On the In?uence of the Power Pro?le on Diversity Combining
Schemes
D.V.Djonin and V.K.Bhargava,Fellow,IEEE
Department of Electrical and Computer Engineering
University of Victoria
Victoria,B.C.,Canada V8W3P6
Tel:+12507216043,Fax:+12507216048,
Email:bhargava,ddjonin@ece.uvic.ca
Abstract
Index Terms—Diversity Combining,Order Statistics,Majorizations,Schur convex functions
Abstract The usage of multichannel receivers that are followed by diversity combining can sig-ni?cantly improve the performance of wireless communications links.In this paper we investigate in some detail three popular techniques for diversity combining,namely maximal ratio combining (MRC),equal gain combining(EGC)and selection combining(SC).The main goal is to investi-gate under which circumstances it can be guaranteed that a certain technique does indeed decrease the probability of error of a multichannel receiver.The analyzed fading model is quite general with the only assumption that fading gains are scaled exchangeable random variables.The crucial mathematical tool used to produce the results of this paper is the powerful theory of stochastic majorization.Among other results,it was shown that the average bit error probability of the MRC receiver with equally distributed average powers always decreases with the addition of a new di-versity branch if the total power is?xed.
I.I NTRODUCTION
The performance analysis of digital communication systems in fading channels has been attract-ing attention of the researchers for a long time[1],[2].In recent years,this area has received a renewed interest due to the appearance of the so-called uni?ed approach to the analysis of fading channels[3],[4],[5].This approach relies on the usage of the moment generating function for representation of fading distribution and its main contribution is that it simpli?es the calculation of the basic performance measures of communication systems in fading channels.This theory can produce closed form results for different fading distributions,different modulation formats,as well as different receiver structures.
It is known that the usage of multichannel receivers followed by certain diversity combining technique in fading channels can signi?cantly improve the performance of the system.The usage of diversity combining techniques is of interest even more in the emerging broadband communi-cation systems(for example Ultra-wide band systems[6]and[7])where the number of diversity branches can be signi?cant due to the strong multipath effects.The diversity combining basically relies on the reception of the replicas of the same information distorted by independent(or near independent)fading paths.The general concepts of diversity combining applies equally to space, polarization,frequency and time diversity.
The results of this paper are intended to complement the uni?ed approach[3],[4],[5]for the analysis of the performance of multichannel receivers in generalized fading channels.The fun-damental relations and inequalities presented in this paper can help a system designer compare performances of two fading channels with the same fading statistics but different power delay pro?les.These results can instruct the system designer under which conditions adding of one or more diversity branches will improve the performance of a diversity combining system.Further-more,this paper gives asymptotic analysis(as the number of diversity branches goes to in?nity)of different diversity combining schemes.
The inequalities derived in this paper rely on the powerful theory of stochastic majorization[8],[9],
[10],[11]and[12].This theory stems from the extension of the vector majorization to certain stochastic applications and was developed initially primarily having in mind the reliability theory. However,as will be shown in the following material,these results can be easily applied to produce some interesting inequalities regarding performances of diversity combining systems. Previously,the majorization theory have found its application in diverse engineering?elds.In particular,the applications of majorization theory have been reported in solving the task assign-ment problems in computer science[13],queuing algorithms[14],?lter design[15]as well as optimal sequence allocation for CDMA systems[16].1
Throughout the paper we discuss three basic performance measures of receivers in fading chan-nels[3]:the signal to noise ratio at the receiver,bit error rate of the analyzed scheme and the outage probability.In the section on maximal ratio combining we also discuss the capacity as a possible performance measure.We will denote with upper case letters the random variables while the lower case letters are reserved for sample values.For example if is a discrete random variable with distribution,we have Prob.
The multichannel receiver with diversity branches and a general diversity combining scheme is shown in Figure1.We denote with normalized random amplitude channel gains while
are normalized random power channel gains.For simplicity it is assumed that E E. The random fading gain at the receiver is assumed to be equal to and the received power in-th branch is for a radiated power.Vector of average received powers corresponds to the power delay pro?le,while g will be called gain pro?le.Note that is the average value of fading gains.Therefore the fading gain of the-th diversity branch is split into the varying random part()and?xed multiplicative part().The model of the-th diversity branch channel is shown in Figure2for easy reference.
Let the total average received power be equal to.Then the random signal to noise ratio of-th diversity branch is given with where is the ratio of During the revision of this paper,the authors became aware of an application of the majorization theory to the performance analysis of maximal ratio combining receiver in correlated fading channels[17].
the symbol energy per noise spectral density of a certain diversity branch.We will assume that noise spectral densities of all branches are equal but this condition can also be easily relaxed.It is assumed that random delays as well as phases(for coherent reception)are perfectly estimated in the receiver.
Several results in this paper are applicable when channel fading gains are so-called exchangeable random variables.The exchangeable random variables are de?ned as:
De?nition1:Random variables are called exchangeable random variables if the distribution of does not depend on the permutation.
