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Suppression of impulsive noise in OFDM system using imperfectchannel state information

Suppression of impulsive noise in OFDM system using imperfectchannel state information
Suppression of impulsive noise in OFDM system using imperfectchannel state information

Optik 127(2016)2111–2115

Contents lists available at ScienceDirect

Optik

j o u r n a l h o m e p a g e :w w w.e l s e v i e r.d e /i j l e

o

Suppression of impulsive noise in OFDM system using imperfect channel state information

Abhishek Bansal,Amit Kumar Kohli ?

Department of Electronics and Communication Engineering,Thapar University,Patiala –147004,Punjab,India

a r t i c l e

i n f o

Article history:

Received 10April 2015

Accepted 9November 2015

Keywords:OFDM

Impulsive noise

Channel state information Noise bucket effect

a b s t r a c t

This paper presents the orthogonal frequency division multiplexing (OFDM)system working under Nakagami-m multipath fading channels,which utilizes the impulsive noise excision technique.Its per-formance is also evaluated under the imperfect channel state information (CSI)constraint.Although the impact of noise reduces due to the noise bucket effect appearing in OFDM systems with longer symbol duration,yet the impulsive noise energy spreads over OFDM subcarriers,which appears as a hazard in the demodulation and detection when the energy of impulsive noise exceeds certain threshold level.Under realistic conditions,the channel estimators cannot provide perfect/ideal channel state informa-tion.In this paper,we use the impulsive noise compensation method as a technique for the suppression of impulsive noise in the frequency-domain after OFDM demodulation and channel equalization.Under the aforementioned scenario,the simulation results are demonstrated for the performance evaluation of underlying OFDM communication system,under the Nakagami-m multipath fading channel,which also focuses on the adverse effects of imperfect CSI at the receiver,in terms of bit error rate.

?2015Elsevier GmbH.All rights reserved.

1.Introduction

In the ?eld of communication,orthogonal frequency division multiplexing (OFDM)is extensively used for the high data rate com-munication applications [1].It is an effective multicarrier digital data transmission technique.The advantage of OFDM system over the single carrier system is its robustness to multipath distortions.Mostly OFDM communication system applications are affected by the man-made noise,typically in the urban environment.Here,the man-made noises are represented by impulsive models [2].These noises could occur due to several reasons such as power lines,microwaves,heavy current switches,elevators,and circuit failure.When digital terrestrial video broadcasting (DVB-T)uses 64-QAM (quadrature amplitude modulation)in the OFDM system [3],the performance of OFDM system could seriously be affected by the impulsive interference.In OFDM communication systems,the nature,origin and prediction of noise sources are essential to develop effective techniques to alleviate bit error rate (BER)[4,5].The OFDM system,being the multicarrier modulation system,is more resistant to the effects of impulsive noise because this system has an ef?cient implementation of fast Fourier transform (FFT)as

?Corresponding author.

E-mail address:drkohli iitr@yahoo.co.in (A.K.Kohli).

compared to the single carrier system.However,its performance degrades whenever the impulsive noise energy exceeds a certain threshold level [6].A simple procedure is usually used to remove the deleterious effects of impulsive noise,which is known as blank-ing non-linearity method.This method is ef?cient and simple to implement.It is incorporated in the time-domain before OFDM demodulation [7].There is another method proposed by Zhidkov [8],which is interpreted as impulsive noise compensation method.This method is implemented in the frequency-domain after OFDM demodulation and channel equalization.In this paper,we mainly focus on impulsive noise compensation method.

The aim of our study is to analyze the performance of the impul-sive noise compensation method with channel state information (CSI)imperfections for the suppression of impulsive noise.First,we evaluate the performance of the impulsive noise compensa-tion method under the Nakagami-m multipath fading channels.The signal received at receiver is represented as

y i =a i u i +n i

where a i is the input from the OFDM system,u i is the fading chan-nel response,n i is the noise component.In the Nakagami-m fading channel,we use the square root of the squares of n zero-mean identically distributed Gaussian random variables (RVs)with fad-ing parameter m =n /2,when m is an integer.This method is also known as “brute force method”[9,10].The improvement in BER

https://www.wendangku.net/doc/5713245525.html,/10.1016/j.ijleo.2015.11.041

0030-4026/?2015Elsevier GmbH.All rights reserved.

