REFERENCES
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英文文献的引用方法与格式-- APA格式所谓APA格式是指美国心理学会(American Psychological Association) 所出版的出版手册(Publication Manual)中,有关投稿该协会旗下所属二十九种期刊时必须遵守的规定而言。
学术界通称为APA格式。
APA引证格式由两部分组成:论文中的文献引用与论文后面的参考文献。
必须注意的是,参考文献部份与文献引用部份息息相关,引用过的文献必须出现在参考文献中,而且参考文献中的每一项文献都被引用过,两者的作者姓氏以及发表年代也必须完全一致。
一、文献引用(Citation in Text)文献引用的目的,一方面是帮助读者进一步直接查阅有关文献的内容,另一方面是尊重与保障他人的知识产权。
文献引用的方式主要有两种,一种是在行文当中直接引用作者姓氏,如:Widdowson (1978) has claimed that native speakers can better understand ungrammatical utterances with accurate vocabulary than those with accurate grammar and inaccurate vocabulary.另一种是直接引用研究的结果或论点,如:Communicative methods have the common goals of bringing language learners into closer contact with the target language (Stern, 1981). APA文献引用的格式主要有下列几种,分述如下:(一)作者为一个人时例1:Stahl (1983) has demonstrated that an improvement in reading comprehension can be attributed to an increase in vocabulary knowledge.[注:若行文中提到作者姓氏,用此例所示格式引用]例2:During the period of Grammar Translation methodology, bilingual dictionaries became common as reference tools (Kelly, 1969). [注:行文中未提到作者姓氏,用此例所示格式引用;句子本身的标点符号位于括号的后面。
apa引用references list
APA(American Psychological Association)引用格式是一种常见的学术引用格式,主要用于社会科学领域。
在APA格式中,参考文献列表的格式要求如下:
参考文献列表应按照作者姓氏的首字母顺序排列,而不是按照引用顺序排列。
参考文献列表中的每一个条目都应该包含作者姓氏、出版年份、文章标题、期刊名和卷号(如果有的话)。
如果有多位作者,只需要列出第一作者的姓氏,然后在括号内列出所有作者的姓氏。
出版年份应该用阿拉伯数字表示,并在括号内用逗号隔开。
文章标题应该用斜体表示,并在引号内用逗号隔开。
期刊名应该用斜体表示,并在引号内用逗号隔开。
卷号应该用阿拉伯数字表示,并在括号内用逗号隔开。
下面是一个APA引用参考文献列表的示例:
Author, A. A., Author, B. B., & Author, C. C. (2001). The title of the article. The Journal
of Relevant Studies, 12(3), 1-20.
在这个示例中,参考文献列表包含一个条目,即一个期刊文章。
条目包含了作者姓氏、出版年份、文章标题、期刊名和卷号。
注意,APA格式要求在括号内使用逗号来分隔不同的信息。
数据库中references的用法数据库中references什么是references?在数据库中,references是用于建立表与表之间关联的机制。
当一个表中的某个列(外键)引用另一个表中的主键时,我们称之为references关系。
references的作用•建立表之间的关联关系:通过使用references,可以在表之间建立关联关系,从而方便进行数据的查询和操作。
•维护数据一致性:通过定义外键关系,可以保证参照表中的数据被正确引用,避免了数据的冗余和不一致。
使用references的语法CREATE TABLE 表名 (列1 数据类型,列2 数据类型,列3 数据类型,...FOREIGN KEY (外键列) REFERENCES 参照表名 (参照列));其中,外键列对应当前表中需要引用另一个表的列,参照表名是被引用的表的名称,参照列是被引用的表中的主键列。
references的用法1.一对一关系:当两个表之间存在一对一的关系时,可以使用references来建立关联。
例如,有一个表存储员工信息,另一个表存储员工的办公室信息。
可以通过在员工表中建立外键引用办公室表的主键,来表示每个员工只能拥有一个办公室。
2.一对多关系:当一个表中的某个列需要引用另一个表中的多个行时,可以使用references来建立关联。
例如,在一个学生表中,每个学生可以有多个课程。
可以在学生表中建立外键引用课程表的主键,来表示每个学生可以参加多门课程。
3.多对多关系:当两个表之间存在多对多的关系时,需要通过中间表来建立关联。
例如,有一个商品表和一个订单表,一个商品可以出现在多个订单中,一个订单中可以包含多个商品。
可以通过在中间表中建立外键分别引用商品表和订单表的主键,来表示商品和订单之间的关系。
4.级联操作:通过定义外键的级联操作,可以自动更新或删除关联表中的数据。
例如,当删除一个课程时,可以通过设置外键的级联操作将学生表中关于该课程的记录一并删除。
英文assignment的写作细节(请各位愿意长期合作的朋友,尽量仔细阅读,在行文中注意这些要求)我们的assignment通常分为两种形式,一是essay, 一是report.二者在形式上有所差别,essay 偏向于理论论述,report则大都结合case进行理论应用。
一篇assignment上面会对写成essay 还是report格式作出明确要求。
在阅读题目时,请尽量仔细。
相同点:1、字体:Times New Roman或者Arial, 字号:小四,行距:1.5倍。
请在写作之前就把这些格式调好,以避免写好后再调会出现一些意相不到的情况。
2、段与段之间隔行。
每段不要求像中文写作那样空两格,而是直接顶格写。
区别:Essay:Essay的写作相对report要简单一些。
通常只包括三个部分,Introduction, Main Body, Conclusion. Introduction 包括topic的背景介绍和论文的结构。
一般占总字数的10%左右。
Main Body是主体部分,占总字数80%左右。
如果题目中作了具体要求,就根据题目提到的几个方面来逐一讨论就可以了。
有的题目没有作具体要求,就根据自己的构思来写。
但要求有逻辑性。
Conclusion也是占10%,在这一段里把文章中的主要观点用一到两句话概括出来。
Essay的body部分不提倡用太多的标题,有的作业要求甚至会直接写明不能用任何的标题,所以为了保证文章结构的清晰性,段落间要有承上启下的句子,使结构清晰明了,文章结构很重要,老师非常重视,直接影响分数的好坏。
Reference的写作是essay和report都要涉及的,我放在最后来详细说。
Report:它的写法大体上和essay差不多,但要求要严格一些。
第一:标题页:顾名思义,将report的题目写在此页第二:Executive summary,是对文章的摘要,要把写这篇报告的目的(也就是为什么要写这篇报告),报告得出的结果,最后的结论,以及报告给出的建议一一交代清楚,但不需要交代题目背景,摘要的目的是让busy reader能快速掌握报告的全部内容。
科学引用格式(SCI的References格式)1.引言科学引用格式(SCI)是一种用于在学术出版物中引用参考文献的标准格式。
SCI格式由美国化学学会(ACS)领导的一组学术出版组织共同制定,目的是为了使学术论文的引用标准化、规范化,方便读者查找和理解参考文献的信息。
2.SCI格式的特点SCI格式的引用特点主要包括以下几点:(1)作者姓氏在前,名字在后,用逗号隔开,而非中文的姓在前,名在后的格式。
(2)标题使用“斜体”,刊物名称用“正体”。
(3)引用的序号要用方括号括起来,而非使用括号。
这些规范的要求使得学术论文的引用信息更加清晰、规范,方便读者查找和理解引用的参考文献。
3.SCI格式的应用范围SCI格式广泛应用于自然科学和工程技术领域的学术出版物中,如物理学、化学、生物学、材料科学等领域。
SCI格式的引用标准被认为是国际上学术界最权威的引用标准之一,因此在相关领域的学术出版物中广泛使用。
4.SCI格式的引用要求SCI格式的引用要求非常严格,引用时需要按照一定的格式和顺序来列出参考文献的信息。
一般来说,SCI格式的引用要求包括以下内容:(1)作者的尊称(姓氏在前,名字在后)。
(2)文献的标题(使用斜体)。
(3)刊物的名称(使用正体)。
(4)刊物的卷号、期号和页码。
(5)出版年份。
5.SCI格式的示例以下是一篇使用SCI格式引用的参考文献示例:[1] Smith, J. A. The effects of climate change on marine ecosystems. Nature, 2015, 523(7561): 418-420.上面的引用示例中,方括号内的数字1表示引用的序号,Smith, J. A.是作者的尊称,The effects of climate change on marine ecosystems是文献的标题,Nature是刊物的名称,2015是出版年份,523是卷号,7561是期号,418-420是页码。
论⽂reference格式写作规范英⽂assignment的写作细节(请各位愿意长期合作的朋友,尽量仔细阅读,在⾏⽂中注意这些要求)我们的assignment通常分为两种形式,⼀是essay, ⼀是report.⼆者在形式上有所差别,essay 偏向于理论论述,report则⼤都结合case进⾏理论应⽤。
⼀篇assignment上⾯会对写成essay 还是report格式作出明确要求。
在阅读题⽬时,请尽量仔细。
相同点:1、字体:Times New Roman或者Arial, 字号:⼩四,⾏距:1.5倍。
请在写作之前就把这些格式调好,以避免写好后再调会出现⼀些意相不到的情况。
2、段与段之间隔⾏。
每段不要求像中⽂写作那样空两格,⽽是直接顶格写。
区别:Essay:Essay的写作相对report要简单⼀些。
通常只包括三个部分,Introduction, Main Body, Conclusion. Introduction 包括topic的背景介绍和论⽂的结构。
⼀般占总字数的10%左右。
Main Body是主体部分,占总字数80%左右。
如果题⽬中作了具体要求,就根据题⽬提到的⼏个⽅⾯来逐⼀讨论就可以了。
有的题⽬没有作具体要求,就根据⾃⼰的构思来写。
但要求有逻辑性。
Conclusion也是占10%,在这⼀段⾥把⽂章中的主要观点⽤⼀到两句话概括出来。
Essay的body部分不提倡⽤太多的标题,有的作业要求甚⾄会直接写明不能⽤任何的标题,所以为了保证⽂章结构的清晰性,段落间要有承上启下的句⼦,使结构清晰明了,⽂章结构很重要,⽼师⾮常重视,直接影响分数的好坏。
Reference的写作是essay和report都要涉及的,我放在最后来详细说。
Report:它的写法⼤体上和essay差不多,但要求要严格⼀些。
第⼀:标题页:顾名思义,将report的题⽬写在此页第⼆:Executive summary,是对⽂章的摘要,要把写这篇报告的⽬的(也就是为什么要写这篇报告),报告得出的结果,最后的结论,以及报告给出的建议⼀⼀交代清楚,但不需要交代题⽬背景,摘要的⽬的是让busy reader能快速掌握报告的全部内容。
reference的用法总结大全(学习版)编制人:__________________审核人:__________________审批人:__________________编制学校:__________________编制时间:____年____月____日序言下载提示:该文档是本店铺精心编制而成的,希望大家下载后,能够帮助大家解决实际问题。
文档下载后可定制修改,请根据实际需要进行调整和使用,谢谢!并且,本店铺为大家提供各种类型的经典范文,如英语单词、英语语法、英语听力、英语知识点、语文知识点、文言文、数学公式、数学知识点、作文大全、其他资料等等,想了解不同范文格式和写法,敬请关注!Download tips: This document is carefully compiled by this editor.I hope that after you download it, it can help you solve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you!In addition, this shop provides various types of classic sample essays, such as English words, English grammar, English listening, English knowledge points, Chinese knowledge points, classical Chinese, mathematical formulas, mathematics knowledge points, composition books, other materials, etc. Learn about the different formats and writing styles of sample essays, so stay tuned!reference的用法总结大全reference的意思n. 参考;参考书;提及,涉及;证明人,介绍人v. 引用;参照;reference的用法用作名词(n.)The play is full of references to the political events of those days.这剧本涉及当时的许多政治事件。
Fuzzy Logic Modeling of Deflection Behaviour Against Dynamic Loading inFlexible PavementsMehmet SaltanSüleyman Demirel University, Department of Civil Engineering, 32260, Isparta, TURKEY.msaltan@.trSuna SaltanSüleyman Demirel University, Department of Mathematics, 32260, Isparta, TURKEY.smercan@.trAhmet ŞahinerSüleyman Demirel University, Department of Mathematics, 32260, Isparta, TURKEY.sahiner@.trAbstract. Flexible pavements are especially affected by moving vehicles. As a result ofthe moving vehicles, the pavement starts to deteriorate. For the determination of thestructural capacity of the pavement, non-destructive testing equipments are used.These are mainly Benkelman Beam, Dynaflect and Falling Weight Deflectometer(FWD). In such a process, the most important thing is to analyze the collected data. Ingeneral, linear elastic theory and finite element method are used for this purpose. Butlinear elastic theory and finite element method are time consuming. A fuzzy Logicapproach is used for the elimination of this drawback during the course of this study.Results indicate that the Fuzzy Logic approach can be used for the modeling of thedeflection behavior against dynamic vehicle loading for flexible pavements.REFERENCES1. Huang, Y.H., ''Pavement analysis and design'', Prentice Hall, Englewood Cliffs,NJ, USA, 1993.2. Stolle, D.F.E., ''Modelling of dynamic response of pavements to impact loading'',Computers and Geotechnics, 11(1), 83-94, 1991.3. Altrock, C.V., ''Fuzzy logic and NeuroFuzzy applications explained'', Prentice Hall,Englewood Cliffs, NJ, 1995.4. Kiszka, J.B., Kochanskia, M.E., Sliwinska, D.S., ''The influence of some fuzzyimplication operators on the accuracy of fuzzy model'', Part I. Fuzzy Sets and Syst., 15, 111-128, 1985.5. Zadeh, L.A., Fuzzy sets, Information control, 8, 338-353, 1965.。
