MS004201-随机过程

研究生课程开设申请表

 开课院（系、所）：       

 课程申请开设类型： 新开□     重开√     更名□（请在□内打勾，下同）

一、课程介绍（含教学目标、教学要求等）（300字以内）

 教学目标：通信与信息工程领域的理论研究涉及大量的随机数学方面的内容，本课程的教学目的就是通过该课程的学习，培养和训练该专业硕士研究生的随机数学方面的基础理论和基本技能，为后继课程的学习和将来的科研奠定坚实的随机数学基础。

 教学要求：要求学生熟练掌握课本内容，理解基本概念，对通信与信息工程中的随机对象有清晰的了解，掌握最基本的数学工具和方法。

二、教学大纲（含章节目录）：（可附页）

 本课程系统介绍从事通信与信息工程领域的科学研究及工程设计所必需的随机数学基础。内容包括：随机现象的数学建模；各种随机对象; 随机数学分析; 随机信号与线性系统; 信号的统计推断; Markov链; 随机对象的计算机模拟等。.

 具体每章内容如下

第1章随机现象的数学建模

本章介绍随机现象形成的原因及其概率空间的数学建模方法，旨在从科学方法论的角度，阐明随机现象的数学建模方法所体现的科学思想。本章内容是全书的纲领，揭示的是随机数学理论中所蕴涵的科学思想，是非常重要的部分，要花一定时间讲透。因为，科学思想是解决实际问题的基本出发点，只有深刻理解了这个基本出发点，才能知道理论知识的“底限”，并能得心应手地加以应用。

 第2章 各种随机对象

详细各种随机对象。尝试从一个统一的框架介绍三类最本质的随机对象，即随机变量、随机向量、随机过程。事实上，这三类随机对象只是样本空间维数的不同，它们的样本空间分别是、、。这样一个框架很好地揭示了随机变量、随机向量、随机过程这三类随机对象之间的联系和差别。从这个框架，读者可以很清楚地看到，随机过程实际上是无穷维的随机向量，是随机向量概念的一个推广；此外，有限维的随机变量和随机向量是描述随机过程的必备基础。该章还介绍描述这些随机对象的指标，如各种概率函数和数字特征等。该章随机过程部分，介绍各种常见的随机过程，如正态随机过程、和过程、Wiener过程、Poisson及其导出过程、更新过程等。通过第2章的学习，可以迅速具备概率论的预备知识，并达到对随机过程概念的深刻理解。

 第3章 随机数学分析

在介绍随机对象函数的基础上，介绍随机变量序列的各种收敛性；在均方收敛的基础上，介绍了均方微积分、二阶矩过程的正交分解、遍历性等概念。这些内容在数学领域内属于“数学分析”的范畴，由于分析的对象是随机对象，所以称之为“随机数学分析”。这一章内容是后续章节内容的理论基础。

 以上三章是全书的数学基础

 第4章 随机信号与线性系统

第4、5章以信息与通信工程中的“随机信号处理”为应用背景，介绍了随机信号的功率谱密度及带宽、随机信号通过线性系统和信号的统计推断这几个方面的基础理论知识。

 第4章介绍了随机信号的功率谱密度和带宽的概念；在此基础上介绍了随机信号通过线性系统的二阶统计特性和概率特性；此外，还介绍带限和带通信号的一些常见性质。

第5章信号的条件推断

介绍信号的统计推断，包括信号检测、参数估计和信号的波形估计（滤波）。在检测问题中，介绍了常见的各种检测准则，如Bayes准则、最小化最大风险准则、最大似然准则、最小错误概率准则等；在参数估计中，也介绍了各种估计准则，如Bayes准则、最小化最大风险准则、最大似然准则、线性最小均方误差准则和最小二乘准则等；在滤波问题中，介绍了匹配滤波、白化滤波、Wiener滤波。