2112 A.Bansal,A.K.Kohli/Optik127(2016)2111–2115 mainly depends on the value of m,i.e.,when m=0.5<1,the diversity

gain deteriorates by3dB as compared to the Rayleigh,but when,

the diversity gain improves by2dB.We also address the problem of

CSI imperfection[10,11]and performance evaluation of an OFDM

receiver that uses an impulsive noise compensation method[8]for

the suppression of impulsive noise.

This paper is organized as follows.In Section2,the OFDM com-

munication system and the fading channel model are introduced.

In Section3,equations for impulsive noise compensation with

imperfect CSI are derived.Simulation results are provided in Sec-

tion4.Finally,concluding remarks and future scope are given in

Section5.

2.System and channel model

In this section,we present the OFDM system model for trans-

mission as well as for reception.Fig.1shows the block scheme

of transmission system.In the OFDM system,?rst the informa-

tion bits are mapped into the baseband modulated symbols{X k}

by using quadrature-amplitude-modulation(QAM)or phase-shift-

keying(PSK).Usually QAM is used in the OFDM communication

system,so each element in the OFDM symbol is a complex number

representing the particular QAM constellation point.In every OFDM

symbol,each element{X k}is transformed by means of inverse fast

Fourier transform(IFFT).Throughout this paper,we use upper case

to represent the frequency-domain and lower case for the time-

domain symbols.Digital to analog conversion of complex baseband

OFDM symbol can be expressed as

x(n)=N?1

k=0

X k e j2 (B/N)n,0

where B is the total bandwidth allocated to the OFDM symbol,N is the number of subcarriers in the OFDM symbol,and T m is the OFDM symbol interval.

B

N

= f(2)

where f represents the frequency separation between two adja-cent subcarriers.Now the output of OFDM symbol from the IFFT block can be expressed as

x(n)=N?1

k=0

X k e j2 fn,0

The received time-domain OFDM signal after analog-to-digital conversion can be represented as

r k=z k+w k+u k,k=0,1,...,N?1(4)where z k,w k,u k are assumed to be mutually independent,and z k is given as

z k=

L

l=1

h l x k?l(5)

where x k=x(kT m/N),h l is the channel impulse response,L is the length of channel impulse response.Now Eq.(4)can be represented as

r k=

L

l=1

h l x k?l+w k+u k,k=0,1,...,N?1(6)

where w k is the additive white Gaussian noise(AWGN)with zero mean,and u k is the impulsive noise.All these quantities are assumed to be complex.The characterization of impulsive noise is quite dif?cult.Let us assume that impulsive noise can be modeled as a Bernoulli–Gaussian random process and is expressed as

u k=b k g k,k=0,1...,N?1(7) It is a product of real Bernoulli process(b k)and a complex Gauss-ian process(g k)with zero mean.We also assume impulsive noise energy is much higher than that of thermal noise.Moreover,the duration of impulsive noise is much shorter than the OFDM symbol duration T m.

After fast Fourier transform of the received signal,it can be expressed as

R k=H k X k+W k+U k(8) where H=[H0,H1,...,H N?1]is the fast Fourier transform(FFT)of channel impulse response, X=[X0,X1,...X N?1]is the FFT of the transmitted signal, W=[W0,W1,...,W N?1]is the FFT of addi-tive white Gaussian noise,and U=[U0,U1,...,U N?1]is the FFT of impulsive noise.

3.Impulsive noise compensation with imperfect channel state information

Previous method[7]for the suppression of impulsive noise is implemented in the time-domain before OFDM demodulation,but impulsive noise compensation method[8]is implemented in the frequency-domain after OFDM demodulation with the estimated channel state information.

However,in practice,the channel is never perfectly known at the receiver.The channel imperfection is caused either by errors in the estimation of the channel or by variations in the channel due to the motion of the transmitter and/or the receiver.At the receiver,we

assume the estimated channel(i.e.,H est

k

=H k+ H k).Now,after the channel equalization by using estimated CSI,an equalized signal can be expressed as

R(eq)

k

=R k(H(est)

k

)

?1

=H k X k(H(est)

k

)

?1

+W k(H(est)

k

)

?1

+U k(H(est)

k

)

?1

,k=0,1,...,N?1

(9) Fig.1.Block-scheme of transmission system.

