Cooperative Beamforming for Wireless Ad Hoc Networks

a r X i v :0708.0805v 1 [c s .I T ] 6 A u g 2007

Cooperative Beamforming for Wireless Ad Hoc

Networks

Lun Dong,Athina P.Petropulu

Department of Electrical and Computer Engineering

Drexel University,Philadelphia,PA 19104

H.Vincent Poor

School of Engineering and Applied Science Princeton University,Princeton,NJ 08544

Abstract —Via collaborative beamforming,nodes in a wireless network are able to transmit a common message over long distances in an energy ef?cient fashion.However,the process of making available the same message to all collaborating nodes in-troduces delays.In this paper,a MAC-PHY cross-layer scheme is proposed that enables collaborative beamforming at signi?cantly reduced collaboration overhead.It consists of two phases.In the ?rst phase,nodes transmit locally in a random access time-slotted fashion.Simultaneous transmissions from multiple source nodes are viewed as linear mixtures of all transmitted packets.In the second phase,a set of collaborating nodes,acting as a distributed antenna system,beamform the received analog waveform to one or more faraway destinations.This step requires multiplication of the received analog waveform by a complex weight,which is independently computed by each cooperating node,and which allows packets bound to the same destination to add coherently at the destination node.Assuming that each node has access to location information,the proposed scheme can achieve high throughput,which in certain cases exceeds one.An analysis of the symbol error probability corresponding to the proposed scheme is provided.

I.I NTRODUCTION

Transmission over long distances often requires signi?cant amounts of energy in order to overcome attenuation.Energy is usually a scarce commodity in wireless ad hoc networks,as nodes typically operate on batteries,which in many cases are dif?cult to replace or recharge.Thus,energy-ef?cient schemes for long-distance transmission in wireless networks have recently been of much interest.In some such situations,multihop may be a preferred solution.However,there are sev-eral challenges in transmitting real-time services over multiple hops.For example,the traditional CSMA/CA based medium access control (MAC)for avoiding collisions does not work well in a multihop scenario because transmitters are often out of reach of other nodes’sensing ranges.Thus,packets traveling across the network experience interference and a large number of collisions,which introduce long delays.Also,multihop networks require a high node density which makes routing dif?cult and affects the reliability of links [1].

Recently,a collaborative beamforming technique was pro-posed in [3],in which randomly distributed nodes in a network cluster form an antenna array and beamform data to a faraway destination without each node exceeding its power constraint.

This work was supported by the National Science Foundation under Grants ANI-03-38807,CNS-06-25637and CNS-04-35052,and by the Of?ce of Naval Research under Grant N00014-07-1-0500.

The destination receives data with high signal power.Beam-forming with antenna arrays is a well studied technology;it provides space-division multiple access (SDMA)which en-ables signi?cant increases in communication rate.A challenge with implementing beamforming in ad hoc networks is that the geometry of the network may change dynamically.In [3],it was shown that randomly distributed nodes can achieve a nice average beampattern with a narrow main lobe and low side lobes.The directivity of the pattern increases as the number of collaborating nodes increases.Such an approach,when applied in the context of a multihop network reduces the number of hops needed,thereby reducing packet delays and improving throughput.However,to study network performance,one must take into account the information-sharing time that is required for node collaboration.If a time-division multiple-access (TDMA)scheme were to be employed,the information-sharing time would increase proportionally to the number of source nodes (i.e.,the nodes having packets to transmit).In this paper we propose a scheme that is based on the idea of collaborative beamforming,and reduces the time required for information sharing.A preliminary version of the proposed scheme appeared in [4].The work in this paper contains error analysis that provides insight into the performance of the pro-posed approach.The main idea is as follows.Different source nodes in the network are allowed to transmit simultaneously.Collaborating nodes receive linear mixtures of the transmitted packets.Subsequently,each collaborating node transmits a weighted version of its received signal.The weights are such that one or multiple beams are formed,each focusing on one destination node,and reinforcing the signal intended for a particular destination as compared to the other signals.Each collaborating node computes its weight based on the estimated channel coef?cients between sources and itself.This scheme achieves higher throughput and lower delay with the cost of lower SINR as compared to [3].In the preliminary version of this work [4],the analysis of interference at the receiving node was done asymptotically,i.e.,as the number of collaborating nodes tends to in?nity.Here we provide analytical expressions for symbol error probability (SEP)that directly depend on the number of collaborating nodes.The analysis shows how SEP is affected by transmission power,signal-to-noise ratio,number of simultaneously transmitting nodes and number of collaborating nodes.

II.B ACKGROUND ON COLLABORATIVE BEAMFORMING For simplicity,let us assume that sources and destinations are coplanar.We index source nodes using a subscript i,with t i denoting the i-th node.At slot n,one source node t m needs to transmit the signal s m(n)to a faraway destination node q m.Suppose that set of N nodes,designated as collaborating nodes c1,...,c N,have access to s m(n).The locations of these collaborating nodes follow a uniform distribution over a disk of radius R.We denote the location of c i in polar coordinates with respect to the origin of the disk by(r i,ψi).Let d im(φm), or simply d im,represent the distance between c i and the destination q m,whereφm is the azimuthal angle of q m with respect to the origin of the disk.d0m(φm)or d0m denotes the distance between the origin of the disk and q m,so the polar coordinates of q m are(d0m,φm).Moreover,let d i(φ)denote the distance between c i and some receiving point with polar coordinate(d0m,φ).The initial phases at the collaborating nodes are set to

Ψi(φm)=?

2π

λ

r i cos(φm?ψi)(2) which requires knowledge of the node’s position relative to some common reference point,and corresponds to the open-loop case[3].In both cases synchronization is needed,which can be achieved via the use of the Global Positioning System (GPS).