摘要委婉语是人类语言中的一种普遍现象,它在人们的日常社交活动中使用得十分广泛,是语言使用中人们协调人际关系的重要手段。
使用委婉语有利于提高交际效果和保持和谐的人际关系。
在人类文明日益发展和人际交往不断扩大的今天,委婉语更是发挥着其不可或缺的作用。
Hugh Rawson(1981)也曾断言“委婉如此深植于我们的语言中,以至于很少有人能一天离得开它,就连那些以说话平铺直叙而自居的人也不例外。
”同样,委婉语也引起了语言学界的极大兴趣。
多年来,语言学者们分别从不同角度对这一语言现象进行分析研究。
同时,它独特的语用功能也成为当前社会语用学研究的重要课题。
本文通过借鉴前人的研究成果,从语言学的角度来分析,探讨委婉语的产生,分类,构成,委婉语的使用对语言系统与交际的影响,委婉语在人际会话中的功能和应用。
本文旨在通过对委婉语产生动因和社会功能意义的分析,为言语交际和社会交流服务,从而认清在人际交往中委婉语使用的重要意义,以减少交际失误,避免人际冲突,改善人际关系。
[关键词] 委婉语;人际会话;功能;应用AbstractEuphemism is a common phenomenon in languages. It has a great effect on daily communication. People use euphemism because they fear something, because they want to save face or because they strongly incline to avoid talking about something. With the development of modern society, it has become an important element in people’s interactions. Hugh Rawson (1981) has also affirmed “Euphemisms are embedded so deeply in our language that few of us, even those who pride themselves on being plain-spoken, even get through a day without using them”. So it is not surprising that euphemism has long been a focus of interest in linguistic circle, and a considerable amount of literature on euphemisms has been accumulating.With the progress of society and development of human civilization, euphemism accompanies the process of language communication of the whole society. Many linguists and scholars have studied the linguistic phenomenon from different angles. Based on their achievements, the paper will have an exploration the principles and ways of using English euphemism, make a brief introduction and classification of euphemism, introduce social function and application of euphemism. Euphemisms are a linguistic technique for people to achieve various goals in communication. Therefore, encoding euphemisms correctly and using them properly are closely related to whether an individual can conduct successful communication.[Key Words] euphemism; communication; function; applicationOn Function and Application of English Euphemism inCommunicationIntroductionPeople all over the world try to use mild and agreeable language while speaking of unpleasant or embarrassing facts. Almost all people, all the time, seem to have certain things or notions that they avoid mentioning directly. Sometimes people would like to use pleasant, polite or at least harmless-sounding even flattery terms instead of those considered unpleasant or offensive even trouble-making.How to use language terms and sentences to avoid mentioning something unpleasant or unlucky; how to avoid using “direct or vulgar words” which usually refer to taboo subjects? Since we are living in the modern world and in a polite, civilized society, we need a certain way to express ourselves in some awkward situations in which euphemism, as an indirect speech, will surely help us.As a very part of language and a common linguistic phenomenon, euphemism is so widely used in our daily life. Every society, every speech community, every social class has its euphemism. To speak euphemistically is a universal trait. What is euphemism? Why people use euphemism? Why should we speak euphemistically? When is euphemism used? How can we read into them? Such kinds of problems are rather complex. For the circumstances and conditions under them differ from person to person, from profession to profession even from class to class, which means that euphemism is not only a linguistic phenomenon but also a cultural and social phenomenon. Therefore, People often use euphemism to make the atmosphere of communication more active, and make the people’s relationship more harmonious.This thesis tries to explore the function and application of English euphemism from pragmatics angle, to show the use of euphemism is very important in daily life to achieve successful social communication.1. A Brief Introduction of Euphemism1.1 The Definition of EuphemismAccording to the explanation in the Concise Oxford English Dictionary, the word “euphemism” originated from Greek euphemismos and from euphemizein which means “use auspicious words”. Analyzing from the formation of this word, it is comprised of the prefix “eu” which means “good” and a foot “pheme” which means “speaking”. Thus the word literally means “to speak with good words or in a pleasant manner”. (Neaman and Silver, 1983:60) That is to say, “euphemism is used as an alternative to unpleasant expression, in order to avoid possible lose of face, either one’s own face or through going offense, that of the audience, or some of third of party”.(Allan and Burridge, 1991:18)Different scholars have different explanations of euphemism from variousperspectives, but all the definitions share the basic idea: Euphemism is an indirect, roundabout and polite mode of expression used to mean something unpleasant. In communication, it can make the unpleasant things sound better, and make people feel good; it can also ensure both the speaker and the hearer safe without losing face.With the fast development of modern society, the meaning of euphemism has been greatly enriched, expanding from the level of word to the level of sentence, paragraph, and even the whole passage; the scope of euphemism has also been extended from the traditional fields of deities and devils, parts of human body, diseases and death to such sensitive fields of contemporary life as occupation, laws, politics, advertisement and so on.1.2 Sociolinguistic Study of EuphemismEuphemism, for a long time, has been discussed by many scholars, such as Rawson, Leech, etc. in their respective fields of research. Their studies are mainly focused on three areas: rhetoric, semantic, lexical and dictionary compiling. The rhetoric view treats euphemism as a figure of speech, closely related to linguistic taboos. It reveals the information, classification of euphemism and their relation to taboos.The semantic point view takes euphemism as an “associative engineering”, i.e. replacing a word having offensive relationship with another expression, which makes no overt reference to the unpleasant side of the subject, and may even be a “positive misnomer” (Leech, 1983:45). The researchers explore the origin and formation of euphemisms in terms of their semantic features. It largely focuses on the semantic causes of euphemisms.Lexical point of view or dictionary compiling is a way widely adopted by many scholars whose major concern is to collect and categorize euphemisms for dictionaries. This way mainly deals with the meaning of each euphemism and its relation to other terms.Euphemism is a socio-cultural language phenomenon. Socio-linguistists study the effect of social classes, gender, age, profession, relationship of human beings and social geography on language. So, this paper will make a research on how some of these factors influence on euphemisms.2. Cooperative Principle and Politeness Principle in Euphemism2.1 Cooperative PrincipleIn social science generally and linguistics specifically, the cooperative principle describes how people interact with one another. Cooperative Principle is proposed by Paul Grice, who has concerned himself with philosophical issues with language. As phrased by Paul Grice, “Make your contribution such as it