A.Bansal,A.K.Kohli /Optik 127(2016)2111–2115

2113

where, H k is an error in the channel estimation.It can be rep-resented by a complex number in the form of H k =a k +jb k ;here a k and b k are independent identically Gaussian distributed random

variables with zero mean and variance 2k

/2.R k (H k + H k )

?1

=H k X k (H k + H k )

?1

+W k (H k + H k )

?1

+U k (H k + H k )

?1

(10)

Taking H ?1

k common on both sides of Eq.(10),which leads to

R k H ?1k

1+

H k H k

?1

=X k

1+

H k H k

?1

+W k H ?1

k

1+

H k H k

?1

+U k H ?1

k

1+

H k H k

?1

(11)

By using Taylor series expansion i.e.,(1+x )?1 (1?x )for x 1,

it can be shown that

R k H ?1

k

1?

H k

H k

=X k

1?

H k H k

+W k H ?1

k

1?

H k

H k

+U k H ?1

k

1?

H k H k

(12)

R (eq)k

=X k

1?

H k H k

+(W k +U k )H ?1

k

1?

H k H k

(13)

Let the estimated transmitted baseband symbol be ?X

k [8]and the estimated noise term be A k =W k +U k ,where k =0,1,...,N ?1,the following expression can be expressed as

A (est)k = R (eq)k

??X

k

1?

H k

H k

H k

1?

H k H k

?1

(14)

A (est)k =

(R k H ?1

k

??X

k )H k

1? H k

k

1?

H k k

?1

(15)A (est)

k

=(R k H ?1k ??X

k )H k

1?

H k

H k

2

(16)

But,it is already known that (R k H ?1k

??X k )H k =W k +U k A (est)

k

=(W k +U k )

1?

H k

H k

2

(17)A (est)

k

=A k +ε

(18)

Here, A

=[A 0,A 1,...,A N ?1]represents the total noise term,and this term is the frequency-domain representation of the impulsive noise and additive white Gaussian noise.However,εrepresents the error in the total noise term.It is due to imperfect CSI at the receiver.In the frequency-domain,the impulsive noise could be repre-sented as the sum of complex sinusoids

U k =S 1e j 2 kl 1/N +S 2e j 2 kl 2/N +···+S M e j 2 kl M /N

(19)

where,M number of samples are affected by impulsive noise,l 1,l 2,...,l m are the locations of these samples and S 1,S 2,...,S M are the amplitudes of impulsive interference.The purpose of the impulsive noise compensation method is to ?nd out the locations l 1,l 2,...,l 3and the amplitudes S 1,S 2,...,S 3of impulsive interference and reconstruct the impulsive noise vector.

?U

=[?U 0,?U 1,...,?U N ?1](20)

For reconstruction of vector,?rst transform the total noise term into the time-domain by means of IFFT.Now apply the output vector of IFFT to peak detector [8]and estimate the

impulsive noise vector in time-domain ?u

=[?u 0,?u 1,...,?u N ?1

].Fig.2.Block-scheme of reception with imperfect CSI.

Transform the impulsive noise vector into the frequency-domain ?U

=[?U 0,?U 1,...,?U N ?1],and then subtract it from the equalizer out-put.Subsequently using impulsive noise compensation [8]method,R (comp)k in Fig.2can be written as

R (comp)k =R (eq)k

??U k (H (est)k

)?1

(21)R (comp)

k

=R (eq)

k

??U k (H k + H k )?1

(22)

R (comp)k

=

R (eq)k

??U k H ?1k

1+

H k H k

?1

(23)

For the performance improvement,the compensated signal can be recursively applied to the impulsive noise compensation algo-rithm.If the amplitude of the impulsive noise is very high,then the impulsive noise compensation method becomes less reliable.In this case,it is advantageous to use the time-domain method (blanking non-linearity [7])before OFDM demodulation.

4.Simulation results

We will try to understand the behavior of impulsive noise com-pensation method with Nakagami-m fading channel in the OFDM system to analyze the effects of impulsive noise on its performance.We will also compare the performance of underlying OFDM system at different values of Nakagami fading parameter m (i.e.,m =0.5,1or 2)under perfect and imperfect channel state information at the receiver.

4.1.Performance evaluation of OFDM system with perfect CSI

The simulation results for the impulsive noise compensation method in the OFDM system with perfect channel estimation are presented in Figs.3–6.These results are obtained for 64-QAM OFDM system with 2048subcarriers.Here,Bernoulli–Gaussian model is used for the generation of impulsive noise [5].The probability of the occurrence of the impulses in single OFDM symbol is set to be 0.01.

10

10

10

m=0.5

SNR in dB

B E R

Fig.3.Simulated performance in the Bernoulli–Gaussian noise and Nakagami chan-nel with fading parameter m =0.5.