The path losses between collaborating nodes and destination are assumed to be identical for all nodes.The corresponding array factor given the collaborating nodes at radial coordinates r=[r1,...,r N]and azimuthal coordinatesψ=[ψ1,...,ψN] at location with polar coordinate(d0m,φ)is

F(φ;m|r,ψ)=1

λ

d i(φ).(3)

Under far-?eld assumptions,the array factor becomes[3] F(φ;m|r,ψ)=

1

2(φm?φ)),and z i=

(r i/R)sin(ψi?1

π

N + 1?1α(φ;φm) 2(6)

where J1(.)is the?rst-order Bessel function of the?rst kind.

When plotted as a function ofφ,P av(φ)exhibits a main lobe

aroundφm,and side lobes away fromφm.It equals one in

the target direction,and the sidelobe level approaches1/N as

the angle moves away from the target direction.The statistical

properties of the beampattern were analyzed in[3],where it

was shown that under ideal channel and system assumptions,

directivity of order N can be achieved asymptotically with N

sparsely distributed nodes.

As we have noted,all of the collaborating nodes must

have the same information to implement beamforming.Thus,

the source nodes need to share their information symbols

with all collaborating nodes in advance.If a TDMA scheme

were to be employed,the information-sharing time would

increase proportionally to the number of source nodes.In

the following,we propose a novel scheme to reduce the

information-sharing time and also allow nodes in the network

to transmit simultaneously.

III.T HE PROPOSED SCHEME

Here we re?ne the model of[3],focusing more directly on

the physical model for the signal,fading channel and noise.

In addition to the above assumptions,we will further assume

the following:

1)The network is divided into clusters,so that nodes in

a cluster can hear each other.In each cluster there is a

node designated as the cluster-head(CH).Nodes in a

cluster do not need to transmit their packets through the

CH.

2)A slotted packet system is considered,in which each

packet requires one slot for its transmission.Perfect

synchronization is assumed between nodes in the same

cluster.

3)Nodes transmit packets consisting of phase-shift keying

(PSK)symbols each having the same powerσ2s.Also,

nodes operate under half-duplex mode,i.e.,they cannot

receive while they are transmitting.

4)Communication takes place over?at fading channels.

The channel gain during slot n between source t i and

collaborating node c j is denoted by a ij(n).It does

not change within one slot,but can change between

slots.The channel gains are independent and identically

distributed(i.i.d.)complex Gaussian random variables

with zero means and variancesσ2a across both time and

space,i.e.,a ij(n)～CN(0,σ2a).

5)The complex baseband-equivalent channel gain between

nodes c i and q m is b im e j2π

The azimuthal angle of destination q i is denoted byφi. The packet transmitted by node t j consists of L symbols s j(n) [s j(n;0),...,s j(n;L?1)].Due to the broadcast nature of the wireless channel,non-source nodes in cluster C hear a collision,i.e.,a linear combination of the transmitted symbols.More speci?cally,node c i hears the signal

x i(n)=

K

j=1a ji(n)s j(n)+w i(n)(7)

where w i(n)=[w i(n;0),...,w i(n;L?1)]represents noise at the receiving node c i.The noise is assumed to be of zero mean and with covariance matrixσ2w I L,where I L is an L×L identity matrix.

Once the CH establishes that there has been a transmission, it initiates a collaborative transmission period(CTP),by send-ing a control bit to all nodes,e.g.,1,via an error-free control channel.The CH will continue sending a1in the beginning of each subsequent slot until the CTP has been completed. The cluster nodes cannot transmit new packets until the CTP is over.

Let q m denote the destination of s m(n).In slot n+m,m= 1,...,K,each collaborating node c i transmits the signal

?x i(n+m)=x i(n)μm a?mi(n)eΨi(φm)(8) whereμm is a scalar used to adjust the transmit power and is the same for all collaborating nodes.μm is of the order of 1/N.

Collaborating nodes need to know which are source nodes and then estimate the channel between all source nodes and

themselves.One possible way to implement

this

is

to use

orthogonal IDs,as discussed in[4],[2].

Also,collaborating nodes require the knowledge of their initial phases.In closed-loop mode,each collaborating node can independently synchronize itself to a beacon sent from the destination and adjusts its initial phase to it[3].In open-loop mode,each collaborating node needs to know its relative position from a predetermined reference point(e.g.the origin of the disk)within the cluster,which can be achieved by the use of GPS.To obtain initial phases,collaborating nodes also require knowledge of the azimuths of the destinations so that the beams can be steered toward desired directions,which may be broadcast by the CH via a control channel.

Given the collaborating nodes at radial coordinates r= [r1,...,r N]and azimuthal coordinatesψ=[ψ1,...,ψN],the received signal at an arbitrary location with polar coordinates (d0m,φ),is

y(φ;m|r,ψ)=

N

i=1b m?x i(n+m)e j2π

σ2sσ2a

.

IV.S YMBOL E RROR P ROBABILITY(SEP)

In the following,for simplicity we omit the time index,and

replace y,?x i,x i,s i,w i and v in the above equations by y,?x i,

x i,s i,w i and v(i.e.,with one of their samples)respectively.

Our analysis will be conditioned on K,the number of

simultaneously transmitting nodes.In general,K is a random

variable,whose distribution is a function of the traf?c char-

acteristics,e.g,traf?c load,traf?c distribution,transmission

control scheme,etc.In the simple case in which each node

transmits with identical probability P t,K has a binomial

distribution.Once the distribution of K is given then we can

determine the SEP as P s= J K=1P(K)P s(K).

From(9),the received signal at the destination q m is

y(φm;m)=μm b m

N

i=1|a mi|2s m

+μm b m

N

i=1a?mi(K j=1j=m a ji s j+w i)+v(10)

where the?rst term is the desired signal and the remaining

terms represent interference and noise.Recall that a ji～

CN 0,σ2a .Since s j is a PSK symbol,the magnitude of a ji s j

isσ2s|a ji|and its phase is still uniformly distributed in[0,2π].