is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged.” The principle is intended as a description of how people normally behavein conversation. In Logic and Conversation, Grice distinguishes it four categories: Quantity, Quality, Relation, and Manner. (Grice, 1975:48)Under these four categories, he further provides Maxims which guide the speaker and hearer in conversations. The followings are the four maxims:The maxim of quantity: a) make your contribution a s informative as required; b) do not make your contribution more informative than required.The maxim of quality: Try to make your contribution one that is true. a) do not say what you believe to be false; b) do not say that for which you lack adequate evidence.The maxim of relation: Make your contribution relevant.The maxim of manner: Be perspicuous, and specifically. a) avoid obscurity; b) avoid ambiguity; c) be brief; d) be orderly.2.2 Politeness PrinciplePoliteness phenomenon is universal almost in all languages and the Politeness Principle is one of the most influential theories concerning politeness. Mentioning the Politeness Principle, one will think of Leech’s Politeness Principle. What is more, PP as one of communicative principles, many scholars have research it. It is generally recognized that the Brown, Levinson and Leech etc. researched this principle in the 1970s, and has greatly contributed to politeness studies. This also shows that more and more people have realized the need and importance to carry out research on politeness. What is more, people need to communicate with other people frequently and politeness is one of the important things they should bear in mind to ensure smooth and successful communication. One of the ground rules in social communication is an agreement between the different parties that everyone should operate with the theory of face and the PP in mind. Every time when people open their mouths they have to consider whether what they say is likely to maintain the face of others and shows that they are polite, because it is conventional to appear to be polite, whatever one’s true feelings. And euphemism is an important means to avoid any potential face affront to the others and to show politeness to the others.On the other hand, advances in science and technology have gradually eliminated the distance of time and space and greatly contributed to easier and more frequent human communication, putting the study of politeness on a high agenda. Where there is communication, there are politeness studies. As a result, politeness as a research topic of much concern has been and is enjoying much popularity with people specialized in the areas of pragmatics, sociolinguistics and intercultural communication etc..2.3 Contradiction and Unification of Two Principles in EuphemismThe application of euphemism reflected in the contradictions in communication is: following the principle of cooperation but violating the principle of politeness, or breaking the principle of cooperation but follow the principle of politeness. The use of euphemism to reflect the unity of communication is: violating cooperation is an act of courtesy, cooperation is also a courtesy, the ultimate aim of which is to accomplish asmooth and successful conversation.Therefore, in the process of practical communication, in order to meet the requirements of communication people have to use long, cumbersome and vague language expression to express the things which are inconvenient, embarrassing or offensive to others, so that the hearer can not grasp the information quickly and accurately. Obviously, such an expression violates the four norms of the principle of cooperation, both parties worked hard to say how to organize and use indirect, unsure, not hurt the listener’s language, letting the listener don’t know what really happened, they had to try their best to figure out how to express the real intention, the result is not only wasted time, but also weakened the information, this kind of expression run in the opposite direction with the cooperation principal in our communications. Therefore, the generation of euphemism is that under certain conditions, speakers and writers, in the violation of the principles of cooperation, select the communication method. People could identify the writer’s true intentions from the perspective of deviation. However, it’s undoubtedly, whether it be from the original intention of using the euphemism of view, or as a result from the use of point of view, the use of euphemisms really defend the face of each other in communication and ultimately achieving a polite, dignified and completed results, although the process of communication seems not very smoothly. We may find that the combination of the CP and PP can give us a pretty good explanation about this and hence we may say that they may complement each other in pragmatic analysis. So just like what Leech has said that the PP can “rescue”the CP to some extent.From above, we can find out that violating cooperation principle is actually a kind of politeness. “Being cooperative is being polite (mostly)”. (Allan, 1986:100)3. Characteristics of Euphemism3.1Classifications of EuphemismEuphemism can be classified into many types from different angles. Hugh Rawson in his A Dictionary of Euphemisms and Other Double-talk divides euphemism into two general categories: positive and negative euphemisms in terms of semantics.The positive euphemisms are also known as stylistic euphemisms, which “inflate and magnify the word meaning, making the euphemized seem altogether grander and more important than they really are”(Rawson, 1981:1). The positive euphemisms include the many fancy occupational titles, saving the workers by elevating their job status. In all cultures, there is a tendency to elevate a low, humble status to a high, decent position. Thus, garbage men are promoted to sanitation engineers, bootblacks to footwear maintenance engineers, secretaries to administrative assistant and so on. This kind of euphemism is usually used widely in the official language and some other formal styles.The negative euphemisms on the contrary deflate and diminish. They are extremelyancient and sometimes referred to as traditional euphemisms. Negative euphemisms usually include “inoffensive names for God, devils, the dead and animals that are hunted or feared” (Raws on, 1981:2). For instance, to avoid directly saying “Jesus”, people more often than not use “Geez” instead. Satan sometimes is referred to as “the yellow fellow”.All euphemisms, whether positive or negative, may be used unconsciously or consciously, depending on whether the speakers are aware of the euphemism’s original meanings or not. (Rawson, 1981:2)Hence there are unconscious euphemism and conscious euphemism. Cemetery, a loan word from Greek, is used to replace the word “graveyard”, yet few people know about its origin. Conscious euphemisms, as the name indicates, are employed consciously by speakers. When a lady says she is going to powder her nose, what she really means is she is going to the lady’s toilet. In this case, she intentionally applies a euphemistic term to be polite.Moreover, many well-known scholars come up with their own classifications of English euphemisms based on different themes. The common themes: religion, sex, human anatomy, bodily functions and illnesses are discussed in their books.3.2 Formations of EuphemismThere are various ways of forming English euphemisms. Generally, they can be divided into four kinds as follows: phonetic device, lexical device, grammatical device and rhetorical device.3.2.1 Lexical