2114

A.Bansal,A.K.Kohli /Optik 127(2016)2111–2115

10

10

10

m=1

SNR in dB

B E R

Fig.4.Simulated performance in the Bernoulli–Gaussian noise and Nakagami chan-nel with fading parameter m =

1.

10

10

10

m=2

SNR in dB

B E R

Fig.5.Simulated performance in the Bernoulli–Gaussian noise and Nakagami chan-nel with fading parameter m =2.

Bernoulli model is represented as u k =b k g k .where b k is indepen-dent and identically distributed sequence of zeros and ones with probability P (b k =1)=0.01,and g k is complex Gaussian noise with zero mean.The standard deviation of g k is kept 10 w ,where w is standard deviation of background noise w k .

The simulation results presented in Figs.3–5under the per-fect CSI,it can be observed that the BER reduces as the value of m increases.The results obtained for Nakagami fading parameter

SNR in dB

B E R

Fig.6.Performance of impulsive noise compensator method for different values m .

1010

10

m=0.5

Channel estimation error (dB)

B E R

Fig.7.Simulated performance of impulsive noise compensation method with imperfect CSI Channel (m =0.5).

at m =1are approximately equivalent to Rayleigh channel.Results presented in Figs.4and 5depict that when parameter m =2,it gives approximately 2dB performance advantage over Nakagami fading parameter m =1.The performance of the impulsive noise compen-sator method is better,when the number of iterations are increased and the Nakagami fading parameter is greater than 1(m >1)under the perfect CSI.

In Fig.6,we have presented the simulation results for the impul-sive noise compensation method with different values of Nakagami fading parameter m on a single graph.It is clear that the impul-sive noise compensation method shows signi?cant performance improvements with single as well as double iterative method.

4.2.Performance evaluation of OFDM system with imperfect CSI

In this section,we present the simulation results obtained with the imperfect knowledge of the transmission channel.The chan-nel state estimator provides imperfect CSI at the receiver,in which the estimation error is H k .In Figs.7–9,all the results are demon-strated for imperfect CSI at the particular value of signal-to-noise (SNR)ratio i.e.,30dB.It is apparent that the degradation in BER performance begins to occur when the channel estimation error is greater than ?40dB.

In case,if the channel estimation error is ?15dB,then the BER is 10?1at SNR 30dB for Nakagami fading parameter m =2in the OFDM system.However at ?40dB channel estimation error,the adverse effects of the CSI imperfections are too low to in?uence the BER

performance.

1010

10

m=1

Channel

estimation error (dB)

B E R

Fig.8.Simulated performance of impulsive compensation method with imperfect CSI channel (m =1).

A.Bansal,A.K.Kohli /Optik 127(2016)2111–2115

2115

1010

10

m=2

Channel estimation

error (dB)

B E R

Fig.9.Simulated performance of impulsive noise compensation method with imperfect CSI channel (m =2).

Therefore,the ef?ciency of proposed scheme is dependent on the performance of channel estimator.However,it is notewor-thy that the blanking nonlinearity method is found to be useful to reduce the amplitude of large scale impulses.

5.Conclusion

This paper presents the impulsive noise compensation method,which is suitable for the suppression of impulsive noise in the OFDM communication system,working under Nakagami-m mul-tipath fading channels.However,the simulation results evidenced that the channel estimator is backbone of proposed technique.As a channel estimator error increases,the BER performance

degradation is observed in all the techniques.However,the proposed method with double iterations outperforms the single iterative scheme and blanking non-linearity method,under the low channel estimation error conditions.Future work includes the investigation of different error correction decoding techniques in combination with presented impulsive noise compensation method with and without the perfect CSI.

References

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[3]W.Yiyan,Performance comparison of ATSC 8-VSB and DVB-T COFDM transmis-sion systems for digital television terrestrial broadcasting,IEEE Trans.Consum.Electron.45(August)(1999)916–924.

[4]D.Middleton,Statistical-physical models of electromagnetic interference,IEEE

https://www.wendangku.net/doc/5713245525.html,pat.EMC-19(August)(1977)106–127.