Thus,a ji s j～CN 0,σ2aσ2s .Therefore,

ηi

K

j=1j=m a ji s j+w i～CN 0,σ2η (11)

whereσ2η (K?1)σ2aσ2s+σ2w.

Given a mi,the instantaneous SINR,γ,equals

γ=

μ2m b2m( N i=1|a mi|2)2σ2sμ2m b2mξσ2η+σ2v(12)

whereξ△= N i=1|a mi|2.

Note that μm is of order 1/N .As N →∞,μ2m b 2m ξσ2

η→0,

and γreduces to μ2m b 2m ξ2σ2s /σ2

v ,which corresponds to the scenario of additive white Gaussian noise (AWGN).Thus,under certain transmit powers,no matter how large N is,the SEP of the proposed scheme is always lower bounded by the SEP under AWGN.

Since |a mi |is Rayleigh distributed,ξ～Erlang(N,σ2

a ).The pdf of the Erlang distribution is

Erlang(k,θ):f (x ;k,θ)=

x k ?1e ?

x

θk (k ?1)!

,x ≥0.(13)

The moment generating function (MGF)of γis

M γ(s )= ∞

?∞exp(sγ)f ξ(ξ)dξ

=

∞

exp(

sμ2m b 2m ξ2σ2

s

σ2a

π

(M ?1)π

sin 2?

d?

=

1

M

∞

exp

?

sin 2(π/M )

μ2m b 2m ξσ2η+σ2v

×

ξN ?1e

?

ξ

σ2N a

(N ?1)!dξd?.(15)

Since there is no closed-form expression for M γ(s )or

P s (K ),in the following we will make some approximations to simplify the above expressions.A.A Simple Bound for SEP

Let us ?x an ?>0,and de?ne ξ0such that P (ξ≤ξ0)=?.Also,let us de?ne ?γ

μ2m b 2m ξ2σ2

s

μ2m b 2m σ2η+σ2v /ξ0

·ξ c ?γξ.

(16)

When ?is small,it holds with probability ≥1??that ?γ≤γ.Since c ?γ>0and s is negative in the range of interest,we can always ?nd a small enough ?so that M ?γ(s )≥M γ(s ).

Note that ?γ～Erlang(N,σ2

a c ?γ)and thus the MGF of ?γis of the following simple form:

M ?γ(s )=(1?sσ2a c ?γ)

?N

.(17)

From (15),the SEP for M-PSK symbols based on ?γis ?P

s (K )=1M )σ2

a c ?γ

M )σ2

a c ?γ

,and using the result of Eq.(5A.17)in [5]we obtain ?P s (K )=1sin 2

?

)?N d?

=M ?1

π

1+c

{(π

[4(1+c )]n

+sin(tan

?1

ζ)

N ?1 n =1n j =1

T jn

c

M

(20)

and

T jn

2n n

M

1+

c

M

)

?N

(22)

which for BPSK becomes

?P

s (K )≤1K ?1+γ?1

1

where ?ξ=ξ/σ2a

～Erlang(N,1).Then,the SINR is deter-mined only by γ1,γ2,K and N .Each packet contains BPSK symbols,so SEP is equivalent to BER.We take ?=0.01.Also,we assume perfect knowledge of channels,number of source nodes and destination information.Only one beampat-tern is formed in each slot.For simulation-based BER,we perform a Monte-Carlo experiment consisting of 106repeated

independent trials.

Fig.1shows the BER versus γ2estimated from the network simulation (?line)when K =4nodes transmit all the time.The parameter γ1is ?xed at 20dB.The estimated BER is in perfect agreement with the analytical result for the exact SEP of (15)(“?”line);in fact the two lines are indistinguishable.The upper bound on the exact SEP,computed by (19),is shown as the solid line.One can see that ?=0.01can guarantee a tight bound under various parameters and SNR ranges.The simple upper bound computed via (23)is also shown (dashed lines).

Extensive simulations con?rm that the simulation-based BER and analytical SEP match well under a wide variety of scenarios.Thus,in the following we will simply use the analytical result of (15)to study the performance of the proposed method.

Fig.2shows how the BER depends on the number of collaborating nodes for γ1=20dB and different values of γ2.Fig.3shows how K affects BER,where γ1=γ2=20dB.As K increases,the SEP increases.Fig.4shows how BER changes with γ1,where γ2=20dB and K =4.Recall that

σ2η

=σ2a σ2

s (K ?1+γ?11).K plays a dominant role in the interference (when K >1).As observed in Fig.4,the SEP decreases only slightly with the increase of γ1.

VI.C ONCLUSIONS

We have proposed a scheme for wireless ad hoc networks that uses the idea of collaborative beamforming and at the same time reduces the time needed for information sharing during the collaborative phase.We have provided an analysis of the SEP,which shows how the performance depends on the number of collaborating nodes,the number of simultaneously source users and noise levels at collaborating nodes and the ?nal destination node.

R EFERENCES

[1]H.Gharavi and K.Ban,“Multihop sensor network design for wide-band

communications,”Proc.IEEE,vol.91,no.8,pp.1221-1234,Aug.2003.[2]R.Lin and A.P.Petropulu,“New wireless medium access protocol based

on cooperation,”IEEE Trans.Signal Process.,vol.53,no 12,pp.4675-4684,Dec.2005.

[3]H.Ochiai,P.Mitran,H.V .Poor and V .Tarokh,“Collaborative beam-forming for distributed wireless ad hoc sensor networks”,IEEE Trans.Signal Process.,vol.53,no.11,pp.4110-4124,Nov.2005.