This de?nition can be interpreted such that the joint distribution of is not depen-dent on the permutation of its arguments.An obvious example of exchangeable random variables are identically and independently distributed(i.i.d.)random variables.However,the de?nition of exchangeable random variables is more general and includes other different classes of mul-tivariate distributions such as multivariate normal distribution with a common mean,a common variance,and common non-negative correlation coef?cient,exchangeable gamma and multivariate exchangeable exponential distribution[18].The reader is referred to[12],Section13for detailed list of exchangeable multivariate distributions.
Also,the class of exchangeable random variables is equivalent to the class of so-called positively dependent by mixture random variables(see[19])that can be de?ned as
x(1) where is a family of indexed univariate distributions.
In the subsequent discussion,the notion of exchangeable fading gains means that multivariate distribution of is exchangeable,or alternatively formulated that normalized received powers are exchangeable.In case of EGC we will consider that are exchangeable. The exchangeable fading model is used for the discussion on bit error probability of MRC and EGC diversity schemes.We note that the results on outage probabilities are however presented only for independent fading gains with Rayleigh(EGC)and exponential distribution(MRC).However
these results might also be extended for a more general class of distributions.
The outline of the paper is as follows.Section II introduces mathematical concepts of the theory of stochastic majorization that will be used in course of the paper.Section III gives results on the probability of error and outage probability of the MRC,EGC and SC diversity systems.
II.M ATHEMATICAL P RELIMINARIES
The results presented in this paper follow from the theory of majorization and its stochastic applications.Considering that the average reader of this journal might not be familiar with the theory of majorization we here review the notation and the most important de?nitions of this theory. The following de?nitions are of crucial interest in proving the results of this paper.
De?nition2:For any vector x,let x denote the non-increasing rearrangement of the vector x,i.e.where is satis?ed.
Now we can introduce the de?nition of vector majorization that will allow us to compare the performances of diversity combining schemes with different power delay pro?les.
De?nition3:For any x y,it is said that y majorizes x,or x y if
(2)
An important example of majorization between vectors of length is the following
(3) Obviously,the previous de?nition of majorization applies only to vectors that have equal sums of all elements.This condition can be relaxed and the following de?nition introduces the so-called “weak majorization”.
De?nition4:For some x,y,
x y if(4)
and
x y if(5) We will give two examples of weak majorization that will be referred to later in the text.Simi-larly to(3),it can be stated that
(6) if and only if
for certain vectors x and y.
The de?nition of the decreasing vector function is an obvious extension.The following result (for the proof see3.A.8.in[8])extends the applicability of the Schur convex functions on vectors that are only weakly majorized.
Theorem1:A real-valued function de?ned on a set satis?es
x y on x y(11) if and only if is increasing and Schur convex on.Similarly,satis?es
x y on x y(12) if and only if is decreasing and Schur convex on.
III.D IVERSITY C OMBINING
The results on the statistical properties of diversity combining schemes presented in this section rely on the theory of stochastic majorization.The following two general results of this theory can be applied to several different cases.
Proposition1:If are exchangeable random variables and is a sym-metric convex function,then function de?ned as
E(13)
is symmetric and convex.Therefore,is Schur convex and a a implies a a.
For the proof of this Proposition see11.B.2.in[8].This result can be readily extended such that its scope covers weakly majorized vectors(11.B.5.in[8]).
Proposition2:Let be exchangeable random variables and functions
and satisfy the following conditions:(a)is convex and increasing while is symmetric,convex and increasing;(b)is convex and decreasing while is symmetric,convex and increasing;then function E is(a)symmetric, convex and increasing;(b)symmetric,convex and decreasing,respectively.
This Proposition can be combined with Theorem1to produce inequalities for weakly majorized vectors.
Up to now we have presented a very powerful tool that can be used to facilitate comparison be-tween performances of different diversity combining schemes with different power delay pro?les. There are,however,two basic limitations of this approach.First,the majorization between two vectors is a partial ordering i.e.it is not possible to compare any two vectors in this manner.We claim that this limitation is not a serious one since many cases of practical interest can be analyzed in this manner.Second limitation is that the results of the next section are applicable to situations where joint distribution of normalized channel fading gains is exchangeable:the case that again models some cases of practical interest.
A.Maximal Ratio Combining
Maximal ratio combining uses optimal weighting of the received diversity signal in order to maximize its output signal to noise ratio.The performance of the maximal ratio combining scheme depends on the signal to noise ratio at the output of this combiner.This signal to noise ratio can be expressed as(see for example[3])
where is a realization of the exchangeable random variables as discussed in Section II.
Now,bit error probabilities of several different modulation schemes with maximal ratio com-bining can be expressed using the same general form
for certain univariate error function that is independent of the number of diversity branches. The long term average error probability can be expressed as
E(16)
It should be noted here that function is convex for several different modulation formats including binary phase shift keying(BPSK),QAM,M-PSK,coherent FSK and Minimum Shift Key(MSK) in additive Gaussian noise channels.