DeviceLexical device is the main source of producing euphemisms. It includes many methods. The common method is substitution, which is using good words to replace the impolite words. For example, the phrase “be sent to big house” just means “be sent to prison”, because most of the prisons are “big house”. Other examples: “tight, incorrect, thrift” used to substitute “stingy, false and economical” respectively.The second method is to use foreign words. The practice of borrowing words from other languages to function as euphemisms is common, especially in today’s Chinese. In English, euphemisms of foreign source are mainly from French and Latin. These words are filled with less negative associations in foreign languages, and thus sound more pleasant, formal or learned. “It is permissible for speakers and writers of English to express almost any thought they wish, as long as the more risqué part of the discussion are rendered in another language, usually French or Latin” (Rawson, 1981:332).French and Latin provide many euphemisms in English, as today English does in Chinese. For examples, euphemisms of women’s underwear like “brassiere”, “lingerie” are from French; “perspire”, “defecate” are from Latin. “Toilet” comes from the French word “toilette”,meaning “bathroom”.Another method is using the stories from religious or literature works. As we all know, “go west”, “go to heaven”, “go to one’s Maker”,“be with God”, “go the way of all flesh”, “return to dust” and so on are all euphemisms for “die”, but you may notknow that they all come from Bible. And“hand in one’s accounts”, “go to one’s (long) account” are both from the story “Day of Judgment” in Bible. The Christians think everyone should hand in the accounts with what he has done in the world to the God, so that “He” can judge this person.3.2.2 Phonetic DeviceEuphemisms sometimes be created by phonetic device—light-reading and phonetic distortion. Light-reading is a popular way of euphemism which means that when people have to talk about something that they feel embarrassed to mention, they can say it in a low voice to achieve a euphemistic effect. Phonetic distortion refers to the change of a sound in word for the purpose to euphemize. It includes abbreviation, acronym and clipping, etc. Usually crude or inauspicious words become acceptable by using these devices. There are abbreviations like “ladies” for “ladies’room”.There are clippings like “Jeeze” for “Jesus”, “vamp”for “vampire”. There ar e acronyms like “JC” for “Jesus Christ”. T here are reduplication like “pee pee” for “piss”.3.2.3 Grammatical DeviceEuphemistic also could be created by grammatical device. Just as American linguist Dwight Bolinger points out: “Euphemism is not restricted to the lexicon, there are grammatical ways of toning something without actually changing the content of the message”(Bolinger, 1981:48). He gave two sentences for example: “He has been known to take a bribe now and then.” And “He is known to have taken a bribe now and then.” Both sentences report the same event, yet the former, by means of perfect tense which suggests less immediacy, is milder and more euphemistic than the later one which contains the simple tense. Using “could, might, would”to replace “can, may, will”correspondingly functions in the same way. The grammatical device of euphemism mainly consists of many aspects:Subjunctive mood in its nature suggests more or less euphemistic tone. When a manager says to his employee: “You could have done it better.” The employee should know that he isn’t being praised, but being criticized, because the connotative meaning of the sentence is “You didn’t do it well.” or “You didn’t try your utmost to do it.” A teacher may say to his students: “You should have fulfilled the task last week.” T he real meaning is “It was your duty to fulfill the task last week, but you failed to do so.” Similarly, “We would rather you did that.” is milder than “We want you to do that.” And I would be happy if you could tell me the truth.” sounds more courteous than“I will be happy if you can tell me t he truth.”You also could use conditional clause. A typical example is “If only the good die young, he should live to a ripe old age.” It seems to be praising him, but the genuine meaning of it is “He is not a good man.” We have learned such a sentence in“The Story of William Tell” in Senior Book II: “If I had missed”, said William Tell, “and had shot too low, I was going to use this arrow on you.” Here from the context, we know that “shot too low” just means “hurt my child”, and “use this on you” equals “kill you withthis arrow.”Euphemisms are often used to substitute negative words or sentences. Thus, for “I think it would be better for us to start off a little earlier tomorrow morning”, we may say “Wouldn’t it be better for us to start off a little ear lier tomorrow morning.” “He and truth are not on very intimate term”, after careful consideration, you may find the real meaning behind it is “He is a liar.” or “He often tells lies.” Another example is the euphemism for “die”. “He is no more in the world.” Everyone knows it conveys the same meaning with “He is dead.”3.2.4 Rhetoric DeviceEuphemism always seems to be romantic with metaphor, so that the style of the language may change a lot. There are numerous euphemistic words for “die” in English. Actually some of them are vivid and informal metaphor. For instance, “go to his long home”, “go to sleep forever” and “cease to think”, etc. If somebody calls you “Hamlet”, you mustn’t think he is praising you because his real meaning is “You are too indecisive”. Moreover, “Old Newton took him” Means “He died in an airplane accident”. As a matter of fact, metaphor in English is always interesting and fancy.Periphrasis is another way of rhetoric device. Actually it is a wording beating about the bush. “Trousers”doesn’t sound well, so “nether garments” replaces it. “Fart” is too unpleasant to the ear, so people say it as “wind from behind”, without thinking it is too long-winded. “Rear end” takes the place of“buttocks”. “Solid human waste” is actually “feces”. “Give the sack”is the euphemism for “fire”, because “sack” originally was th e workbasket with which the workers went outside to work. If the employer wants to fire some employees, he will give the sack to the workers. Another euphemism for “fire”—“declare staff redundant” is also a kind of periphrasis.4. Social FunctionEuphemism is not only a common phenomenon in languages, but also a cultural phenomenon in society. The using of it has important social functions. The contradiction in daily life is always caused by misnomer, so in the process of communication we often use euphemism to show courtesy, to avoid stimulation or to cooperate. Proper use of euphemism in social communication can be doubly effective. The social function of euphemism has evasive function, polite function and cosmetic function etc..4.1 Evasive FunctionThe evasive function of euphemism is to evade using taboos, enabling the speaker to talk about tabooed things freely. The production of euphemism was probably begun with taboos. These tabooed things are believed to be dangerous to certain individuals, or to the society as a whole, or to be disgusting and unpleasant, and cause fear. (Chen, 2000:53) Such tabooed things include: disease, disabilities, death, sex, body excretion and body elimination process, etc.People can use euphemisms to talk about what cannot be talked directly. Forexamples, they use the backward nations, developing nations or emerging nations instead of poor nations, call old people the senior