[4] A.P.Petropulu,L.Dong and H.V .Poor,“A high-throughput cross-layer

scheme for distributed wireless ad hoc networks,”Proc.Conference on Information Sciences and Systems ,Baltimore MD,Mar.2007.

[5]M.K.Simon and M.-S.Alouini,Digital Communication over Fading

Channels (second edition).John Wiley &Sons,New York,2005.

[6] D.Tse and P.Viswanath,Fundamentals of Wireless Communication.

Cambridge Univ Press,Cambridge,UK,2005.

Fig.1.BER vs.γ2(K =4,γ1=20dB);N =8,16,32;empirical results,analytical exact results and upper bounds.

Fig.2.BER vs.N (K =4,γ1=20dB);N =8,16,32;analytical exact results and upper bounds.

Fig.3.BER vs.K (γ1=γ2=20dB);N =8,16,32;analytical exact results and upper bounds.

Fig.4.BER vs.γ1(K =4,γ2=20dB);N =8,16,32;analytical exact results and upper bounds.

初中英语介词用法总结

初中英语介词用法总结 介词(preposition)：也叫前置词。在英语里，它的搭配能力最强。但不能单独做句子成分需要和名词或代词（或相当于名词的其他词类、短语及从句）构成介词短语，才能在句中充当成分。 介词是一种虚词，不能独立充当句子成分，需与动词、形容词和名词搭配，才能在句子中充当成分。介词是用于名词或代词之前，表示词与词之间关系的词类，介词常与动词、形容词和名词搭配表示不同意义。介词短语中介词后接名词、代词或可以替代名词的词（如：动名词v-ing）.介词后的代词永远为宾格形式。介词的种类： （1）简单介词：about, across, after, against, among, around, at, before, behind, below, beside, but, by, down, during, for, from, in, of, on, over, near, round, since, to, under, up, with等等。 （2）合成介词：inside, into, outside, throughout, upon, without, within （3）短语介词：according to, along with, apart from, because of, in front of, in spite of, instead of, owing to, up to, with reguard to （4）分词介词：considering, reguarding, including, concerning 介词短语：构成 介词+名词We go to school from Monday to Saturday. 介词+代词Could you look for it instead of me? 介词+动名词He insisted on staying home. 介词+连接代/副词I was thinking of how we could get there. 介词+不定式/从句He gives us some advice on how to finish it. 介词的用法： 一、介词to的常见用法 1.动词+to a)动词+ to adjust to适应, attend to处理；照料, agree to赞同,

超全的英语介词用法归纳总结

超全的英语介词用法归纳总结常用介词基本用法辨析 表示方位的介词：in, to, on 1. in 表示在某地范围之内。 Shanghai is/lies in the east of China. 上海在中国的东部。 2. to 表示在某地范围之外。 Japan is/lies to the east of China. 日本位于中国的东面。 3. on 表示与某地相邻或接壤。 Mongolia is/lies on the north of China. 蒙古国位于中国北边。 表示计量的介词：at, for, by 1. at 表示“以……速度”“以……价格”。 It flies at about 900 kilometers an hour. 它以每小时900公里的速度飞行。 I sold my car at a high price. 我以高价出售了我的汽车。 2. for 表示“用……交换，以……为代价”。 He sold his car for 500 dollars. 他以五百元把车卖了。 注意：at表示单价(price) ，for表示总钱数。

3. by 表示“以……计”，后跟度量单位。 They paid him by the month. 他们按月给他计酬。 Here eggs are sold by weight. 在这里鸡蛋是按重量卖的。 表示材料的介词：of, from, in 1. of 成品仍可看出原料。 This box is made of paper. 这个盒子是纸做的。 2. from 成品已看不出原料。 Wine is made from grapes. 葡萄酒是葡萄酿成的。 3. in 表示用某种材料或语言。 Please fill in the form in pencil first. 请先用铅笔填写这个表格。They talk in English. 他们用英语交谈。 表示工具或手段的介词：by, with, on 1. by 用某种方式，多用于交通。 I went there by bus. 我坐公共汽车去那儿。 2. with表示“用某种工具”。 He broke the window with a stone. 他用石头把玻璃砸坏了。注意：with表示用某种工具时，必须用冠词或物主代词。

lovestory歌词中英文对照

We were both young when I first saw you 当我第一次看见你的时候，我们都还年轻 I close my eyes and the flashback starts 我闭上眼睛，一幕幕往事又在脑海中重现 I'm standing there on a balcony in summer air 我站在阳台上，空气里，浓浓的，是夏天的味道 See the lights, see the party, the ball gowns 看见灯火，看见热闹的舞会，华丽的盛装 See you make your way through the crowd 看见你穿越人群向我走来 And say hello 对我说“hello” little did I know 我却一无所知 That you were Romeo 当时我并不知道你是我的罗密欧 You were throwing pebbles 在你抛砖引玉向我示爱之后 And my daddy said “stay away from Juliet .” 我爸爸气急败坏地叫你离我远一点 And I was crying on the staircase 我却蜷坐在楼梯间里偷偷地抹眼泪 Begging you “please don't go ” 祈求你不要离开 And I said 我说 Romeo, take me somewhere we can be alone 罗密欧，带我走吧，一起去到一个我们可以相依相偎的地方I'll be waiting, all there's left to do is run 我一直在等待（这一天），只有逃离才能让我们摆脱束缚You'll be the prince and I'll be the princess （到那时）我们就可以像王子和公主一样（快乐地在一起）It's a love story, baby, just say yes 这是多么美好的爱情故事呀，亲爱的，对吧 So I sneak out to the garden to see you 于是，我偷偷摸摸地溜到小花园去见你 We keep quiet 'cause we're dead if they knew 我们压抑着声息，被他们发现我们就死定了 So close your eyes 那么，闭上你的双眼 Escape this town for a little while 逃避这个喧嚣的尘世，即使只有如此短暂的一刻 Oh, oh, oh Cause you were Romeo, 正因为你的出现 I was a scarlet letter 我的生命才有了如此鲜艳的光彩 And my daddy said “stay away from Juliet ” 我爸爸气急败坏地叫你离我远一点 But you were everything to me