A.1Average BER of BPSK Modulation
We discuss here only the case of BPSK modulation but the discussion can be applied also for other mentioned modulation formats.For BPSK modulation,we have[20]
)and coherent BFSK with minimum correlation().It is easy to see that is a convex function since its derivative with respect to,
An interesting consequence of the previous equation can be produced when majorization exam-ple(3)is used and constant is interpreted as the?xed normalized total power through all diversity branches.Then,if powers are equally distributed through all the diversity branches,the average probability of error is decreasing with the number of branches.Furthermore,in case of independent identically distributed fading gains with probability density function,asymptot-ically,as increases to in?nity,the average bit error probability with equal distribution of powers in diversity branches is non-increasing and converges to
E(20)
where the?rst equality follows from the weak law of large numbers.Note that E E. The above discussion can be extended to the comparison of two power delay pro?les that do not have equal total powers.In this case we resort to the de?nition of the weak majorization and apply Proposition2on the function de?ned in(18).The function that would correspond to the statement of the Proposition2would be which is an increasing and convex function. Therefore,case(a)of this Proposition is applicable and we conclude that function is convex, symmetric and increasing or alternatively,using the Theorem1
g g g g(21) This analysis carries on to different modulation formats(like QAM,MPSK,FSK...)whenever bit error probability can be expressed as a convex function of.
A.2Outage Probability
The long term average bit error probability analysis is not applicable in all cases.For example, if fading is very slow or when there are restriction on instantenous bit error probabilities,the knowledge of average bit error probability is not useful.In these cases,the appropriate measure is outage probability de?ned as
g Prob Prob
for a certain threshold.
The results in this section are valid for independent Rayleigh distributed fading gains.We start with the following Proposition that follows from[11]and[8].
Proposition3:Let be independent random variables with the same exponential distribution
Prob(23) Let p where for all.Also denote with p the ordered(from the weakest to the strongest)version of the random vector p.Then for certain vectors
(24)
it follows that
Prob p Prob p(25)
for any increasing function and vectors p and p. Proof:
The proof follows by application of12.H.1.a and the generalization of stochastic ordering of section17.A(Equation(3’))in[8].
In order to apply this Proposition to the analysis of the outage probability given in(22),increas-ing function has to be the function that sums all its arguments and multiplies the result by. Therefore,applying directly Proposition3,we can state that
(26)
for certain gain pro?les g and g.
The outage probability inequality of this section is applicable for independently and expo-nentially distributed power channel gains but this analysis can also be extended to distribution functions that fall into the category of so-called proportianaly hazard function(see for example 12.H.2.[8]).These details will not be analyzed any further in this section.
Regarding the behavior of outage probability of the MRC with equal power distribution in case of increase in the number of branches,we note the https://www.doczj.com/doc/615149434.html,ly,we compare a system with branches and power delay pro?le
p(27)
and system with branches and power delay pro?le
p(28)
where fading gains in two cases are g p and g p.Now,according to(26)and (5)the outage probability is guaranteed to decrease with the increase in the number of branches if
or
(30)
and where ergodic capacity for fast changing fading channels is de?ned as g E
E
of stochastic majorization.Noting that function
can be expressed as E.Now,in order to show that stochastic majorization results of Section III.A carry over to the case of equal gain combining,it is necessary
to explore if function
(34)
is convex for certain error function.Note that if is convex,then function as de?ned in (33)is also convex.In the case of BPSK/BFSK modulation
(35) This function is always convex since its derivative is always increasing.Note that function as de?ned in(33)is also increasing function of with respect to
the De?nition6.
Therefore,using the same argumentation that was previously used in Section III.A.(namely Proposition2and Theorem1),the most general conclusion on the behavior of the average bit error probability of the equal gain combiner with diversity branches is that
(36)
for two modi?ed gain pro?les de?ned as and. It is straightforward to show that these results also hold for M-PSK and M-AM signals.
Now we compare branch EGC combiner having equal gain pro?le elements with
branch EGC combiner having equal gain pro?le.In that case condition(36)that guarantees
the decrease in the probability of error with the addition of a diversity branch is given with
(37) which satis?ed if and only if
This condition is satis?ed if the total power is?xed i.e.when
(39)
which follows from the weak law of large numbers.Here E.To obtain better insight in the difference of asymptotic performance of the MRC and the EGC we use the example of Rayleigh fading with.In this case the average asymptotic BER of MRC is while for EGC it is
(40) where
for orthogonal non-coherently detected FSK,and for binary DPSK.The total SNR is given as the sum of individual branch signal to noise ratios,similarly to the expression for total SNR of MRC receiver(14).
It has been observed that is convex function in for every integer valued .This observation is based on numerical calculation of the second derivative of(40)
and showing that it is positive for.Maximal number of diversity branches of explored in our numerical observations should be suf?cient for most practical applications.In ad-dition we here state a conjecture that function(40)is convex for any integer,but no formal proof is available at this time.
