示不同网络状态的传输策略；U表示效用函数，可以根据不同的环境状态
8、来选择不同的效用函数表示。而不同的效用函数则代表了不同的博弈模型和不同的解决方法。,贝叶斯博弈模型： G =其中N=1,2,.,N表示网络中的用户集；A表示参与者的行为空间；T是参与者的类型空间，每一个类型都对应着博弈方i不同的收益函数的可能情况，其取值是博弈方i自己知道而其他博弈方并不清楚的，反映了静态贝特斯博弈中信息不完全的特性 ；P是定义在T上的概率联合分布函数，代表用户对其他用户可能类型的先验知识，U是参与者的收益，收益是用户所有行为的函数，也是参与者类型的函数。,通信网络状况具有不确定性,博弈论用于解决频谱利用率低的问题,知名学者,Prof. Joseph Mitola III, T
9、ekn. Dr. School of Engineering and ScienceVice President for the Research Enterprise School of Systems and Enterprises Stevens Institute of TechnologyAllen B. MacKenzie，Assistant Professor Bradley Department of Electrical and Computer Engineering Virginia Tech,经典文章,（1）C.A. St. Jean and B. Jabbari,“B
10、ayesian game-theoretic modelling of uplink power determination in uniform,self-organising network，” ELECTRONICS LETTERS ,Vol. 40 No. 8,PP.483-484,Apr.2004 （2）Xiao, M., Shroff, N.B., and Chong, E.K.P.: “A utility-based power-control scheme in wireless cellular systems“, IEEE=ACM Trans. Netw., 2003, 1
11、1,(2), pp. 210221 （3） C. U. Saraydar, N. B. Mandayam, and D. J. Goodman, “Efcient power control via pricing in wireless data networks,” IEEE Trans. Commun.vol. 50, no. 2, pp. 291303, Feb. 2002. （4）Allen B.MacKenzie and LuizA.DaSilva, “Game Theory for Wireless Engineer“, Virginia Polytechnic Institut
12、e and State University,通信传输的目的,在给定的时延（ ）内将数据从信源X传输到目的地Y,Y,X,输入 (数据量的要求约束条件) Input (d bps ) Input (d bytes ),输出（数据量） Output(d bps) Output(d bytes),X(s1, t1),Y(s2, t2),所见即所得 所想即所得,资源管理的目的,Y,X,X(s1, t1),Y(s2, t2),Networks,资源的表示,Frequency: (start, end) Hz, e.g. , (825MHz, 826MHz);（无线媒介） Network: xx bps,
13、 xx bps, e.g. ,10Mbps,1000Mbps;（有线物理媒介和标准的能力） Computing: MIPS(FLOPS), e.g., 10MIPS;（处理和控制能力） Delay: s, e.g. 100ms （存储和交换的能力） Identification: operator, standard,e.g. ,OS2, UMTS（归属，技术标准）,资源表示的使用,动态资源管理-遗传算法-刘鑫一,遗传算法模拟生物进化机制 ,具有在寻优空间中进行全局搜索的能力 ,适合解决各种复杂的优化问题 ,包括多目标优化问题。,多目标最优化问题,遗传算法擅长解决的问题是全局最优化问题，跟传统
14、的算法比，遗传算法能够跳出局部最优而找到全局最优点。而且遗传算法允许使用非常复杂的目标函数（包括多目标函数），并对变量的变化范围可以加以限制。而如果是传统的算法，对变量范围进行限制意味着复杂的多的解决过程。,多目标优化问题数学模型：,为维数为n的适应度函数，X为输入参数的集合，Y为维数的集合。,Tx的“场”描述,Allowed transmitting capacity at any s:,How to match T with dynamically?,网络间的平滑切换和信息汇集？,汇聚,汇聚,学者介绍,Christian James Rieser Virginia Tech Electri
15、cal and Computer Engineering Johns Hopkins University Applied Physics LaboratoryL. M. PatnaikProfessorElectrical and Computer EngineeringElectrical Sciences Division at Indian Institute of Science,经典文章,C. J. Rieser, “Biologically Inspired Cognitive Radio Engine Model Utilizing Distributed Genetic Al
16、gorithms for Secure and Robust Wireless Communications and Networking,” Ph.D. Dissertation, Virginia Tech, Aug., 2004. H. Lu and G. G. Yen, “Multiobjective optimization design via genetic algorithm,” IEEE Proc. International Conference on Control Applications, pp. 1190 1195, Sept. 2001. M. Srinivas
17、and L. M. Patnaik, “Adaptive Probabilities of Crossover and Mutation in Genetic Algorithms,” IEEE Transactions on Systems, Man and Cybernetics, vol. 24, No. 4, pp. 656-666, 1994. C. M. Fonseca and P. J. Fleming, “Genetic Algorithms for multiobjective optimization: formulation, discussion, and genera
18、lization,” Proc. Int. Conf. Genetic Algorithms, pp. 416 423, 1993. Thomas W. Rondeau, Bin Le , Christian J. Rieser, Charles W. Bostian,“Cognitive Radios With Genetic Algorithms: Intelligent Control Of Software Defined Radios”,优化分解:网络结构的数学理论（张琰）,优化分解：网络结构的数学理论,Basic NUM,Network Utility Maximization,优
19、化分解：网络结构的数学理论,在网络效用最大化（Network Utility Maximization NUM）的模型下，垂直分解将总体的优化目标分解为若干个子问题而每一个子问题对应着网络协议中的一层，该问题中的拉格朗日对偶变量则对应各协议层之间传递的参数。 水平分解可以将原优化问题转化到各个子网，并且实现分布式计算和控制。不同分解方法可以形成不同的分层结构，而且根据优化理论可以分析出不同的分层结构的最优特性以及鲁棒性，另外不同的分解结构还存在计算和交互的折中，可以根据不同的网络类型和要求来进行选择和调整。 优化分解还可以是多个层次，这使得网络跨层协议体系变得更加灵活，针对在不同网络环境、不同
20、的业务需求采用不同的分解方法，形成不同的协议结构。 通过应用对偶分解理论来可以建立兼容并包的网络跨层协议体系，从而实现网络及应用的“无处不在”，为用户提供自由畅快的信息体验。,Introduction,Core Idea Decomposition theory naturally provides the mathematical language to build an analytic foundation for design of modularized and distributed control of network.,The first unifying view and s
21、ystematic approach Network: Generalized NUM Layering architecture: Decomposition scheme Layers: Decomposed subproblems Interfaces: Functions of primal or dual variablesVertical decompositions: subproblems (layers) and functions of primal or Lagrange dual variables (interfaces) Horizontal decompositi