(完整版)介词for用法归纳

介词for用法归纳 用法1：(表目的)为了。如： They went out for a walk. 他们出去散步了。 What did you do that for? 你干吗这样做？ That’s what we’re here for. 这正是我们来的目的。 What’s she gone for this time? 她这次去干什么去了？ He was waiting for the bus. 他在等公共汽车。 【用法说明】在通常情况下，英语不用for doing sth 来表示目的。如： 他去那儿看他叔叔。 误：He went there for seeing his uncle. 正：He went there to see his uncle. 但是，若一个动名词已名词化，则可与for 连用表目的。如： He went there for swimming. 他去那儿游泳。(swimming 已名词化) 注意：若不是表目的，而是表原因、用途等，则其后可接动名词。(见下面的有关用法) 用法2：(表利益)为，为了。如： What can I do for you? 你想要我什么？ We study hard for our motherland. 我们为祖国努力学习。 Would you please carry this for me? 请你替我提这个东西好吗？ Do more exercise for the good of your health. 为了健康你要多运动。 【用法说明】(1) 有些后接双宾语的动词(如buy, choose, cook, fetch, find, get, order, prepare, sing, spare 等)，当双宾语易位时，通常用for 来引出间接宾语，表示间接宾语为受益者。如： She made her daughter a dress. / She made a dress for her daughter. 她为她女儿做了件连衣裙。 He cooked us some potatoes. / He cooked some potatoes for us. 他为我们煮了些土豆。 注意，类似下面这样的句子必须用for： He bought a new chair for the office. 他为办公室买了张新办公椅。 (2) 注意不要按汉语字面意思，在一些及物动词后误加介词for： 他们决定在电视上为他们的新产品打广告。 误：They decided to advertise for their new product on TV. 正：They decided to advertise their new product on TV. 注：advertise 可用作及物或不及物动词，但含义不同：advertise sth＝为卖出某物而打广告；advertise for sth＝为寻找某物而打广告。如：advertise for a job=登广告求职。由于受汉语“为”的影响，而此处误加了介词for。类似地，汉语中的“为人民服务”，说成英语是serve the people，而不是serve for the people，“为某人的死报仇”，说成英语是avenge sb’s death，而不是avenge for sb’s death，等等。用法3：(表用途)用于，用来。如： Knives are used for cutting things. 小刀是用来切东西的。 This knife is for cutting bread. 这把小刀是用于切面包的。 It’s a machine for slicing bread. 这是切面包的机器。 The doctor gave her some medicine for her cold. 医生给了她一些感冒药。 用法4：为得到，为拿到，为取得。如： He went home for his book. 他回家拿书。 He went to his friend for advice. 他去向朋友请教。 She often asked her parents for money. 她经常向父母要钱。

(完整版)SeasonsintheSun_中文歌词翻译_中英对照

Seasons in the Sun_中文歌词翻译_中英对照 goodbye to you my trusted friend.再见了,我忠实的朋友. we're known each other we're 9 or 10.我们从孩提时就已相识相知. together we've climb hills trees.我们一起爬山上树. learned of love abc.一起学习. skinned our hearts skinned our knees.我们心意相通,情如手足. goodbye my friend it's hard to die.再见了，朋友们,我本不愿离去. when all the birds are singing in the sky.当所有的鸟儿在天空歌唱. now the spring is in the air.空气中弥漫着春天的气息. pretty girls are everywhere.到处是漂亮女孩. think of me and i'll be there.想我,我便与你同在. we had joy,we had fun.我们曾如此快乐. we had seasons in the sun.也曾充满阳光. but the hills that we climbed were just seasons out of time.那些日子已然逝去. goodbye papa please pray for me.再见了爸爸,请为我祈祷. i was the black sheep of the family.我是家里的害群之马. u tried 2 teach me right from wrong.你费尽心思教我明辨是非. too much wine too much song.我却沉醉于歌酒狂欢. wonder how i got along.真不知那些日子是如何度过. goodbye papa is hard 2 die.再见了爸爸,我本不愿离去. when all the birds are singing in the sky.当所有的鸟儿在天空歌唱. now the spring in the air.空气中弥漫着春天的气息. little children everywhere.孩子们到处嬉戏. when u see them i'll be there.当你看见他们,我便会与你同在. we had joy,we had fun.我们曾如此快乐. we had seasons in the sun.也曾有阳光季节. but the wild the song.但昔日的歌酒狂欢. like the season has all gone.犹如季节更迭已消逝. we had joy,we had fun.我们曾如此快乐. we had seasons in the sun.也曾有阳光季节. but the wild the song.但昔日的歌酒狂欢. like the season has all gone.犹如季节更迭已消逝. goodbye michelle my little one.再见了蜜雪儿,我的贝比. u gave me love help me find the sun.你给我爱,给我希望. and every time that i was down.当我意志消沉时.