[5]K.L.Blackard,T.S.Rappaport,C.W.Boston,Measurements and models of radio

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英语中的比较级与最高级 详解

比较级与最高级 1.as...as 与(not) as(so)...as as...as...句型中,as的词性 第一个as是副词,用在形容词和副词的原级前,常译为“同样地”。第二个as是连词,连接与前面句子结构相同的一个句子(相同部分常省略),可译为“同..... He is as tall as his brother is (tall) . (后面的as 为连词) 只有在否定句中,第一个as才可换为so 改错: He is so tall as his brother.(X) 2.在比较状语从句中,主句和从句的句式结构一般是相同的 与as...as 句式中第二个as一样,than 也是连词。as和than这两个连词后面的从句的结构与前面的句子大部分情况下结构是相同的,相同部分可以省略。 He picked more apples than she did. 完整的表达为: He picked more apples than she picked apples. 后而的picked apples和前面相同,用did 替代。 He walked as slowly as she did.完整表达为: He walked as slowly as she walked slowly. she后面walked slowly与前面相同,用did替代。

3.谓语的替代 在as和than 引导的比较状语从句中,由于句式同前面 主句相同,为避免重复,常把主句中出现而从句中又出现的动词用do的适当形式来代替。 John speaks German as fluently as Mary does. 4.前后的比较对象应一致 不管后面连词是than 还是as,前后的比较对象应一致。The weather of Beijing is colder than Guangzhou. x than前面比较对象是“天气”,than 后面比较对象是“广州”,不能相比较。应改为: The weather of Bejing is colder than that of Guangzhou. 再如: His handwriting is as good as me. 应改为: His handwriting is as good as mine. 5.可以修饰比较级的词 常用来修饰比较级的词或短语有: Much,even,far,a little,a lot,a bit,by far,rather,any,still,a great deal等。 by far的用法: 用于强调,意为“...得多”“最最...”“显然”等,可修饰形容词或副词的比较级和最高级,通常置于其后,但是若比较级或最高级前有冠词,则可置于其前或其后。

The way常见用法

The way 的用法 Ⅰ常见用法: 1)the way+ that 2)the way + in which(最为正式的用法) 3)the way + 省略(最为自然的用法) 举例:I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法: 在当代美国英语中,the way用作为副词的对格,“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2)The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3)The way =how/ how much No one can imagine the way he missed her. 4)The way =because

人教版(新目标)初中英语形容词与副词的比较级与最高级

人教版(新目标)初中英语形容词与副词的比较级与最高级 (一)规则变化: 1.绝大多数的单音节和少数双音节词,加词尾-er ,-est tall—taller—tallest 2.以不发音的e结尾的单音节词和少数以-le结尾的双音节词只加-r,-st nice—nicer—nicest , able—abler—ablest 3.以一个辅音字母结尾的重读闭音节词或少数双音节词,双写结尾的辅音字母,再加-er,-est big—bigger—biggest 4.以辅音字母加y结尾的双音节词,改y为i再加-er,-est easy—easier—easiest 5.少数以-er,-ow结尾的双音节词末尾加-er,-est clever—cleverer—cleverest, narrow—narrower—narrowest 6.其他双音节词和多音节词,在前面加more,most来构成比较级和最高级 easily—more easily—most easily (二)不规则变化 常见的有: good / well—better—best ; bad (ly)/ ill—worse—worst ; old—older/elder—oldest/eldest many / much—more—most ; little—less—least ; far—farther/further—farthest/furthest

用法: 1.原级比较:as + adj./adv. +as(否定为not so/as + adj./adv. +as)当as… as中间有名字时,采用as + adj. + a + n.或as + many / much + n. This is as good an example as the other is . I can carry as much paper as you can. 表示倍数的词或其他程度副词做修饰语时放在as的前面 This room is twice as big as that one. 倍数+as+adj.+as = 倍数+the +n.+of Your room is twice as larger as mine. = Your room is twice the size of mine. 2.比较级+ than 比较级前可加程度状语much, still, even, far, a lot, a little, three years. five times,20%等 He is three years older than I (am). 表示“(两个中)较……的那个”时,比较级前常加the(后面有名字时前面才能加冠词) He is the taller of the two brothers. / He is taller than his two brothers. Which is larger, Canada or Australia? / Which is the larger country, Canada or Australia? 可用比较级形式表示最高级概念,关键是要用或或否定词等把一事物(或人)与其他同类事物(或人)相分离 He is taller than any other boy / anybody else.