If function(40)is convex it is also convex and symmetric in the individual signal to noise ratios.We note here that(40)is also increasing in the individual signal to noise ratios. Therefore,the conclusions of the Section III.A.1carry over to the case of non-coherent EGC.The majorization between power delay pro?les implies the relationship between average bit-error rates of the non-coherent receiver with branches i.e.
g g g g(42)
where g is the average bit-error probability of the branch non-coherent receiver with power delay pro?le g.The previous result is also valid only for fading gains of individual branches having an exchangeable joint distribution.
Note that due to the postdetection performed in the non-coherent EGC combiner,(42)allows only the comparison of the average bit error probabilities of the receiver having?xed number of diversity branches with different diversity pro?les.In order to compare receivers with different numbers of diversity branches we have to use different expressions for the probability of error. Note that with the increase of the number of diversity branches and the same total SNR,the bit error probability of non-coherent EGC can increase(for smaller values of total SNR)and the receiver can suffer from a combining loss,as was noted in([20],Section12).
B.1Outage Probability
As is the case with the discussion on outage probability of the MRC,the outage probability of coherent EGC will be discussed only in the case of independent Rayleigh distributed amplitude fading gains.We?rst note that Rayleigh distribution falls into the class of proportionally hazard distributions(see Section12.H.in[8])and that it is equivalent to the Weibull distribution with
parameter.The following Proposition that follows from12.H.4.in[8]will be needed to characterize the behavior of the outage probability of coherent EGC with Rayleigh distributed fading gains.
Proposition4:Let be independent identically distributed random variables with Weibull distribution given(for some)by
Prob(43) If then
Prob Prob(44)
for certain univariate increasing function.
Proof:The proposition is straightforward extension of12.H.4.in[8]to weak majorization. Now,the previous Proposition can be directly applied to the outage probability of the EGC with Rayleigh distributed amplitude fading gains.By comparing the expression for the signal to noise ratio at the output of the EGC(32)with(44)and using,we can state that for branch coherent EGC diversity scheme
(45)
for certain power delay pro?les and.The previous equation follows from Proposition4 having for and.Note,that the same conclusion was derived for the outage probability of the MRC diversity scheme.
C.Selection Combining
Selection combining is less complex than the other two linear diversity combining schemes MRC and EGC,since it processes only one of the diversity branches.In selection combining approach,the receiver processes only the signal with the largest signal to noise ratio,or in case of equal noise powers in branches,the signal with largest received power.The signal to noise ratio at
the output of the selection combiner is then
(46)
where are considered realizations of exchangeable random variables as discussed in Section II. In this section we will be only able to produce results on the average signal to noise ratio
E.By observing that the function is convex,symmetric and increasing(see for example11.B.2.b.in[8]),and invoking Proposition2and Theorem1we can state that
g g g g(47) In the case of?xed average total received power,the previous relation implies that the increase in the number of equitably power distributed diversity branches decreases the average signal to noise ratio of the selection combiner.In fact,it can be demonstrated using the asymptotic order statistics approach(see[22],[23]and[24]),that the average signal to noise ratio converges in probability to0as the number of equal power distributed branches increases to in?nity!This fact is a consequence of the decrease in the average power per branch which is dominating the effect of the selection of the branch with the strongest power.The proof of this claim will be omitted due to its simplicity.Similarly,in the asymptotic case,the average error probability of the selection combiner converges to0.5.
If the selection combiner is used,we can not state results similar to(36)and(21)since the error function of parameters is not necessarily convex.This is due to the fact that the composition of two convex functions is always convex only if the outer function is increasing.This is obviously not true in the case of error function which are always decreasing with the increase of signal to noise ratios.Therefore we can expect that the increase in the number of equitably power distributed diversity branches for smaller number of branches can both increase and decrease the probability of error of SC.However,taking into account the asymptotic results,for large number of diversity branches,adding a new one will de?nitely increase the error probability.
C.1Outage Probability
Similar to the Section III.A.2,the outage probability of the Selection combiner is de?ned as
g Prob(48) where is de?ned with(46).Now,in order to produce comparisons similar to that of the Section III.A.2we again apply Proposition3.It is assumed that channel gains are independent and exponentially distributed.The increasing function is now chosen to be the function that returns its last argument(i.e.the maximal argument).In that case,Proposition3can be applied straightforwardly and the outage probabilities of the selection combiner also satisfy(26).
IV.C ONCLUSIONS
This paper discusses some fundamental relations that characterize the diversity combining sys-tems.For exchangeable fading gains,certain partial ordering conditions between power delay pro?les were shown to guarantee the decrease of the average bit error probability.Starting from one such relation,it was shown that bit error probability of a MRC decreases with the addition of a diversity branch for the case of?xed equally distributed total average received power.Similarly for the coherent EGC receiver,the increase in number of equal power diversity branches with?xed total power and equal per path noise spectral density decreases the bit error probability.The non-coherent EGC case is also addressed and it is shown that majorization between gain pro?les of two systems implies the relationship between bit error rates of two systems.Also,asymptotic results for large number of diversity branches on the average bit error probability of MRC,EGC and SC receivers were discussed.The majorization conditions on power delay pro?les that decrease the outage probability of the MRC and SC receivers in Rayleigh fading channels were also explored.