22、ons: distributed computation and control over geographically disparate network elementsHorizontal and vertical decompositions through implicit message passing (e.g., queuing delay, SIR) explicit message passing (local or global)3 Steps: G.NUM A solution architecture Alternative architectures,Example
23、,网络效用最大化（Network Utility Maximization NUM）的模型下，利用对偶分解理论是跨层设计以及分布式算法设计的重要途径,学者简介,Mung Chiang Associate Professor Electrical Engineering &Computer Science Princeton University, USA,Steven H. Low Professor Electrical Engineering &Computer Science California Institute of Technology, USA,经典文章,M. Chiang,
24、S. H. Low, A. R. Calderbank, and J. C. Doyle, Layering as optimization decomposition: A mathematical theory of network architectures, Proceedings of the IEEE, vol. 95, no. 1, pp. 255-312, January 2007. M. Chiang, Balancing Transport and Physical Layers in Wireless Multihop Networks: Jointly Optimal
25、Congestion Control and Power Control, IEEE Journal of Selected Areas in Communications, vol. 23, no. 1, pp. 104-116, January 2005 This paper becomes the Fast Breaking Paper in Computer Science in 2006 according to ISI citation frequency. David X. Wei, Cheng Jin, Steven H. Low and Sanjay Hegde. FAST
26、TCP: motivation, architecture, algorithms, performance IEEE/ACM Transactions on Networking, 14(6):1246-1259, Dec 2006 D. Palomar and M. Chiang, A tutorial on decomposition methods and distributed network resource allocation, IEEE Journal of Selected Aresa in Communications, vol. 24, no. 8, pp. 1439-
27、1451, August 2006.,基于网络编码的无线协议(杨辉),Network Coding Application,Wireless protocols using network coding has shown significant improvements over traditional wireless transmission methods through data processing (for example: xor in fig.1.) in the intermediate nodes.,Each node stores packets that it ove
28、rheard and periodically reports to its neighbor nodes which packets it currently stores. Hence, each node has information on packets that each of its neighbor nodes stores.,By using this information, a node（for example: node1） can encode several native packets （P2 xor P3 xor P4） together and broadca
29、st to node2,3 and 4.Thus ,node 2 extracts p2, node 3 extracts p3, node 4 extracts p4,which results in further reducing the number of required transmissions.,Fig.1. Opportunistic coding,Network Coding Application,Thus, how to design of adapted wireless protocols using network coding ,which range from
30、 theoretical approaches and seek an optimal resource allocation by formulating complex optimization problems to practical approaches involving modifications from the physical to the transport and application layer, is a key question.,under scheduled access for n 4.,The optimal value of,for broadcast
31、 communication,for,and,Joint Optimization,of,The total sum-delivered throughput andthe minimum transmitted throughput,Network Coding Application,Scholars,1. Dina Katabi, Professor MIT Computer Science & Artificial Intelligence Lab. 2. Sachin Katti, Associate Professor, Electrical Engineering & Compu
32、ter Science Stanford University,USA 3. Tracey Ho, Assistant Professor ,California Institute of Technology ,USA 4. Christos Gkantsidis Systems and Networking Group of Microsoft Research at Cambridge, UK 5. Yalin Evren Sagduyu Electrical Engineering & Computer Science Northwestern University, USA,Main
33、 References,1 Embracing wireless interference: analog network coding， Sachin Katti, Shyamnath Gollakota, and Dina Katabi. In SIGCOMM 07, pages 397-408, New York, NY, USA, 2007. ACM. 2 Xors in the air: practical wireless network coding，Sachin Katti, Hariharan Rahul, Wenjun Hu, Dina Katabi, Muriel Med
34、ard,and Jon Crowcroft. In SIGCOMM 06,pages 243-254, New York, NY, USA, 2006. ACM Press. 3 Effecient retransmission scheme for wireless lans, Eric Rozner, Anand Padmanabha Iyer, Yogita Mehta, Lili Qiu, and MansoorJafry. In CoNEXT 07,pages1-12, New York, NY, USA, 2007. ACM. 4 Symbol-level network codi
35、ng for wireless mesh networks, Sachin Katti, Dina Katabi, Hari Balakrishnan, and Muriel Medard. SIGCOMM Comput. Commun. Rev., 38(4):401-412, 2008. 5 Trading structure for randomness in wireless opportunistic routing, Szymon Chachulski, Michael Jennings, Sachin Katti, and Dina Katabi. SIGCOMM Comput.