citizens. They described death as “go to his long”or “home goes to sleep forever”. People want to have a good health, so most people avoid talking about a disease directly; especially the diseases which is seriously harm people’s life. They use other words to weaken them, such as “cancer”changed to “the big C”, “heart attack disease”to “heart condition”. We can say the concepts which were considered as taboos in people’s mind are not easy to eliminate in people’s thought. Even today, European and American people still avoid with number 13.4.2 Polite FunctionPoliteness is another important function that euphemisms serve in the social life. Politeness is the symbol of human’s civilization and one of the important principles guiding people’s activities. As a kind of sign ificant social activity, language activity must observe this principle, too. When we have to talk something unpleasant, we should choose euphemistic way to express in order not to hurt others. Being polite is a reasonable action that anyone who wants to save face. The polite function of euphemism is tried to avoid being harsh or impolite in the communication. In other words, euphemisms are to minimize impolite expressions and maximize polite expressions. For instance, when a teacher comments on a student’s moral behavior and school work in front of the student or his or her parent, the teacher should take into consideration the student’s psychological endurance and the parent’s face. So the euphemistic way to express might be “The student is a bit slow for his or her age” instead of “The student is stupid”.The polite function of English euphemism is embodied in every occupational language. Occupational discrimination gives people pressure and emotional irritation. Although euphemisms cannot uproot this kind of phenomenon, at least, they can give them some psychological comfort by upgrading of career name. Therefore, “engineer, manager, etc.” have become more and more fashionable. “Dustman” is changed to “sanitary engineer”; “mechanic” to “automobile engineer”, “gardener” to “landscape architect”, “shoemaker” to “shoe rebuilder” In English, there are many adjectives about people’s appearance, such as “good looking, handsome, pretty, charming, attractive”, etc. They are all commendatory words. When talking about someone who is not pretty, we cannot use “ugly” or “awful”. We had better use some euphemisms such as “plain, ordinary, not particularly looking”, etc. instead of them. So euphemism’s polite function can save people’s face in their process of communicatio n. It is so important that we cannot neglect it.4.3 Cosmetic FunctionBesides the evasive and polite function, euphemism has the cosmetic function. This kind of euphemism is usually used in the government, military, politics and commerce. It refers to using good words to beautify things, which are not beautiful inreality and make the thing be more acceptable. Because euphemism has the nature of vagueness, to some extent, it is deceptive. Traditionally speaking, euphemism plays a positive role in social life. Using it, people can avoid some embarrassed occasion. But just as every coin has two sides, euphemism has no exception. Using it suitably can coordinate social relationships, but abusing it will mislead the public, will cover up the essence of things. For example, in modern w estern society, the poor is called as “the needy”, later it was changed to “the culturally deprived”, then to “the underprivileged”, at last to “the disadvantaged”. So it will confuse people that this country is so rich that there is no poor people at all.Firstly, the government and the military often use them to pretend the reality from truth. They describe “economic crisis” as “recession” or “depression”; “attack” as “active defense”. At the beginning of 20th century, the rela tionship between labor and capital become strained, and the strike became a serious social problem. In order to hide the fact, politicians call the strained labor-capital relationship as “industrial climate”, striking as “industrial action”. If the negotia tion between labor and capital is successful, it will be claimed as “productive”; on the contrary, it is “counter-productive”.Secondly, this kind of euphemism is widely used in commerce. It is often used to play tricks and to deceive customers. The commercial exaggerates the production’s function and quality. In the same way, the English euphemism is also used to make customers feel pleased. For example, in order to meet the passengers’ sense of dignity, some Airlines call First Class Deluxe Class or Premium Class; Second Class First Class; and Third Class become Business Class, Economic Class, or Tourist Class. Doing like these, it seems that all passengers’ position are promoted. Their purpose is to attract more passengers and gain more profits by using euphemisms in the communication, meanwhile, the customers feel more decent, and it helps customers save face.5. Application of Euphemism in Life5.1 Euphemism in AdvertisementAdvertising English is an applied language. It includes informative advertising and persuasive advertising. Euphemism really plays an important role in it.As we know that the language in advertisements is the key of success, which should be easy to understand as well as attractive to the public. Euphemism is “(the use of a) mild or vague or periphrastic expression as a substitute for blunt precision or disagreeable truth.”(Fowler, 1991:24) It is obvious that euphemism has such characteristics that it suits for the purposes of advertisement very well. In order to achieve the persuasive effect, the language in advertisements should also be correct, concise and vivid, to impress the consumers deeply and arouse their desire to buy the products. For these reasons, the advertisement designer should have a good grasp of both the features and the functions of euphemism that it can cater for the business purpose. For example, a coffee brand named Maxwell House put its advertising in this way, “Good to the last drop!” I t shows that it’s so good drinking that customers will eat the last drop. To some people, it really calls their attention to this brand。
TABLE IIII NPUT I MPEDANCES OF AN8-E LEMENT L OW S IDE-L OBE D IPOLE A RRAY B ACKED BY A G ROUND P LANE W ITH AND W ITHOUT A R EAL S IZET ANGENTIAL O GIVE A-S ANDWICH R ADOME AT S BANDthe radome inner surface,resulting in a strong interaction between the radome and the array.Table III presents the input impedances of the array with and without the radome.The radome effects on the input impedances of the array are clearly noted.IV.C ONCLUSIONSThe hybrid IE/PO method has been successfully used to predict the directive gain patterns and input impedance of electric dipole array in the presence of electrically large3-D radomes.Other interesting perfor-mance indicators such as realized gain pattern and VSWR,etc,of the radome-enclosed array can also be obtained.The principal disadvan-tage of the technique is that discretization is required on the dielectric radome,leading to high computation complexity for larger array.R EFERENCES[1]D.J.Kozakoff,Analysis of Radome-Enclosed 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Symp.on Electromagnetic Compati-bility,Feb.2003,pp.257–261.[14]U.Jakobus,“Overview of recent extensions in the electromagneticscomputer code FEKO and their application,”in20th Annu.Review ofProgress in Applied Computational Electromagnetics,Syracuse,N.Y.,Apr.2004,Applied Computational Electromagnetics Society.[15]P.L.Overfelt,“Superspheroids:A new family of radome shapes,”IEEE Trans.Antennas Propag.,vol.AP-43,no.2,pp.215–220,1995.