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一般过去式 时间状语：yesterday just now (刚刚) the day before three days ag0 a week ago in 1880 last month last year 1. I was in the classroom yesterday. I was not in the classroom yesterday. Were you in the classroom yesterday. 2. They went to see the film the day before. Did they go to see the film the day before. They did go to see the film the day before. 3. The man beat his wife yesterday. The man didn’t beat his wife yesterday. 4. I was a high student three years ago. 5. She became a teacher in 2009. 6. They began to study english a week ago 7. My mother brought a book from Canada last year. 8.My parents build a house to me four years ago . 9.He was husband ago. She was a cooker last mouth. My father was in the Xinjiang half a year ago. 10.My grandfather was a famer six years ago. 11.He burned in 1991
●I wonder if it’s because I have been at school for so long that I’ve grown so crazy about going home. ●It is because she wasn’t well that she fell far behind her classmates this semester. ●I can well remember that there was a time when I took it for granted that friends should do everything for me. ●In order to make a difference to society, they spent almost all of their spare time in raising money for the charity. ●It’s no pleasure eating at school any longer because the food is not so tasty as that at home. ●He happened to be hit by a new idea when he was walking along the riverbank. ●I wonder if I can cope with stressful situations in life independently. ●It is because I take things for granted that I make so many mistakes. ●The treasure is so rare that a growing number of people are looking for it. ●He picks on the weak mn in order that we may pay attention to him. ●It’s no pleasure being disturbed whena I settle down to my work. ●I can well remember that when I was a child, I always made mistakes on purpose for fun. ●It’s no pleasure accompany her hanging out on the street on such a rainy day. ●I can well remember that there was a time when I threw my whole self into study in order to live up to my parents’ expectation and enter my dream university. ●I can well remember that she stuck with me all the time and helped me regain my confidence during my tough time five years ago. ●It is because he makes it a priority to study that he always gets good grades. ●I wonder if we should abandon this idea because there is no point in doing so. ●I wonder if it was because I ate ice-cream that I had an upset student this morning. ●It is because she refused to die that she became incredibly successful. ●She is so considerate that many of us turn to her for comfort. ●I can well remember that once I underestimated the power of words and hurt my friend. ●He works extremely hard in order to live up to his expectations. ●I happened to see a butterfly settle on the beautiful flower. ●It’s no pleasure making fun of others. ●It was the first time in the new semester that I had burned the midnight oil to study. ●It’s no pleasure taking everything into account when you long to have the relaxing life. ●I wonder if it was because he abandoned himself to despair that he was killed in a car accident when he was driving. ●Jack is always picking on younger children in order to show off his power. ●It is because he always burns the midnight oil that he oversleeps sometimes. ●I happened to find some pictures to do with my grandfather when I was going through the drawer. ●It was because I didn’t dare look at the failure face to face that I failed again. ●I tell my friend that failure is not scary in order that she can rebound from failure. ●I throw my whole self to study in order to pass the final exam. ●It was the first time that I had made a speech in public and enjoyed the thunder of applause. ●Alice happened to be on the street when a UFO landed right in front of her. ●It was the first time that I had kept myself open and talked sincerely with my parents. ●It was a beautiful sunny day. The weather was so comfortable that I settled myself into the