36、 Commun. Rev, 37(4):169-180, October 2007. 6 Cross-Layer Optimization of MAC and Network Coding in Wireless Queueing Tandem Networks, Yalin Evren Sagduyu, Anthony Ephremides. IEEE Transactions on Information Theory, VOL. 54, p 554-571 NO. 2, February 2008,干扰信道的自由度(马延军),干扰信道的自由度,“X networks”的收发端天线数不同
37、时候，其自由度一般来讲是未知的。作为”X networks”的一个特例，蜂窝网的自由度研究最近取得了很大进展，然而获得这些自由度的方法非常复杂。因此找到一种能获取蜂窝网自由度并且可以在实际环境中可应用的方法就变得非常重要。 wireless X networks, i.e. networks of M distributed single antenna transmitters and N distributed single antenna receivers where every transmitter has an independent message to every recei
38、ver.,K-Cell cellular networks,X networks,M x N X networks (An antenna per node),M x N K-user MIMO IC,K-user IC (An antenna per node),2-user Gaussian IC capacity within one bit,2-user MIMO IC,Cellular networks,Unknown in general,The Degrees of Freedom of Interference Channel?,学者简介,Syed Ali Jafar, Ass
39、ociate Professor Electrical Engineering & Computer Science Henry Samueli School of Engineering, UNIVERSITY OF CALIFORNIA, IRVINE, USA,经典文章,1 V. R. Cadambe and S. A. Jafar, “Interference alignment and degrees of freedom of the K-user interference channel,” Information Theory, IEEE Transactions on, vo
40、l. 54, no. 8, pp. 34253441, 2008. 2 Tiangao Gou, Syed A. Jafar. “Degrees of Freedom of the K User M x N MIMO Interference Channel,” http:/arxiv.org/abs/0809.0099,2008. 3 Akbar Ghasemi, Abolfazl Seyed Motahari, Amir Keyvan Khandani, “Interference Alignment for the K User MIMO Interference Channel,” h
41、ttp:/arxiv.org/abs/0909.4604,2009.,多址接入信道和广播信道（陈睿）,多址接入信道,广播信道,MIMO广播信道和多址接入信道容量,当发射机和接收机获得的信道信息不完全/不完美时，MIMO系统的广播信道和多址接入信道的容量仍是一个开放且有待解决的问题。 找到一种简单的脏纸编码结构也是当前及未来研究的热点问题。,学者简介,A. Lee Swindlehurst Professor University of California, USA. Email:swindleuci.edu Andrea Goldsmith Professor Stanford Facult
42、y Senate Chair at Stanford University, USA. Email: andrea at ee.stanford.edu,复对称矩阵的奇异值分解问题（姚俊良）,Decorrelation of a complex random vector,In wireless communications system, we usually need to remove the second-order correlation between the components of a complex random vector (c.r.vc). A c.r.vc X ha
43、s uncorrelated components if and only if,thus, decorrelation of X can be expressed as,The matrix Q can be found by employing symmetric singular value decomposition (SSVD). However, the SSVD is not always exist, what is the existence condition?,References,1 B.G.Angelika and B.G.William, “Singular val
44、ue decompositions of complex symmetric matrices”. Journal of Computational and Applied Mathematics, 21 (1988): 41-54. 2 C. Guo and S. Qiao, “A stable lanczos tridiagonalization of complex symmetric matrices”. Technique Report CAS 03-08-SQ, Department of Computing and Software, McMaster University, J
45、un. 2003.,学者简介,Angelika Bunse-Gerstner Professor Chair of the Numerical Analysis group of the Zentrum fur Technomathematik at the university Bremen, German. Email: bunse-gerstnermath.uni-bremen.de,大规模网络,55,大规模网络,几十个节点（第一代）,几百个节点（第二代）,研究的重点问题： 如何解决网络控制开销随网络节点数指数增加的问题？ 如何进行高效的路由？ 如何有效支持方向天线和MIMO等新技术的应用，提升自适应传输和多址技术的性能？,初始探索阶段,谢谢！,