第6章 Markov链

以信息与通信工程中的“系统分析和网络流量分析”为应用背景，介绍Markov链及其排队论方面的基础理论知识。分别介绍了离散时间Markov链的状态方程、状态分类、应用举例，以及连续时间Markov链的状态停留时间、状态微分方程和应用举例等，嵌入Markov链概念的引进，使得可以用离散时间Markov链来分析连续时间Markov链的极限性质。本章还着重介绍了M/M型、M/G/1和G/M/1排队系统。M/M型排队系统可以用一种特殊的连续时间Markov链------生灭过程来建模，M/G/1和G/M/1排队系统可以用嵌入Markov链来进行分析。一个排队系统，不仅要对等待顾客数、系统顾客数等顾客参量的分布进行分析，还要对等待时间、系统时间、忙期、闲期等时间参量的分布进行分析。

第7章随机对象的计算机仿真

 以信息与通信工程中的仿真实验为应用背景，介绍了随机过程的计算机模拟方法，也即在计算机仿真实验中，如何生成一个具有指定概率分布或其他统计特性的随机对象。

三、教学周历

四、主讲教师简介：

 陈明：1968年10月出生于江苏省扬州市。1990年、1993年和1996年于南京大学数学系分别获理学学士、硕士、博士学位。1996年7月毕业分配到东南大学信息科学与工程学院移动通信国家重点实验室，从事移动通信领域的科研和教学工作至今。1996年受聘为讲师，1998年受聘为副教授和硕士生导师，2003年受聘为教授，2004年受聘为博士生导师。

2004年1月－2005年12月，兼职受聘为中科院上海微系统与信息技术研究所客座研究员；2006年至今，兼任《电波学报》杂志的编委；2006年入选为教育部新世纪人才。

 主要研究方向包括：①现代信息论与编码；②未来移动通信系统中的基带信号处理；③移动通信系统中的无线资源管理分配算法研究。涉及过的具体研究领域有：CDMA通信中的多用户检测；智能天线；Turbo和LDPC编解码；MIMO系统的信号检测和信道估计；空时编解码；3.5G移动通信系统的仿真分析；无线资源管理算法研究（包括调度算法、自适应调制编码、HARQ、快速小区选择、准入控制、负载均衡、信道分配等）；认知无线电；分布式无线网络；无线通信系统之间的干扰分析等。

 至今为止，在国内外学术期刊上发表科研论文50余篇，其中被SCI收录20余篇，被Ei收录30余篇；发表国际会议论文30余篇，其中被ISTP收录20篇；获国家发明专利7项，国际发明专利4项。作为项目负责人，主持完成国家863高技术发展科研项目2项、国际合作科研项目7项、企业横向科研合作项目6项。作为参研人之一完成的科研成果，获2005年度江苏省科技进步一等奖。研究成果“2500-2690MHz频段的卫星系统与地面3G移动通信系统的干扰分析”获2006年度中国通信标准化协会三等奖。

 从1996年开始，主讲本系硕士生的学位基础课程《随机过程》达17次，并编写出版了该课程的教材《通信与信息工程中的随机过程》；2002年该课程被评为“江苏省研究生创新工程优秀研究生课程”，2003年该课程被评为“江苏省研究生开放课程”，2004年获江苏省“研究生学位课程教学改革”一等奖。

五、任课教师信息（包括主讲教师）：

Application Form For Opening Graduate Courses

School (Department/Institute)：School of Information Science and Engineering

Course Type: New Open □   Reopen√    Rename □（Please tick in □, the same below）

1. Course Introduction (including teaching goals and requirements) within 300 words:

Teaching Goals: The theoretic researches in communication and information engineering field needs a large amount of knowledge of Random mathematics, the teaching goals of this course is to cultivate and train the students and improve their levels of theory and abilities of random mathematics, and establish the base of random mathematics for future studies and researches.

Teaching Requirements: master the contents of textbook, understand the basic concepts and random objects in communications and information engineering, master the tools and methods of random processes.

2. Teaching Syllabus (including the content of chapters and sections. A sheet can be attached):

This course introduces the basic random mathematics knowledge needed when one goes in for the studies and researches of communication and information engineering (CIE) field. The contents of these knowledge contain: Random phenomena and problems in CIE field; fundaments of probability and random processes; probability models and properties of frequent random processes; fundaments of analysis of random signals, such as orthogonal decomposition of random signals, properties of frequent random signals, detection and filtering of signals; Markov chains and fundaments of queuing theory; computer generation of random variables and processes, etc.