高中英语~词性~句子成分~语法构成 第一章节：英语句子中的词性 1.名词：n. 名词是指事物的名称，在句子中主要作主语.宾语.表语.同位语。 2.形容词;adj. 形容词是指对名词进行修饰~限定~描述~的成份，主要作定语.表语.。形容词在汉语中是（的）.其标志是: ous. Al .ful .ive。. 3.动词：vt. 动词是指主语发出的一个动作，一般用来作谓语。 4.副词：adv. 副词是指表示动作发生的地点. 时间. 条件. 方式. 原因. 目的. 结果.伴随让步. 一般用来修饰动词. 形容词。副词在汉语中是（地）.其标志是：ly。 5.代词：pron. 代词是指用来代替名词的词，名词所能担任的作用，代词也同样.代词主要用来作主语. 宾语. 表语. 同位语。 6.介词：prep.介词是指表示动词和名次关系的词，例如：in on at of about with for to。其特征：
介词后的动词要用—ing形式。介词加代词时，代词要用宾格。例如：give up her（him）这种形式是正确的，而give up she（he）这种形式是错误的。 7.冠词：冠词是指修饰名词，表名词泛指或特指。冠词有a an the 。 8.叹词：叹词表示一种语气。例如：OH. Ya 等 9.连词：连词是指连接两个并列的成分，这两个并列的成分可以是两个词也可以是两个句子。例如：and but or so 。 10.数词：数词是指表示数量关系词，一般分为基数词和序数词 第二章节：英语句子成分 主语：动作的发出者，一般放在动词前或句首。由名词. 代词. 数词. 不定时. 动名词. 或从句充当。 谓语：指主语发出来的动作，只能由动词充当，一般紧跟在主语后面。 宾语：指动作的承受着，一般由代词. 名词. 数词. 不定时. 动名词. 或从句充当. 介词后面的成分也叫介词宾语。 定语：只对名词起限定修饰的成分，一般由形容
M A: Has the case been closed yet? B: No, the magistrate still needs to decide the outcome. magistrate n.地方行政官，地方法官，治安官 A: I am unable to read the small print in the book. B: It seems you need to magnify it. magnify vt.１．放大，扩大；２．夸大，夸张 A: That was a terrible storm. B: Indeed, but it is too early to determine the magnitude of the damage. magnitude n.１．重要性，重大；２．巨大，广大 A: A young fair maiden like you shouldn’t be single. B: That is because I am a young fair independent maiden. maiden n.少女，年轻姑娘，未婚女子 a.首次的，初次的 A: You look majestic sitting on that high chair. B: Yes, I am pretending to be the king! majestic a.雄伟的，壮丽的，庄严的，高贵的 A: Please cook me dinner now. B: Yes, your majesty, I’m at your service. majesty n.１．［Ｍ－］陛下（对帝王，王后的尊称）；２．雄伟，壮丽，庄严 A: Doctor, I traveled to Africa and I think I caught malaria. B: Did you take any medicine as a precaution? malaria n.疟疾 A: I hate you! B: Why are you so full of malice? malice n.恶意，怨恨 A: I’m afraid that the test results have come back and your lump is malignant. B: That means it’s serious, doesn’t it, doctor? malignant a.１．恶性的，致命的；２．恶意的，恶毒的 A: I’m going shopping in the mall this afternoon, want to join me? B: No, thanks, I have plans already. mall n.（由许多商店组成的）购物中心 A: That child looks very unhealthy. B: Yes, he does not have enough to eat. He is suffering from malnutrition.
意见应以事实为根据. 3 来自辞典例句 192. The bombers swooped ( down ) onthe air base. 轰炸机 突袭 空军基地. 来自辞典例句 193. He mounted their engines on a rubber base. 他把他们的发动机装在一个橡胶垫座上. 14 来自辞典例句 194. The column stands on a narrow base. 柱子竖立在狭窄的地基上. 14 来自辞典例句 195. When one stretched it, it looked like grey flakes on the carvas base. 你要是把它摊直, 看上去就象好一些灰色的粉片落在帆布底子上. 18 来自辞典例句 196. Economic growth and human well - being depend on the natural resource base that supports all living systems. 经济增长和人类的福利依赖于支持所有生命系统的自然资源. 12 1 来自辞典例句 197. The base was just a smudge onthe untouched hundred - mile coast of Manila Bay. 那基地只是马尼拉湾一百英里长安然无恙的海岸线上一个硝烟滚滚的污点. 6 来自辞典例句 198. You can't base an operation on the presumption that miracles are going to happen. 你不能把行动计划建筑在可能出现奇迹的假想基础上.
英语造句大全English sentence 在句子中，更好的记忆单词！ 1、(1)、able adj. 能 句子：We are able to live under the sea in the future. (2)、ability n. 能力 句子：Most school care for children of different abilities. (3)、enable v. 使。。。能句子：This pass enables me to travel half-price on trains. 2、(1)、accurate adj. 精确的句子：We must have the accurate calculation. (2)、accurately adv. 精确地 句子：His calculation is accurately. 3、(1)、act v. 扮演 句子：He act the interesting character. （2）、actor n. 演员 句子：He was a famous actor. (3)、actress n. 女演员 句子：She was a famous actress. (4)、active adj. 积极的 句子：He is an active boy. 4、add v. 加 句子：He adds a little sugar in the milk. 5、advantage n. 优势 句子：His advantage is fight. 6、age 年龄n. 句子：His age is 15. 7、amusing 娱人的adj. 句子：This story is amusing. 8、angry 生气的adj. 句子：He is angry. 9、America 美国n.