【备战高考】英语介词用法总结(完整)

【备战高考】英语介词用法总结(完整) 一、单项选择介词 1． passion, people won't have the motivation or the joy necessary for creative thinking. A．For . B．Without C．Beneath D．By 【答案】B 【解析】 【详解】 考查介词辨析。句意：没有激情，人们就不会有创新思维所必须的动机和快乐。A. For 对于；B. Without没有； C. Beneath在……下面 ; D. By通过。没有激情，人们就不会有创新思维所必须的动机和快乐。所以空处填介词without。故填without。 2．Modern zoos should shoulder more social responsibility _______ social progress and awareness of the public. A．in light of B．in favor of C．in honor of D．in praise of 【答案】A 【解析】 【分析】 【详解】 考查介词短语。句意：现代的动物园应该根据社会的进步和公众的意识来承担更多的社会责任。A. in light of根据，鉴于；B. in favor of有利于，支持；C. in honor of 为了纪念；D. in praise of歌颂，为赞扬。此处表示根据，故选A。 3．If we surround ourselves with people _____our major purpose, we can get their support and encouragement. A．in sympathy with B．in terms of C．in honour of D．in contrast with 【答案】A 【解析】 【详解】 考查介词短语辨析。句意：如果我们周围都是认同我们主要前进目标的人，我们就能得到他们的支持和鼓励。A. in sympathy with赞成；B. in terms of 依据；C. in honour of为纪念； D. in contrast with与…形成对比。由“we can get their support and encouragement”可知，in sym pathy with“赞成”符合句意。故选A项。 4．Elizabeth has already achieved success_____her wildest dreams. A．at B．beyond C．within D．upon

英语介词for的用法归纳总结.doc

英语介词for的用法归纳总结用法1：(介词for表目的)为了 They went out for a walk. 他们出去散步了。 What did you do that for? 你干吗这样做? That s what we re here for. 这正是我们来的目的。 What s she gone for this time? 她这次去干什么去了? He was waiting for the bus. 他在等公共汽车。 【用法说明】在通常情况下，英语不用for doing sth 来表示目的 他去那儿看他叔叔。 误：He went there for seeing his uncle. 正：He went there to see his uncle. 但是，若一个动名词已名词化，则可与for 连用表目的 He went there for swimming. 他去那儿游泳。(swimming 已名词化) 注意：若不是表目的，而是表原因、用途等，则其后可接动名词。(见下面的有关用法) 用法2：(介词for表利益)为，为了 What can I do for you? 你想要我什么? We study hard for our motherland. 我们为祖国努力学习。 Would you please carry this for me? 请你替我提这个东西好吗?

Do more exercise for the good of your health. 为了健康你要多运动。 【用法说明】(1) 有些后接双宾语的动词(如buy, choose, cook, fetch, find, get, order, prepare, sing, spare 等)，当双宾语易位时，通常用for 来引出间接宾语，表示间接宾语为受益者 She made her daughter a dress. / She made a dress for her daughter. 她为她女儿做了件连衣裙。 He cooked us some potatoes. / He cooked some potatoes for us. 他为我们煮了些土豆。 注意，类似下面这样的句子必须用for： He bought a new chair for the office. 他为办公室买了张新办公椅。 (2) 注意不要按汉语字面意思，在一些及物动词后误加介词for： 他们决定在电视上为他们的新产品打广告。 误：They decided to advertise for their new product on TV. 正：They decided to advertise their new product on TV. 注：advertise 可用作及物或不及物动词，但含义不同：advertise sth=为卖出某物而打广告;advertise for sth=为寻找某物而打广告advertise for a job=登广告求职。由于受汉语为的影响，而此处误加了介词for。类似地，汉语中的为人民服务，说成英语是serve the people，而不是serve for the people，为某人的死报仇，说成英语是avenge sb s death，而不是avenge for sb s death，等等。 用法3：(介词for表用途)用于，用来 Knives are used for cutting things. 小刀是用来切东西的。

介词for用法完全归纳

用法1：(表目的)为了。如： They went out for a walk. 他们出去散步了。 What did you do that for? 你干吗这样做? That’s what we’re here for. 这正是我们来的目的。 What’s she gone for this time? 她这次去干什么去了? He was waiting for the bus. 他在等公共汽车。 【用法说明】在通常情况下，英语不用for doing sth 来表示目的。如：他去那儿看他叔叔。 误：He went there for seeing his uncle. 正：He went there to see his uncle. 但是，若一个动名词已名词化，则可与for 连用表目的。如： He went there for swimming. 他去那儿游泳。(swimming 已名词化) 注意：若不是表目的，而是表原因、用途等，则其后可接动名词。(见下面的有关用法) 用法2：(表利益)为，为了。如： What can I do for you? 你想要我什么? We study hard for our motherland. 我们为祖国努力学习。 Would you please carry this for me? 请你替我提这个东西好吗? Do more exercise for the good of your health. 为了健康你要多运动。 【用法说明】(1) 有些后接双宾语的动词(如buy, choose, cook, fetch, find, get, order, prepare, sing, spare 等)，当双宾语易位时，通常用for 来引出间接宾语，表示间接宾语为受益者。如：

seasonsinthesun_中文歌词翻译_中英对照

Seasons?in?the?Sun_中文歌词翻译_中英对照 goodbye to you my trusted friend.再见了,我忠实的朋友. we're known each other we're 9 or 10.我们从孩提时就已相识相知. together we've climb hills trees.我们一起爬山上树. learned of love abc.一起学习. skinned our hearts skinned our knees.我们心意相通,情如手足. goodbye my friend it's hard to die.再见了，朋友们,我本不愿离去. when all the birds are singing in the sky.当所有的鸟儿在天空歌唱. now the spring is in the air.空气中弥漫着春天的气息. pretty girls are everywhere.到处是漂亮女孩. think of me and i'll be there.想我,我便与你同在. we had joy,we had fun.我们曾如此快乐. we had seasons in the sun.也曾充满阳光. but the hills that we climbed were just seasons out of time.那些日子已然逝去. goodbye papa please pray for me.再见了爸爸,请为我祈祷. i was the black sheep of the family.我是家里的害群之马. u tried 2 teach me right from wrong.你费尽心思教我明辨是非. too much wine too much song.我却沉醉于歌酒狂欢. wonder how i got along.真不知那些日子是如何度过. goodbye papa is hard 2 die.再见了爸爸,我本不愿离去. when all the birds are singing in the sky.当所有的鸟儿在天空歌唱. now the spring in the air.空气中弥漫着春天的气息. little children everywhere.孩子们到处嬉戏. when u see them i'll be there.当你看见他们,我便会与你同在. we had joy,we had fun.我们曾如此快乐. we had seasons in the sun.也曾有阳光季节. but the wild the song.但昔日的歌酒狂欢. like the season has all gone.犹如季节更迭已消逝. we had joy,we had fun.我们曾如此快乐. we had seasons in the sun.也曾有阳光季节. but the wild the song.但昔日的歌酒狂欢. like the season has all gone.犹如季节更迭已消逝. goodbye michelle my little one.再见了蜜雪儿,我的贝比. u gave me love help me find the sun.你给我爱,给我希望. and every time that i was down.当我意志消沉时.