The contents of every chapter are as follows:

Chapter 1 Random processes in CIE (2 hours): This chapter introduces the reason that random phenomena appear, mathematical modeling of random phenomena, the random objects in CIE. Goals of the chapter is to give students a straightforwardintuitionistic knowledge, the understand the reason that random phenomena appear.

Chapter 2 Random Objects (10 hours): The contents of this chapter are the bases of the whole knowledge of the text. The goal is to review the concepts of probability theory and random variables, and to introduce the concept of random processes. The students are inquired to master the concepts of probability space, random variables, random processes, and the definitions and properties of five probability functions (probability mass function, cumulative distribution function, generation function, characteristic function), and concepts of number characteristics of variables, such as mean, variance etc.

Chapter 3 The basic classes of random processes (8 hours): This chapter introduces basic classes of random processes in CIE. The students are inquired to master the definitions and properties of Gaussian random processes, definition and description of memory of random processes, definition of stationary processes. Especially for memory random processes, the students are inquired to master frequent independent increment processes such as sum processes, Poisson processes, etc.

Chapter 4 Random signals pass the linear systems and nonlinear systems (8 hours): This chapter introduces the properties that random signals pass the linear systems and nonlinear systems. In order to obtain the mathematical expression of random signals passing the linear systems, the concepts of limit of a random sequence, mean square calculus and power spectral density. The students are required to master the properties of random signals passing the linear systems, including time-continuous and time-discrete systems. Furthermore, the analysis methods that random signal pass nonlinear systems are also required to be mastered.

Chapter 5 Fundamental analysis of Random signals (10 hours): This chapter introduces fundamental analysis of random signals, including: the orthogonal decomposition of random signal, the properties of frequent random signals such as band-limited signals, narrow band signals, the detection and filtering of random signal.

Chapter 6 Markov chains (8 hours): This chapter introduces fundamental knowledge of time-discrete and time-continuous Markov chains. The students are required to master the concepts of recurrent and transient states, classification and decomposition of states, period and ergodicity of states for time-discrete Markov chain, state-staying time and state systems of differential equations for time-continuous Markov chain. Especially, the birth-and-death processes should be mastered clearly.

Chapter 7 Markov chains (8 hours): This chapter introduces elements of queuing theory. The methods how to analyze M/M/1,M/M/n,M/M/n/K,M/G/1 queuing models should be mastered.

Chapter 8 Computer method of generating random variables and processes (4 hours): This chapter introduces how to generate random variables. The students are required to master how to generate a random variable and processes with given PDF.

3. Teaching Schedule:

Note: 1.Above one, two, and three items are used as teaching Syllabus in Chinese and announced on the Chinese website of Graduate School. The four and five items are preserved in Graduate School.

2. Course terms: Spring, Autumn , and Spring-Autumn term.  

3. The teaching languages for courses: Chinese, English or Chinese-English.

4. Applicable range of discipline: public, first-class discipline, second-class discipline, and third-class discipline.

5. Practice includes: experiment, investigation, research report, etc.

6. Teaching methods: lecture, seminar, practice, etc.

7. Examination for degree courses must be in paper.

8. Teaching material websites are those which have already been announced.

9. Brief introduction of chief lecturer should include: personal information (date of birth, gender, degree achieved, professional title), research direction, teaching and research achievements. (within 100-500 words)

4. Brief Introduction of Chief lecturer:

Ming Chen received his B.Sc.,M.Sc.and Ph.D. degrees from mathematics department of Nanjing University, Nanjing, China, in 1990,1993 and 1996 respectively. In July of 1996, he came to National Mobile Communications Research Laboratory of Southeast University in Nanjing to be a Lecturer. From April of 1998 to March of 2003 he has been an Associate Professor and from April of 2003 to now he has been a Professor at the laboratory. His research interests include signal processing and radio resource management of mobile communication systems.

5. Lecturer Information (include chief lecturer)