主语+谓语 1. 理解主谓结构 1) The students arrived. The students arrived at the park. 2) They are listening. They are listening to the music. 3) The disaster happened. 2．体会状语的位置 1) Tom always works hard. 2) Sometimes I go to the park at weekends.. 3) The girl cries very often. 4) We seldom come here. The disaster happened to the poor family. 3. 多个状语的排列次序 1) He works. 2) He works hard. 3) He always works hard. 4) He always works hard in the company. 5) He always works hard in the company recently. 6) He always works hard in the company recently because he wants to get promoted. 4. 写作常用不及物动词 1. ache My head aches. I’m aching all over. 2. agree agree with sb. about sth. agree to do sth. 3. apologize to sb. for sth. 4. appear (at the meeting, on the screen) 5. arrive at / in 6. belong to 7. chat with sb. about sth. 8. come (to …) 9. cry 10. dance 11. depend on /upon 12. die 13. fall 14. go to … 15. graduate from 16. … happen 17. laugh 18. listen to... 19. live 20. rise 21. sit 22. smile 23. swim 24. stay (at home / in a hotel) 25. work 26. wait for 汉译英： 1.昨天我去了电影院。 2.我能用英语跟外国人自由交谈。 3.晚上7点我们到达了机场。 4.暑假就要到了。 5.现在很多老人独自居住。 6.老师同意了。 7.刚才发生了一场车祸。 8.课上我们应该认真听讲。9. 我们的态度很重要。 10. 能否成功取决于你的态度。 11. 能取得多大进步取决于你付出多少努力。 12. 这个木桶能盛多少水取决于最短的一块板子的长度。
【it's time to和it's time for】 ——————这其实是一个句型,只不过后面要跟不同的东西. ——————It's time to跟的是不定式（to do）.也就是说,要跟一个动词,意思是“到做某事的时候了”.如： It's time to go home. It's time to tell him the truth. ——————It's time for 跟的是名词.也就是说,不能跟动词.如： It's time for lunch.(没必要说It's time to have lunch) It's time for class.(没必要说It's time to begin the class.) They can't wait to see you Please ask liming to study tonight. Please ask liming not to play computer games tonight. Don’t make/let me to smoke I can hear/see you dance at the stage You had better go to bed early. You had better not watch tv It’s better to go to bed early It’s best to run in the morning I am enjoy running with music. With 表伴随听音乐 I already finish studying You should keep working. You should keep on studying English Keep calm and carry on 保持冷静继续前行二战开始前英国皇家政府制造的海报名字 I have to go on studying I feel like I am flying I have to stop playing computer games and stop to go home now I forget/remember to finish my homework. I forget/remember cleaning the classroom We keep/percent/stop him from eating more chips I prefer orange to apple I prefer to walk rather than run I used to sing when I was young What’s wrong with you There have nothing to do with you I am so busy studying You are too young to na?ve I am so tired that I have to go to bed early
《The Kite Runner》追风筝的人--------------------------------美句摘抄 1.I can still see Hassan up on that tree, sunlight flickering through the leaves on his almost perfectly round face, a face like a Chinese doll chiseled from hardwood: his flat, broad nose and slanting, narrow eyes like bamboo leaves, eyes that looked, depending on the light, gold, green even sapphire 翻译：我依然能记得哈桑坐在树上的样子，阳光穿过叶子，照着他那浑圆的脸庞。他的脸很像木头刻成的中国娃娃，鼻子大而扁平，双眼眯斜如同竹叶，在不同光线下会显现出金色、绿色，甚至是宝石蓝。 E.g.: A shadow of disquiet flickering over his face. 2.Never told that the mirror, like shooting walnuts at the neighbor's dog, was always my idea. 翻译：从来不提镜子、用胡桃射狗其实都是我的鬼主意。E.g.:His secret died with him, for he never told anyone. 3.We would sit across from each other on a pair of high
一、翻译 1. The idea of consciously seeking out a special title was new to me., but not without appeal. 让我自己挑选自己最喜欢的书籍这个有意思的想法真的对我具有吸引力。 2.I was plunged into the aching tragedy of the Holocaust, the extraordinary clash of good, represented by the one decent man, and evil. 我陷入到大屠杀悲剧的痛苦之中，一个体面的人所代表的善与恶的猛烈冲击之中。 3.I was astonished by the the great power a novel could contain. I lacked the vocabulary to translate my feelings into words. 我被这部小说所包含的巨大能量感到震惊。我无法用语言来表达我的感情（心情）。 4，make sth. long to short长话短说 5.I learned that summer that reading was not the innocent(简单的) pastime(消遣) I have assumed it to be., not a breezy, instantly forgettable escape in the hammock(吊床)，( though I’ ve enjoyed many of those too ). I discovered that a book, if it arrives at the right moment, in the proper season, will change the course of all that follows. 那年夏天，我懂得了读书不是我认为的简单的娱乐消遣，也不只是躺在吊床上，一阵风吹过就忘记的消遣。我发现如果在适宜的时间、合适的季节读一本书的话，他将能改变一个人以后的人生道路。 二、词组造句 1. on purpose 特意，故意 This is especially true here, and it was ~. (这一点在这里尤其准确，并且他是故意的) 2.think up 虚构，编造，想出 She has thought up a good idea. 她想出了一个好的主意。 His story was thought up. 他的故事是编出来的。 3. in the meantime 与此同时 助记：in advance 事前in the meantime 与此同时in place 适当地... In the meantime, what can you do? 在这期间您能做什么呢？ In the meantime, we may not know how it works, but we know that it works. 在此期间，我们不知道它是如何工作的，但我们知道，它的确在发挥作用。 4.as though 好像，仿佛 It sounds as though you enjoyed Great wall. 这听起来好像你喜欢长城。 5. plunge into 使陷入 He plunged the room into darkness by switching off the light. 他把灯一关，房
The effective sentences:(improve the sentences!) 1.She hopes to spend this holiday either in Shanghai or in Suzhou. 2.Showing/to show sincerity and to keep/keeping promises are the basic requirements of a real friend. 3.I want to know the space of this house and when it was built. I want to know how big this house is and when it was built. I want to know the space of this house and the building time of the house. 4.In the past ten years,Mr.Smith has been a waiter,a tour guide,and taught English. In the past ten years,Mr.Smith has been a waiter,a tour guide,and an English teacher. 5.They are sweeping the floor wearing masks. They are sweeping the floor by wearing masks. wearing masks,They are sweeping the floor. 6.the drivers are told to drive carefully on the radio. the drivers are told on the radio to drive carefully 7.I almost spent two hours on this exercises. I spent almost two hours on this exercises. 8.Checking carefully,a serious mistake was found in the design. Checking carefully,I found a serious mistake in the design.