for的用法完全归纳

for的用法完全归纳 用法1：(表目的)为了。如： They went out for a walk. 他们出去散步了。 What did you do that for? 你干吗这样做？ That’s what we’re here for. 这正是我们来的目的。 What’s she gone for this time? 她这次去干什么去了？ He was waiting for the bus. 他在等公共汽车。 在通常情况下，英语不用for doing sth 来表示目的。如：他去那儿看他叔叔。 误：He went there for seeing his uncle.正：He went there to see his uncle. 但是，若一个动名词已名词化，则可与for 连用表目的。如： He went there for swimming. 他去那儿游泳。(swimming 已名词化) 注意：若不是表目的，而是表原因、用途等，则其后可接动名词。 用法2：(表利益)为，为了。如： What can I do for you? 你想要我什么？ We study hard for our motherland. 我们为祖国努力学习。 Would you please carry this for me? 请你替我提这个东西好吗？ Do more exercise for the good of your health. 为了健康你要多运动。 (1)有些后接双宾语的动词(如buy, choose, cook, fetch, find, get, order, prepare, sing, spare 等)，当双宾语易位时，通 常用for 来引出间接宾语，表示间接宾语为受益者。如： She made her daughter a dress. / She made a dress for her daughter. 她为她女儿做了件连衣裙。 He cooked us some potatoes. / He cooked some potatoes for us. 他为我们煮了些土豆。 注意，类似下面这样的句子必须用for： He bought a new chair for the office. 他为办公室买了张新办公椅。 (2) 注意不要按汉语字面意思，在一些及物动词后误加介词for： 他们决定在电视上为他们的新产品打广告。 误：They decided to advertise for their new product on TV. 正：They decided to advertise their new product on TV. 注：advertise 可用作及物或不及物动词，但含义不同：advertise sth＝为卖出某物而打广告；advertise for sth＝为寻找某物而打广告。如：advertise for a job=登广告求职。由于受汉语“为”的影响，而此处误加了介词for。类似地，汉语中的“为人民服务”，说成英语是serve the people，而不是serve for the people，“为某人的死报仇”，说成英语是avenge sb’s death，而不是avenge for sb’s death，等等。 用法3：(表用途)用于，用来。如： Knives are used for cutting things. 小刀是用来切东西的。 This knife is for cutting bread. 这把小刀是用于切面包的。 It’s a machine for slicing bread. 这是切面包的机器。 The doctor gave her some medicine for her cold. 医生给了她一些感冒药。 用法4：为得到，为拿到，为取得。如： He went home for his book. 他回家拿书。 He went to his friend for advice. 他去向朋友请教。 She often asked her parents for money. 她经常向父母要钱。 We all hope for success. 我们都盼望成功。 Are you coming in for some tea? 你要不要进来喝点茶？ 用法5：给(某人)，供(某人)用。如： That’s for you. 这是给你的。 Here is a letter for you. 这是你的信。 Have you room for me there? 你那边能给我腾出点地方吗？ 用法6：(表原因、理由)因为，由于。如：

歌剧魅影全套歌词中英对照高级翻译超

Turn your face away 把你的脸转向这里 from the garish light of day Night-time sharpe ns 夜色渐浓 heighte ns each sen sati on 知觉萌动 Darkn ess stirs and wakes imag in ati on 冥冥黑暗引领想象出笼 Sile ntly the sen ses aba ndon their defe nces ... 寂静之中感觉幵始放纵 Slowly, gen tly ni ght un furls its sple ndour 夜晚显现魅力缓慢轻柔 Grasp it, sense it - tremulous and tender 抓住它感觉它 颤抖中带着温柔 tur n your thoughts away 把你的心转向这里 from cold, un feeli ng light 脱离那冰冷无情的光 and listen to the music of the night ... 尽情聆听这夜的乐章 Close your eyes and surre nder to your 闭上双眼尽情放纵 darkest dreams! 心灵深处的梦想 不要再看俗气的日光

you knew before! 全部主张! Close your eyes, 闭上双眼 let your spirit start to soar! 让你的灵魂去飞翔! And you'll live 你将拥有新的生活 as you've n ever lived before ... 在你从未生活过的地方 Softly, deftly 不知不觉中 music shall surro und you ... 音乐将你包容 Feel it, hear it, 去感受去聆听 clos ing in aro und you ... 让它进入你的心 Ope n up your mi nd 让你的思想翱翔 let your fan tasies unwind 为你的幻想松绑 in this dark ness which 在这黑暗之中 you know you cannot fight 你知道自己无力抵抗