英语中的比较级和最高级

大多数形容词有三种形式,原级,比较级和最高级, 以表示形容词说明的性质在程度上的不同。 形容词的原级: 形容词的原级形式就是词典中出现的形容词的原形。例如: poor tall great glad bad 形容词的比较级和最高级: 形容词的比较级和最高级形式是在形容词的原级形式的基础上变化的。分为规则变化和不规则变化。 规则变化如下: 1) 单音节形容词的比较级和最高级形式是在词尾加 -er 和 -est 构成。 great (原级) (比较级) (最高级) 2) 以 -e 结尾的单音节形容词的比较级和最高级是在词尾加 -r 和 -st 构成。wide (原级) (比较级) (最高级) 3)少数以-y, -er, -ow, -ble结尾的双音节形容词的比较级和最高级是在词尾加 -er 和 -est 构成。 clever(原级) (比较级) (最高级) 4) 以 -y 结尾,但 -y 前是辅音字母的形容词的比较级和最高级是把 -y 去掉,加上 -ier 和-est 构成. happy (原形) (比较级) (最高级) 5) 以一个辅音字母结尾其前面的元音字母发短元音的形容词的比较级和最高级是双写该辅音字母然后再加 -er和-est。 big (原级) (比较级) (最高级) 6) 双音节和多音节形容词的比较级和最高级需用more 和 most 加在形容词前面来构成。 beautiful (原级) (比较级) (比较级) difficult (原级) (最高级) (最高级) 常用的不规则变化的形容词的比较级和最高级: 原级------比较级------最高级 good------better------best many------more------most much------more------most bad------worse------worst far------farther, further------farthest, furthest 形容词前如加 less 和 least 则表示"较不"和"最不 形容词比较级的用法: 形容词的比较级用于两个人或事物的比较,其结构形式如下: 主语+谓语(系动词)+ 形容词比较级+than+ 对比成分。也就是, 含有形容词比较级的主句+than+从句。注意从句常常省去意义上和主句相同的部分, 而只剩下对比的成分。

The way的用法及其含义(二)

The way的用法及其含义(二) 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语: 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势,忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中

英语比较级和最高级的用法归纳

英语比较级和最高级的用法归纳 在学习英语过程中,会遇到很多的语法问题,比如比较级和最高级的用法,对于 这些语法你能够掌握吗?下面是小编整理的英语比较级和最高级的用法,欢迎阅读! 英语比较级和最高级的用法 一、形容词、副词的比较级和最高级的构成规则 1.一般单音节词和少数以-er,-ow结尾的双音节词,比较级在后面加-er,最高级 在后面加-est; (1)单音节词 如:small→smaller→smallest short→shorter→shortest tall→taller→tallest great→greater→greatest (2)双音节词 如:clever→cleverer→cleverest narrow→narrower→narrowest 2.以不发音e结尾的单音节词,比较在原级后加-r,最高级在原级后加-st; 如:large→larger→largest nice→nicer→nicest able→abler→ablest 3.在重读闭音节(即:辅音+元音+辅音)中,先双写末尾的辅音字母,比较级加-er,最高级加-est; 如:big→bigger→biggest hot→hotter→hottest fat→fatter→fattest 4.以“辅音字母+y”结尾的双音节词,把y改为i,比较级加-er,最高级加-est; 如:easy→easier→easiest heavy→heavier→heaviest busy→busier→busiest happy→happier→happiest 5.其他双音节词和多音节词,比较级在前面加more,最高级在前面加most; 如:bea utiful→more beautiful→most beautiful different→more different→most different easily→more easily→most easily 注意:(1)形容词最高级前通常必须用定冠词 the,副词最高级前可不用。 例句: The Sahara is the biggest desert in the world. (2) 形容词most前面没有the,不表示最高级的含义,只表示"非常"。 It is a most important problem. =It is a very important problem.

(完整版)the的用法

定冠词the的用法: 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...