M1 U1 一. 把下列短语填入每个句子的空白处（注意所填短语的形式变化）： add up (to) be concerned about go through set down a series of on purpose in order to according to get along with fall in love (with) join in have got to hide away face to face 1 We’ve chatted online for some time but we have never met ___________. 2 It is nearly 11 o’clock yet he is not back. His mother ____________ him. 3 The Lius ___________ hard times before liberation. 4 ____________ get a good mark I worked very hard before the exam. 5 I think the window was broken ___________ by someone. 6 You should ___________ the language points on the blackboard. They are useful. 7 They met at Tom’s party and later on ____________ with each other. 8 You can find ____________ English reading materials in the school library. 9 I am easy to be with and _____________my classmates pretty well. 10 They __________ in a small village so that they might not be found. 11 Which of the following statements is not right ____________ the above passage? 12 It’s getting dark. I ___________ be off now. 13 More than 1,000 workers ___________ the general strike last week. 14 All her earnings _____________ about 3,000 yuan per month. 二.用以下短语造句： 1.go through 2. no longer/ not… any longer 3. on purpose 4. calm… down 5. happen to 6. set down 7. wonder if 三. 翻译： 1.曾经有段时间，我对学习丧失了兴趣。（there was a time when…） 2. 这是我第一次和她交流。（It is/was the first time that …注意时态） 3.他昨天公园里遇到的是他的一个老朋友。（强调句） 4. 他是在知道真相之后才意识到错怪女儿了。（强调句） M 1 U 2 一. 把下列短语填入每个句子的空白处（注意所填短语的形式变化）： play a …role (in) because of come up such as even if play a …part (in) 1 Dujiangyan(都江堰) is still ___________in irrigation(灌溉) today. 2 That question ___________ at yesterday’s meeting. 3 Karl Marx could speak a few foreign languages, _________Russian and English. 4 You must ask for leave first __________ you have something very important. 5 The media _________ major ________ in influencing people’s opinion s. 6 _________ years of hard work she looked like a woman in her fifties. 二.用以下短语造句： 1.make (good/full) use of 2. play a(n) important role in 3. even if 4. believe it or not 5. such as 6. because of
English sentence 1、(1)、able adj. 能 句子：We are able to live under the sea in the future. (2)、ability n. 能力 句子：Most school care for children of different abilities. (3)、enable v. 使。。。能 句子：This pass enables me to travel half-price on trains. 2、(1)、accurate adj. 精确的 句子：We must have the accurate calculation. (2)、accurately adv. 精确地 句子：His calculation is accurately. 3、(1)、act v. 扮演 句子：He act the interesting character.（2）、actor n. 演员 句子：He was a famous actor. (3)、actress n. 女演员 句子：She was a famous actress. (4)、active adj. 积极的 句子：He is an active boy. 4、add v. 加 句子：He adds a little sugar in the milk. 5、advantage n. 优势 句子：His advantage is fight. 6、age 年龄n. 句子：His age is 15. 7、amusing 娱人的adj. 句子：This story is amusing. 8、angry 生气的adj. 句子：He is angry. 9、America 美国n. 句子：He is in America. 10、appear 出现v. He appears in this place. 11. artist 艺术家n. He is an artist. 12. attract 吸引 He attracts the dog. 13. Australia 澳大利亚 He is in Australia. 14.base 基地 She is in the base now. 15.basket 篮子 His basket is nice. 16.beautiful 美丽的 She is very beautiful. 17.begin 开始 He begins writing. 18.black 黑色的 He is black. 19.bright 明亮的 His eyes are bright. 20.good 好的 He is good at basketball. 21.British 英国人 He is British. 22.building 建造物 The building is highest in this city 23.busy 忙的 He is busy now. 24.calculate 计算 He calculates this test well. 25.Canada 加拿大 He borns in Canada. 26.care 照顾 He cared she yesterday. 27.certain 无疑的 They are certain to succeed. 28.change 改变 He changes the system. 29.chemical 化学药品