介词for 的常见用法归纳

介词for 的常见用法归纳 贵州省黔东南州黎平县黎平一中英语组廖钟雁介词for 用法灵活并且搭配能力很强，是一个使用频率非常高的词，也是 高考必考的重要词汇，现将其常见用法归纳如下，供参考。 1.表时间、距离或数量等。 ①意为“在特定时间，定于，安排在约定时间”。如： The meeting is arranged for 9 o’clock. 会议安排在九点进行。 ②意为“持续达”，常于last、stay 、wait等持续性动词连用，表动作持续的时间，有时可以省略。如： He stayed for a long time. 他逗留了很久。 The meeting lasted （for）three hours. 会议持续了三小时。 ③意为“（距离或数量）计、达”。例如： He walked for two miles. 他走了两英里。 The shop sent me a bill for $100.商店给我送来了100美元的账单。 2. 表方向。意为“向、朝、开往、前往”。常与head、leave 、set off、start 等动词连用。如： Tomorrow Tom will leave for Beijing. 明天汤姆要去北京。 He put on his coat and headed for the door他穿上大衣向门口走去。 介词to也可表示方向，但往往与come、drive 、fly、get、go、lead、march、move、return、ride、travel、walk等动词连用。 3.表示理由或原因,意为“因为、由于”。常与thank、famous、reason 、sake 等词连用。如: Thank you for helping me with my English. 谢谢你帮我学习英语。 For several reasons, I’d rather not meet him. 由于种种原因，我宁可不见他。 The West Lake is famous for its beautiful scenery.西湖因美景而闻名。 4.表示目的,意为“为了、取、买”等。如: Let’s go for a walk. 我们出去散步吧。 I came here for my schoolbag.我来这儿取书包。 He plays the piano for pleasure. 他弹钢琴是为了消遣。 There is no need for anyone to know. 没必要让任何人知道。 5.表示动作的对象或接受者,意为“给、为、对于”。如: Let me pick it up for you. 让我为你捡起来。 Watching TV too much is bad for your health. 看电视太多有害于你的健康。 Here is a letter for you. 这儿有你的一封信。

see-you-again整理歌词中英文对照

see you again It's been a long day without you my friend 没有老友你的陪伴日子真是漫长 And I'll tell you all about it when I see you again 与你重逢之时我会敞开心扉倾诉所有 We've come a long way from where we began 回头凝望我们携手走过漫长的旅程 Oh I'll tell you all about it when I see you again 与你重逢之时我会敞开心扉倾诉所有 When I see you again 与你重逢之时 Damn who knew all the planes we flew 谁会了解我们经历过怎样的旅程 Good things we've been through 谁会了解我们见证过怎样的美好 That I'll be standing right here 我都会在这里 Talking to you about another path 与你聊聊另一种选择的可能 I know we loved to hit the road and laugh 我懂我们都喜欢速度与激情 But something told me that it wouldn't last 但有个声音告诉我这美好并不会永恒 Had to switch up look at things different see the bigger picture 如何才能改变观点用更宏观的视野看这世界 Those were the days hard work forever pays 有付出的日子终有收获的时节 Now I see you in a better place 此刻我看到你走进更加美好的未来 Now I see you in a better place 此刻我看到你走进更加美好的未来 How could we not talk about family when family's all that we got?当家人已是我们唯一的牵绊时我们怎么能忘却最可贵的亲情Everything I went through you were standing there by my side 无论历经怎样的艰难坎坷总有你相伴陪我度过 And now you gonna be with me for the last ride 而今你将陪我走完这最后一段旅程 It's been a long day without you my friend 没有老友你的陪伴日子真是漫长 And I'll tell you all about it when I see you again 与你重逢之时我会敞开心扉倾诉所有 We've come a long way from where we began

英语介词的用法总结

介词的用法 1.表示地点位置的介词 1)at ,in, on, to，for at (1)表示在小地方; (2)表示“在……附近，旁边” in (1)表示在大地方; (2)表示“在…范围之内”。 on 表示毗邻，接壤，“在……上面”。 to 表示在……范围外，不强调是否接壤；或“到……” 2)above, over, on 在……上 above 指在……上方,不强调是否垂直，与below相对； over指垂直的上方,与under相对,但over与物体有一定的空间，不直接接触。 on表示某物体上面并与之接触。 The bird is flying above my head. There is a bridge over the river. He put his watch on the desk. 3)below, under 在……下面 under表示在…正下方 below表示在……下，不一定在正下方 There is a cat under the table. Please write your name below the line. 4)in front [frant]of, in the front of在……前面 in front of…意思是“在……前面”，指甲物在乙物之前，两者互不包括；其反义词是behind（在……的后面）。There are some flowers in front of the house.(房子前面有些花卉。) in the front of 意思是“在…..的前部”，即甲物在乙物的内部.反义词是at the back of…（在……范围内的后部）。 There is a blackboard in the front of our classroom. 我们的教室前边有一块黑板。 Our teacher stands in the front of the classroom. 我们的老师站在教室前.(老师在教室里) 5）beside，behind beside 表示在……旁边 behind 表示在……后面 2.表示时间的介词 1)in , on，at 在……时 in表示较长时间，如世纪、朝代、时代、年、季节、月及一般（非特指）的早、中、晚等。 如in the 20th century, in the 1950s, in 1989, in summer, in January, in the morning, in one’s life , in one’s thirties等。 on表示具体某一天及其早、中、晚。 如on May 1st, on Monday, on New Year’s Day, on a cold night in January, on a fine morning, on Sunday afternoon等。 at表示某一时刻或较短暂的时间，或泛指圣诞节，复活节等。 如at 3:20, at this time of year, at the beginning of, at the end of …, at the age of …, at Christmas，at night, at noon, at this moment等。 注意：在last, next, this, that, some, every 等词之前一律不用介词。如：We meet every day. 2)in, after 在……之后 “in +段时间”表示将来的一段时间以后； “after+段时间”表示过去的一段时间以后； “after+将来的时间点”表示将来的某一时刻以后。 3)from, since 自从…… from仅说明什么时候开始，不说明某动作或情况持续多久；