英语比较级和最高级的用法

More than的用法 A. “More than+名词”表示“不仅仅是” 1)Modern science is more than a large amount of information. 2)Jason is more than a lecturer; he is a writer, too. 3) We need more than material wealth to build our country.建设我们国家,不仅仅需要物质财富. B. “More than+数词”含“以上”或“不止”之意,如: 4)I have known David for more than 20 years. 5)Let's carry out the test with more than the sample copy. 6) More than one person has made this suggestion. 不止一人提过这个建议. C. “More than+形容词”等于“很”或“非常”的意思,如: 7)In doing scientific experiments, one must be more than careful with the instruments. 8)I assure you I am more than glad to help you. D. more than + (that)从句,其基本意义是“超过(=over)”,但可译成“简直不”“远非”.难以,完全不能(其后通常连用情态动词can) 9) That is more than I can understand . 那非我所能懂的. 10) That is more than I can tell. 那事我实在不明白。 11) The heat there was more than he could stand. 那儿的炎热程度是他所不能忍受的 此外,“more than”也在一些惯用语中出现,如: more...than 的用法 1. 比……多,比……更 He has more books than me. 他的书比我多。 He is more careful than the others. 他比其他人更仔细。 2. 与其……不如 He is more lucky than clever. 与其说他聪明,不如说他幸运。 He is more (a)scholar than (a)teacher. 与其说他是位教师,不如说他是位学者。 注:该句型主要用于同一个人或物在两个不同性质或特征等方面的比较,其中的比较级必须用加more 的形式,不能用加词尾-er 的形式。 No more than/not more than 1. no more than 的意思是“仅仅”“只有”“最多不超过”,强调少。如: --This test takes no more than thirty minutes. 这个测验只要30分钟。 --The pub was no more than half full. 该酒吧的上座率最多不超过五成。-For thirty years,he had done no more than he (had)needed to. 30年来,他只干了他需要干的工作。 2. not more than 为more than (多于)的否定式,其意为“不多于”“不超过”。如:Not more than 10 guests came to her birthday party. 来参加她的生日宴会的客人不超过十人。 比较: She has no more than three hats. 她只有3顶帽子。(太少了) She has not more than three hats. 她至多有3顶帽子。(也许不到3顶帽子) I have no more than five yuan in my pocket. 我口袋里的钱最多不过5元。(言其少) I have not more than five yuan in my pocket. 我口袋里的钱不多于5元。(也许不到5元) more than, less than 的用法 1. (指数量)不到,不足 It’s less than half an hour’s drive from here. 开车到那里不到半个钟头。 In less than an hour he finished the work. 没要上一个小时,他就完成了工作。 2. 比……(小)少 She eats less than she should. 她吃得比她应该吃的少。 Half the group felt they spent less than average. 半数人觉得他们的花费低于平均水平。 more…than,/no more than/not more than (1)Mr.Li is ________ a professor; he is also a famous scientist. (2)As I had ________ five dollars with me, I couldn’t afford the new jacket then. (3)He had to work at the age of ________ twelve. (4)There were ________ ten chairs in the room.However, the number of the children is twelve. (5)If you tel l your father what you’ve done, he’ll be ________ angry. (6)-What did you think of this novel? -I was disappointed to find it ________ interesting ________ that one. 倍数表达法 1. “倍数+形容词(或副词)的比较级+than+从句”表示“A比B大(长、高、宽等)多少倍” This rope is twice longer than that one.这根绳是那根绳的三倍(比那根绳长两倍)。The car runs twice faster than that truck.这辆小车的速度比那辆卡车快两倍(是那辆卡车的三倍)。 2. “倍数+as+形容词或副词的原级+as+从句”表示“A正好是B的多少倍”。

“the way+从句”结构的意义及用法

“theway+从句”结构的意义及用法 首先让我们来看下面这个句子: Read the followingpassageand talkabout it wi th your classmates.Try totell whatyou think of Tom and ofthe way the childrentreated him. 在这个句子中,the way是先行词,后面是省略了关系副词that或in which的定语从句。 下面我们将叙述“the way+从句”结构的用法。 1.the way之后,引导定语从句的关系词是that而不是how,因此,<<现代英语惯用法词典>>中所给出的下面两个句子是错误的:This is thewayhowithappened. This is the way how he always treats me. 2.在正式语体中,that可被in which所代替;在非正式语体中,that则往往省略。由此我们得到theway后接定语从句时的三种模式:1) the way+that-从句2)the way +in which-从句3) the way +从句 例如:The way(in which ,that) thesecomrade slookatproblems is wrong.这些同志看问题的方法

不对。 Theway(that ,in which)you’re doingit is comple tely crazy.你这么个干法,简直发疯。 Weadmired him for theway inwhich he facesdifficulties. Wallace and Darwingreed on the way inwhi ch different forms of life had begun.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 This is the way(that) hedid it. I likedthe way(that) sheorganized the meeting. 3.theway(that)有时可以与how(作“如何”解)通用。例如: That’s the way(that) shespoke. = That’s how shespoke.