[16]R.W.McMillan,M.C.Wicks,and G.J.Genello,“A model for deter-mination of radome transmission,reflection,depolarization,loss,andeffects on antenna patterns,”in Proc.IEEE Radar Conf.,Dallas,TX,1998,pp.349–354.Passive Localization of Near-Field Sources With aPolarization Sensitive ArrayYuntao Wu,H.C.So,Chaohuan Hou,and Jun Li Abstract—The least squares-virtual ESPRIT algorithm(LS-VESPA)is extended to jointly estimate the direction-of-arrival(DOA)and ranges of multiple near-field sources impinging on an array of crossed dipoles.The algorithm utilizes fourth-order cumulants for direct estimation of the ar-rival angle and range parameters via the eigenvalues of certain constructed pared with several existing algorithms,the loss of array aper-ture is effectively avoided.As a result,the proposed method can estimate DOAs and ranges of(1)polarized near-field sourcesusing dual-polarization sensors.Simulation results show that the proposed method outperforms a fourth-order statistics based ESPRIT-like method.Index Terms—Least squares-virtual ESPRIT algorithm(LS-VESPA), near-field,polarization,source localization.I.I NTRODUCTIONMany methods for estimation of directions of arrival(DOAs)of emitted sources impinging on an array of sensors have been developed in thefield of array signal processing[1],such as multiple signal clas-sification(MUSIC)and estimation of signal parameters via rotational invariance techniques(ESPRIT).Most of them assume that the sources of interest are located relatively far from the array so that the wave-fronts from them can be regarded as plane waves,which implies that each source location is characterized by a single DOA[1].Apparently, this assumption is no longer valid when the source is close to the array, such as in near-field applications of sonar[2],seismic exploration[3], and electronic surveillance[4].For near-field sources,they must be characterized by spherical wavefronts at the array aperture and need to be localized by both range and DOA[2]–[5].Since the available methods based on the far-field assumption cannot be directly applied to the near-field scenario,near-field source localiza-tion is typically solved by other means,such as maximum likelihood (ML)[2],multidimensional search[4],2D-MUSIC[5]–[9],and higher order statistics[10].To avoid the multidimensional search,Challa and Shamsunder[10],[11]have developed a total least squares ESPRIT-like algorithm as well as unitary ESPRIT method based on fourth-order cumulants.An optimally-weighted linear prediction method for near-field source localization is also recently presented in[12],where Manuscript received August14,2006;revised December20,2006.Y.Wu and H.C.So are with the Department of Electronic Engineering,City University of Hong Kong,Kowloon,Hong Kong(e-mail:wuyuntao6@hotmail. com).C.Hou is with the Integrated Digital System Laboratory,Institute of Acous-tics,Chinese Academy of Sciences,Beijing,100080,China.J.Li is with the National Key Laboratory for Radar Signal Processing,Xidian University,Xian,710071,China.Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TAP.2007.9019120018-926X/$25.00©2007IEEEmultiple optimally weighted least squares problems need to befirstly solved for parameter estimation.All aforementioned methods for near-field source localization do not exploit the polarization information at the received array.Never-theless,the advantages of different polarization-sensitive arrays have been utilized in wireless communications and various types of radar systems[14],[16].The problem of parameter estimation of far-field signal source with a diversely polarized array has been extensively studied[14]–[16].This is motivated by the fact that polarization has also been incorporated in array antennas for improved estimation of far-field signal parameters.Recently,an enhanced method for near-field source localization with a polarization sensitive array has been presented in[17],which shows that the incorporation of the source po-larization information can provide improved performance over the case of ignoring the available polarization information.Although direct es-timation of the DOA and range parameters can be performed in a com-putationally attractive manner using the methods of[10]–[12],[17], they need to exploit the symmetric structure of the sensor position co-ordinate system.As a result,the effective aperture of array is reduced by half.In order to enhance the estimation performance and increase the resolution accuracy particularly for closely-spaced sources,more sensors and larger array aperture are required.This implies the need of more complex system hardware and increased computation burden. The goal of this paper is to reduce the loss of the array aperture in conventional ESPRIT-like methods for localization of near-field sources,and then obtain the performance improvement of resolving closely spaced signals with a small number of sensors.By using the cumulant-based matrices instead of those used in the conventional ESPRIT-like methods[17],a uniform linear array with N dual-polar-ization sensors can be used to resolve DOAs of up to(N01)signals, which is twice the maximum number of DOAs that can be estimated by several available methods[10]–[12],[17].In fact,this paper can also be regarded as an extension of the least squares-virtual ESPRIT algorithm(LS-VESPA)proposed in[19]to the problem of near-field source localization.This paper is organized as follows.Section II describes the data model of near-field source localization with a polarization sensi-tive array and the problem formulation.Section III shows how the LS-VESPA can be utilized to estimate the two dimensional parame-ters of near-field sources.Finally,simulation results are provided in Section IV,followed by a conclusion in Section V.II.P ROBLEM F ORMULATIONConsider P near-field narrow-band sources impinging on a uniform linear array of N dual-polarization sensors with inter-element spacing d.The array configuration is shown in Fig.1,where all the sensors, namely,01;0;...;N02,lie on the y-axis.The pair of variables ( i;r i)denotes the DOA and range of source i at the reference sensor0. Given a transverse electromagnetic(TEM)wave propagating into the array,we consider the polarization ellipse produced by its electric field as the incoming wave is viewed from the coordinate origin. Suppose the electricfield has transverse components~E=E~ +E~ (1)where E is the horizontal component and E is the vertical compo-nent,and~ and~ are the spherical unit vectors along the azimuth and elevation angles and ,respectively.For simplicity,it is assumed that the source signal is in the y0z plane perpendicular to that of the array which is located in the x0y plane.Then, =90 ,~ =0~x and~E=0E~x+E ~ =0E ~x+E cos( )~y0E sin( )~z(2)Fig.1.Uniformly spaced linear array configuration.with~x,~y and~z representing the unit vectors along the x,y and z direc-tions,respectively.Alternatively,the polarized signal can be describedasEE=E0cos( )E0sin( )ej(3)where and denote the magnitude ratio and the phase between thetwo polarization components,and E0represents the signal amplitudewhich is an arbitrary nonzero complex constant.With the use of(3),(2)can be written as~E=E0(0cos( )~x+cos( )sin( )e j ~y0sin( )sin( )e j ~z):(4)The signal component in the~z direction is eliminated using the specificorientation of the cross-polarized array of Fig.1.Apparently,the valueof in(4)varies at each of the N sensors.It is straightforward to showthat the DOA of the i th source signal at sensor m,denoted by mi,ismi=sin01r i sin( i)0mdr2i+md02r i md sin( i):(5)The received signals at sensor m for polarization x and y,denotedby u[x]m(t)and u[y]m(t),can be approximated as[17]u[x]m(t)=0Pi=1s i(t)cos( i)e j(!m+ m)+n[x]m(t)andu[y]m(t)=Pi=1s i(t)cos( mi)sin( i)e j e j(!m+ m)+n[y]m(t)m=01;0;1;...;N02(6)where n[l]m(t);l=x;y,is the noise component for polarization l atthe m th sensor and s i is the i th source signal.The parameters!i andi are functions of the azimuth angle i and range r i of the i th source,and they are related as!i=02d sin( i)and i= d2r icos2( i)(7)where denotes the wavelength of the source wavefronts.The task isto estimate the parameters f 1;...; P;r1;...;r P g of the P sourcesfrom the received array data f u l01(t);...;u l N02(t)g;l=x;y.For unique parameter estimation,we have made the followingassumptions.