初中英语比较级和最高级讲解与练习

初中英语比较级和最高级讲解与练习 形容词比较级和最高级 一.绝大多数形容词有三种形式,原级,比较级和最高级, 以表示形容词说明的性质在程度上的不同。 1. 形容词的原级: 形容词的原级形式就是词典中出现的形容词的原形。例如: poor tall great glad bad 2. 形容词的比较级和最高级: 形容词的比较级和最高级形式是在形容词的原级形式的基 础上变化的。分为规则变化和不规则变化。 二.形容词比较级和最高级规则变化如下: 1) 单音节形容词的比较级和最高级形式是在词尾加-er 和-est 构成。 great (原级) greater(比较级) greatest(最高级) 2) 以-e 结尾的单音节形容词的比较级和最高级是在词尾加-r 和-st 构成。 wide (原级) wider (比较级) widest (最高级) 3) 少数以-y, -er, -ow, -ble结尾的双音节形容词的比较级和最高级是在词尾加 -er 和-est构成。 clever(原级) cleverer(比较级) cleverest(最高级), slow(原级) slower(比较级) slowest (最高级) 4) 以-y 结尾,但-y 前是辅音字母的形容词的比较级和最高级是把-y 去掉,加上-ier 和-est 构成. happy (原形) happier (比较级) happiest (最高级) 5) 以一个辅音字母结尾其前面的元音字母发短元音的形容词的比较级和最高级是双写该 辅音字母然后再加-er和-est。 原形比较级最高级原形比较级最高级 big bigger biggest hot hotter hottest red redder reddest thin thinner thinnest 6) 双音节和多音节形容词的比较级和最高级需用more 和most 加在形容词前面来构 成。 原形比较级最高级 careful careful more careful most careful difficult more difficult most difficult delicious more delicious most delicious 7)常用的不规则变化的形容词的比较级和最高级: 原级比较级最高级 good better best 好的 well better best 身体好的 bad worse worst 坏的 ill worse worst 病的 many more most 许多 much more most 许多 few less least 少数几个 little less least 少数一点儿 (little littler littlest 小的) far further furthest 远(指更进一步,深度。亦可指更远) far farther farthest 远(指更远,路程)

way 用法

表示“方式”、“方法”,注意以下用法: 1.表示用某种方法或按某种方式,通常用介词in(此介词有时可省略)。如: Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法,其后可接不定式或of doing sth。 如: It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词),也可跟由that 或in which 引导的定语从句,但是其后的从句不能由how 来引导。如: 我不喜欢他说话的态度。 正:I don’t like the way he spoke. 正:I don’t like the way that he spoke. 正:I don’t like the way in which he spoke. 误:I don’t like the way how he spoke. 4.注意以下各句the way 的用法: That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看,你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题: ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A,而不选其他几项,则要弄清选项中含way的四个短语的不同意义和用法,下面我们就对此作一归纳和小结。 一、in a way的用法 表示:在一定程度上,从某方面说。如: In a way he was right.在某种程度上他是对的。注:in a way也可说成in one way。 二、on the way的用法 1、表示:即将来(去),就要来(去)。如: Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示:在路上,在行进中。如: He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示:(婴儿)尚未出生。如: She has two children with another one on the way.她有两个孩子,现在还怀着一个。 She's got five children,and another one is on the way.她已经有5个孩子了,另一个又快生了。 三、by the way的用法

英语比较级和最高级

形容词比较级和最高级的形式 一、形容词比较级和最高级的构成 形容词的比较级和最高级变化形式规则如下 构成法原级比较级最高级 ①一般单音节词末尾加 er 和 est strong stronger strongest ②单音节词如果以 e结尾,只加 r 和 st strange stranger strangest ③闭音节单音节词如末尾只有一个辅音字母, 须先双写这个辅音字母,再加 er和 est sad big hot sadder bigger hotter saddest biggest hottest ④少数以 y, er(或 ure), ow, ble结尾的双音节词, 末尾加 er和 est(以 y结尾的词,如 y前是辅音字母, 把y变成i,再加 er和 est,以 e结尾的词仍 只加 r和 st) angry Clever Narrow Noble angrier Cleverer narrower nobler angriest cleverest narrowest noblest ⑤其他双音节和多音节词都在前面加单词more和most different more different most different 1) The most high 〔A〕mountain in 〔B〕the world is Mount Everest,which is situated 〔C〕in Nepal and is twenty nine thousand one hundred and fourty one feet high 〔D〕 . 2) This house is spaciouser 〔A〕than that 〔B〕white 〔C〕one I bought in Rapid City,South Dakota 〔D〕last year. 3) Research in the social 〔A〕sciences often proves difficulter 〔B〕than similar 〔C〕work in the physical 〔D〕sciences. 二、形容词比较级或最高级的特殊形式:

高中英语的比较级和最高级用法总结

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