(A1)The P sources f s1(t);...;s P(t)g are assumed to be zeromean,statistically independent of each other and have nonzerofourth-order cumulants,whereas the additive noise componentsTABLE IC OMPARISON OFD IFFERENT A LGORITHMS FOR N DOA S ESTIMATIONRemark:the proposed method for estimation of N signal sources needs only N +1sensors,but other methods without 2D search computation need a minimum of 2N sensors.n [x ]m (t )and n [y ]m (t )are zero mean,Gaussian distributed and inde-pendent of the source signals.(A2)The inter-element spacing between two adjacent dipole pairs d satis fies d =4to avoid ambiguity problem of angle estima-tion.It is noteworthy that in [10],[11],the use of cumulants to linearize the quadratic phase in (6)renders the near-field sources to be equivalent to multiple far-field sources observed with a vir-tual array of sensors spaced 2d apart.As a result,(A2)is required so that the effective sensor spacing is again =2as dictated by the spatial Nyquist criterion.(A3)The number of required sensors is N >P ,whose minimum is around half of those in [10],[12],[17].Table I shows a require-ment comparison of different DOA estimation algorithms.In practice,there is mutual coupling between the array elements.Since effective methods have already been introduced to compensate the coupling effect in the ESPRIT direction finding algorithm [20],[21],we can employ them to pre-process the received array data or for pre-calibration.As a result,we assume that the mutual coupling effect has been removed in advance.Furthermore,both the sensor position errors as well as gain and phase errors of all sensors are assumed to be negligible.From (6),the array outputs can be written in matrix form asu [l ](t )=A [l ]s [l ](t )+n [l ](t );l =x;y (8)whereu [l ](t )=[u [l ]01u [l ]u [l ]1111u [l ]N 02]Ts [x ](t )=0[s 1(t )cos( 1);111s P (t )cos( P )]T s [y ](t )=[s 1(t )sin( 1)e j ;111s P (t )sin( P )ej ]Tandn [l ]=[n [l ]01n [l ]111n [l ]N 02]T ;l =x;ywhere T denotes transpose.The columns of the polarization-dependent N 2P steering matrices A [x ]and A [y ]area [x ]i ( i ;r i )=[e j (01)!+j (01)1e j (!+ )111e j (N 02)!+j (N 02) ]TA [x ]=[a 1;...;a P ]a [y ]i ( i ;r i )=[e j (01)!+j (01)cos( 01i )cos( 0i );...;e j (N 02)!+j (N 02)cos( (N 02)i )]TandA [y ]=[a [y ]1;...;a [y ]P ]:Note that the source polarization appears in both s [l ](t )and A [y ].III.T HE P ROPOSED A LGORITHMDue to the quadratic dependence of signal phase on sensor loca-tion in (6),far-field source localization methods cannot be directly ap-plied to the case of near-field sources.Our key idea is to explore the possibility to reduce the polynomial order of the exponent in (6),so that existing algorithms based on far-field assumption can be utilized.Since second-order correlations have only one lag,it is not possible to achieve the polynomial order reduction.On the other hand,cumulants with multiple lags can provide the desired extra degrees of freedom.In this work,cumulant matrices generated from (9)will be used for the development of the near-field source localization algorithm.Since the available dual-polarization is exploited,it is expected that the de-veloped algorithm will yield better estimation performance than those without utilizing it.We first de fine the fourth-order cumulant of the complexmeasurements of f u [l ]0(t );u [l ]30(t );u [l ]k (t );u [l ]3h (t )g ,where “3”represents the complex conjugate,which is denoted as cum (u [l ]0(t );u [l ]30(t );u [l ]k (t );u [l ]3h (t )).From (6)and the cumulant proper-ties in [18],it follows that:cum(u [l ]0(t );u [l ]30(t );u [l ]k (t );u [l ]3h (t ))=Pi =1c 4;s e j (k 0h )!+j (k 0h )(9)where c [l ]4;s ,i =1;2;...;P ,denotes the kurtosis of the i th signal source for polarization l and is de fined asc [l ]4;s =cum f s 3[l ]i (t );s [l ]i (t );s 3[l ]i (t );s [l ]i (t )g =E fj s [l ]i (t )j 4g (10)where E denotes the expectation operator and s [l ]i (t )is the i th element in s [l ](t ).According to the independence of the source signals in (A1),we havecum(s [l ]k (t );s [l ]3k (t );s [l ]k (t );s [l ]3k (t ))=c 4;s ;if k 1=k 2=k 3=k 40;otherwise.(11)A.Extended LS-VESPA DerivationIn order to obtain the required rotational matrix in our proposed algo-rithm,we assign the sensor m =0as the phase reference point which is different from the center-symmetric array requirement in [17].Com-pared to the ESPRIT-like method [17],three constant guiding sensors,namely,01,0and 1,are exploited to construct the required cumulant matrices in the LS-VESPA.For k;h =01;...;N 02,the auto-polarized cumulant matrix is obtained asC [ll ]cum(u [l ]0(t );u [l ]30(t );u [l ](t );u [l ]H (t ))=A [l ]C [ll ]4s A [l ]H ;l =x;y:(12)Using (11)and different polarizations,we get the cross-polarized and auto-polarized kurtosis of the k th signalC [xx ]4s =PC 4s P C [xy ]4s =PC 4s Q and C [yy ]4s =QC 4s Q (13)where P =diag(cos 2( 1);...;cos 2( N )),Q =diag(sin 2( 1);...;sin 2( N ))and C 4s =diag(c 4s ;...;c 4s ).Similarly,with the use of different sensor lags,we construct the fol-lowing cumulant matrices C [ll ]1and C [ll ]2,l =x;yC [ll ]1cum(u [l ]0(t );u [l ]301(t );u [l ](t );u [l ]H (t ))=A [l ]81C [ll ]4s A [l ]H(14)andC [ll ]2cum(u [l ]1(t );u [l ]301(t );u [l ](t );u [l ]H(t ))=A [l ]82C [ll ]4s A [l ]H (15)where 81=diag(ej (!0 );...;e j (!0)),82=diag (ej 2!;...;e j 2!)and H stands for Hermitian transposition.We further de fine the following cross-polarized cumulant matrices:C [lq ]0cum(u [l ]0(t );u [q ]30(t );u [l ](t );u [q ]H (t ))=A [l ]C [lq ]4s A [q ]H(16)C [lq ]1cum(u [l ]0(t );u [q ]301(t );u [l ](t );u [q ]H (t ))=A [l ]81C [lq ]4s A [q ]H(17)andC [lq ]2cum(u [l ]1(t );u [q ]301(t );u [l ](t );u [q ]H (t ))=A [l ]82C [lq ]4s A [q ]H :(18)The first two elements in C [lq ]0;C [lq ]1,and C [lq ]2;l;q=x;y ,namely,u [l ]01;u [l ]0,and u [l ]1,are guiding sensors for constructing C [lq ]0;C [lq ]1,and C [lq ]2,respectively.The sensor m =0is set to be the phase ref-erence point in our method while the phase reference point must lo-cate at the symmetry center of array in [10],[12],[17].We exploitef ficiently the symmetry of sensor pair f u [l ]01;u [l ]1g ,l =x;y ,to con-struct the cumulant matrix C [lq ]2and then yield the rotational matrix 82which is a function of f !i g only.This also suggests the importantusage of symmetry of sensor pair f u [l ]01;u [l ]1g ,l =x;y ,is to eliminate the quadratic phase i of the signal model of (6)by cumulant com-putation.Assuming that the steering matrix A [l ],l =x;y ,and C [lq ]s ,l;q =x;y ,are of full rank,(12)–(18)satisfy all the requirements of the LS-VESPA .Combining the cumulant matrices C [lq ]0;C [lq ]1,and C [lq ]2;l;q =x;y ,we form four 3N 2N matricesC [lq ]c=C [lq ]C [lq ]1C [lq ]2;l;q =x;y:(19)Now applying the LS-VESPA method and we easily obtain the dual-polarized matrix C=C [xx ]c C [xy ]c C [yx ]cC [yy ]c=~A [x ]~A[y]C 4s [A [x ]P A [y ]Q ]H (20)where ~A[x ]=A [x ]PA [x ]P 81A [x ]P 82and~A[y ]=A [y ]QA [y ]Q 81A [y ]Q 82:(21)From (20),it is evident that the polarization diversity doubles the space dimension of the conventional problem formulation without polariza-tion information.Using the idea of the ESPRIT algorithm,the signal subspace E s of the matrix C can be obtained by the P eigenvectors of the cumulant matrix C corresponding to the P nonzero eigenvaluesE s =f e 1;...;e P g=(E [x ]0)T (E [x ]1)T (E [x ]2)T (E [y ]0)T (E [y ]1)T (E [y ]2)TT=[(~A [x ])T (~A[y ])T ]T F (22)where F P 2P is an invertible matrix.Combining the de finitions of ~A[x ]and ~A [y ]and using the rotational invariance of subspace,we obtain[(E [x ]1)T(E [y ]1)T ]T =[(E [x ]0)T(E [y ]0)T ]T 91(23)and[(E [x ]2)T(E [y ]2)T ]T =[(E [x ]0)T(E [y ]0)T ]T 92:(24)Furthermore,91and 92can be computed by using least-squares91=([(E [x ]0)T (E [y ]0)T ]T )#[(E [x ]1)T (E [y ]1)T ]T and92=([(E [x ]0)T(E [y ]0)T ]T )#[(E [x ]2)T(E [y ]2)T ]T(25)where #denotes the pseudo-inverse of a matrix.According to (21)and (22),we have 91=F 01181F 1and92=F 01282F 2(26)where the columns of F 1and F 2are the eigenvectors of 91and 92,respectively.Hence the eigenvalues of 91and 92give the estimates of the diagonal elements of 81and 82,respectively.Since the independent eigendecompositions of 91and 92lead to ar-bitrary ordering of the diagonal elements in 81and 82,we first need to pair the elements of the two sets of parameters f !i 0 i g ;f 2!i g .For-tunately,the eigenvalues of 91and 92correspond to the same eigen-vector of F in (22),which can then be used to restore the correct pa-rameter pairs.In fact,pairing of 81and 82is equivalent to pairing of the eigen-vectors of 91and 92.Here we repeat the same pairing procedure of Liu and Mendel in [19].The procedure is based on projecting the columns of F 1onto eigenspaces of 92.Let f 1k ,k =1;2;...;P ,be the k -th column of F 1,then each entry in the complex projectionrow vector f H1k F 2represents the eigenspaces will have their magni-tudes less than unity since we are in the complex domain.In the pres-ence of noise,we pick f 2l ,l 2f 1;2;...;P g ,such that the magni-tude of f H 1k f 2l is closest to unity.Next,we form the eigenvalue pair f 81(k;k );82(l;l )g ,k;l =1;2;...;P ,where their associated eigen-vectors are f 1k and f 2l from F 1and F 2,respectively.From each pair of (^!i ;^ i ),i =1;2;...;P ,the DOA and range parameters are computed as^i =sin 010 ^!i2d(27)and^r i = d 2cos 2(^i ) ^i :(28)Fig.2.The RMSE of estimated DOA for source 1versus input SNR.The pa-rameters of two sources are (40;5 ;20;3:5 ).There are four sensors and 1000snapshots areused.Fig.3.The RMSE of estimated DOA for source 2versus input SNR.The pa-rameters of two sources are (40;5 ;20;3:5 ).There are four sensors and 1000snapshots are used.The procedure of our proposed algorithm is summarized as follows:•ComputeC [lq ]0;C [lq ]1,andC [lq ]2,l;q =x;y ,de fined in (12)–(18);•Perform singular value decomposition (SVD)of C to estimate the number of incident signals P using the well-known minimum description length (MDL)criterion [22]and then obtain the E s in (22);•Compute the 91and 92using (25).•Eigendecompose 91and 92to obtain 81;F 1,82,and F 2;•Align 81(i;i )and 82(i;i );i =1;...;P and obtain the estimates of !i and i ;•Compute ^ i and ^r i ;i =1;2;...;P using (27)and (28).IV .S IMULATION R ESULTSTo verify the performance of the proposed method,a set of com-puter simulations is carried out.We consider a uniform lineararrayFig.4.The RMSE of estimated range for source 1versus input SNR.The pa-rameters of two sources are (40;5 ;20;3:5 ).There are four sensors and 1000snapshots areused.Fig.5.The RMSE of estimated range for source 2versus input SNR.The pa-rameters of two sources are (40;5 ;20;3:5 ).There are four sensors and 1000snapshots are used.consisting of several crossed dipoles with the inter-spacing d = =4.The reference sensor is sensor 0.Two equal power uncorrelated TEM waves with non-Gaussian distribution are impinging on this array and are modelled as e j ,where the phases t are uniformly distributed in the interval [0;2 ].The sensor noise is additive Gaussian process.The estimation performance is measured by the root mean square error (RMSE).The RMSE of range parameter is normalized by the signal wavelength .The polarization parameters ( ; )of the two sources are (10 ;0 )and (80 ;0 ).In the first experiment,the first source is located at 1=40 with a range of r 1=5 while the second source is located at 2=20 with a range of r 2=3:5 .The number of sensors is N =4and the number of samples at each sensor is T =1000.All provided results are aver-ages of 100independent runs.The results for range and DOA estimates of the two sources are shown in Figs.2–5.For comparison,the results using the ESPRIT-like algorithm [17]are also shown.Figs.2and 3show that the proposed method outperforms the ESPRIT algorithm inFig.6.The RMSE of estimated DOA for source 1plotted as a function of the DOA of source 2.The DOA of source 1is fixed at 50and there are four sensors.The ranges of two sources are (5 ;0:5 ).The input SNR is 5dB and 200snapshots areused.Fig.7.The RMSE of estimated DOA for source 2plotted as a function of the DOA of source 2.The DOA of source 1is fixed at 50and there are four sensors.The ranges of two sources are (5 ;0:5 ).The input SNR is 5dB and 200snapshots are used.DOA estimation for smaller signal-to-noise ratio (SNR)condition al-though they have almost identical performance at higher SNRs.While from Figs.4and 5,we observe that the proposed scheme is superior to [17]for all SNRs in range estimation.It is also seen that the RMSE of the range estimate for the second source,which is closer to the array,is smaller than that of the first source.These phenomena agree with the theoretical analysis in [13],which indicates that the standard deviation of range estimate for the source closer to the array is smaller than that of the source far away from it while the standard deviations of DOA estimates are similar for all sources.In the second experiment,the performance in angle resolving capa-bility of the proposed method is compared with that of the ESPRIT-like method.The DOA of the first source is fixed at 50 and we vary the DOA of the second source.The ranges of the first and second sources are 5 and 0:5 ,respectively.The input SNR of the two sources isset Fig.8.The RMSE of estimated DOA for source 1versus input snapshots.The parameters of two sources are (40;5 ;20;3:5 ).There are four sensors and SNR =0dB.Fig.9.The RMSE of estimated DOA for source 2versus input snapshots.The parameters of two sources are (40;5 ;20;3:5 ).There are four sensors and SNR =0dB .to be SNR =5dB and 200samples are taken at each sensor.The RMSEs of the DOA estimates are shown in Figs.6and 7and we can see the superiority of the proposed algorithm for all cases.In the third experiment,the two sources have the DOA and range parameters as in the first experiment and we vary the number of snap-shots used for estimation.The input SNRs of the two sources are fixed at SNR =0dB .The RMSEs of the DOA estimates are shown in Figs.8and 9and the superiority of the proposed algorithm for all cases is again observed.It is because the effective aperture size of the pro-posed method is much larger than that in the ESPRIT-like method.Finally,Figs.10and 11show that the proposed algorithm can resolve two sources with identical DOA,namely, 1= 2=20 ,or range,namely,r 1=r 2=0:5 .It is noteworthy that the number of sensors N =3is less than 2P with P =2and thus the ESPRIT-like method cannot be employed in this test.。