Generalized Interference Alignment—Part II Application to Wireless Secrecy

Generalized Interference Alignment—Part II: Application to Wireless Secrecy Liangzhong Ruan,Member,IEEE,Vincent https://www.wendangku.net/doc/aa5559868.html,u,Fellow,IEEE,and Moe Z.Win,Fellow,IEEE

Abstract—In contrast to its wired counterpart,wireless commu-nication is highly susceptible to eavesdropping due to the broadcast nature of the wireless propagation medium.Recent works have proposed the use of interference to reduce eavesdropping capabil-ities in wireless wiretap networks.However,the concurrent effect of interference on both eavesdropping receivers(ERs)and legiti-mate receivers has not been thoroughly investigated,and careful engineering of the network interference is required to harness the full potential of interference for wireless secrecy.This two-part ar-ticle addresses this issue by proposing a generalized interference alignment(GIA)technique,which jointly designs the transceivers at the legitimate partners to impede the ERs without interfering with LRs.In Part I,we have established a theoretical framework for the GIA technique.In Part II,we will?rst propose an ef?-cient GIA algorithm that is applicable to large-scale networks and then evaluate the performance of this algorithm in stochastic wire-less wiretap network via both analysis and simulation.These re-sults reveal insights into when and how GIA contributes to wireless secrecy.

Index Terms—MIMO,interference alignment,wireless secrecy.

I.I NTRODUCTION

A.Background and Survey

C ONFIDENTIAL exchange of messages securely in wire-

less networks has become increasingly important for the modern information society.In contrast to its wired counter-part,wireless transmission is highly susceptible to eavesdrop-ping due to the broadcast nature of the wireless propagation medium[1].Contemporary wireless security systems,based on cryptographic primitives,evolved from schemes developed for traditional wired applications.To overcome challenges associ-ated with broadcast communication,one must augment contem-porary wireless security techniques using strategies that exploit the intrinsic properties of the wireless propagation medium.

A key observation in exploiting these properties is that the broadcast nature generates contrasting effects:It makes the

Manuscript received November05,2014;revised March16,2015;accepted May05,2015.Date of publication August28,2015;date of current version April14,2016.The associate editor coordinating the review of this manuscript and approving it for publication was Dr.Pengfei Xia.This work was supported, in part,by the National Science Foundation under Grants CCF-1116501and CCF-1525705.

L.Ruan and M.Z.Win are with the Laboratory for Information and Decision Systems(LIDS),Massachusetts Institute of Technology,Cambridge,MA02139 USA(e-mail:lruan@https://www.wendangku.net/doc/aa5559868.html,;moewin@https://www.wendangku.net/doc/aa5559868.html,).

https://www.wendangku.net/doc/aa5559868.html,u is with the Electrical and Computer Engineering Department, Hong Kong University of Science and Technology(HKUST),Clear Water Bay, Hong Kong(e-mail:eeknlau@ust.hk).

Color versions of one or more of the?gures in this paper are available online at https://www.wendangku.net/doc/aa5559868.html,.

Digital Object Identi?er10.1109/TSP.2015.2474295secrecy information from a certain legitimate transmitter(LT) vulnerable to malicious interception,but at the same time enables other legitimate partners to impede the eavesdrop-ping receivers(ERs)via interference.Therefore,interference emerges as a potentially valuable resource for wireless network secrecy[2],[3].The idea of enhancing network secrecy through the use of interference has been investigated in several recent works,under the name of arti?cial noise[4],[5],arti?cial noise alignment[6],[7],friendly jamming[8],[9],or cooperative jamming[10]–[12].A major challenge in utilizing interference to enhance secrecy is that while impeding the ERs,interference affects the LRs as well.Hence,without proper coordination, interference may be of little help or even harmful to wireless secrecy in some network con?gurations[8].We envision that a greater secrecy gain will be achieved by simultaneously coordinating multiple legitimate partners such that aggregated interference causes negligible effects at the legitimate receivers (LRs)while impeding ERs.This motivates the need to develop coordinative interference engineering strategies for wireless wiretap networks,which will be referred to as wireless-tap networks.1

Several secrecy-enhancing interference engineering strate-gies have been proposed for small networks with one LT[6]–[8] or one LR[9]–[12].Coordinating aggregated interference from multiple LTs at multiple LRs imposes new challenges on secrecy transmission strategy design.A promising candidate to overcome this challenge is interference alignment(IA)[13].A few studies have adopted the IA scheme proposed in[13]to promote wireless secrecy[14]–[16].However,the scheme in [13]is based on in?nite dimensional symbols that require time or frequency domain symbol extension,making it dif?cult to implement in practice.

To avoid the in?nite dimension issue,researchers have devel-oped spatial-domain IA techniques in which no symbol exten-sion is involved and interference is coordinated and canceled via the?nite signal dimension provided by multiple antennas [17].In Part I,a theoretical framework has been established to address the two key issues of spatial-domain IA,i.e.,feasibility conditions and transceiver design.Moreover,to further enhance the network’s capability of secrecy protection,legitimate jam-mers(LJs)are incorporated to better impede ERs without inter-fering with the LRs.In this paper,this technique is referred to as generalized interference alignment(GIA).To apply the GIA technique to practical wireless-tap networks,the following is-sues need to be addressed:

1“Wireless wiretap”is referred to as“wireless-tap”to emphasize the wireless nature of the propagation medium.

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?Design of effective scalable GIA algorithms:In large-scale networks,the limited policy space in transceiver de-sign is insuf?cient to cancel interference on all cross links.

Existing works applying IA to large-scale networks[18],

[19]address this issue by?rst dividing a large network into

small clusters and then performing IA separately on each cluster.However,under this approach,the inter-cluster in-terference is not addressed,and some of it may be the strongest interference perceived by the LRs on a cluster edge.On the other hand,if every LR wishes to cancel the strongest interference it perceives,the feasibility con-ditions of the entire network are coupled together,which normally requires centralized approaches that are not ap-plicable to large networks.Hence,designing effective scal-able GIA algorithms is dif?cult.

?Characterization of the performance of GIA in sto-chastic networks:To obtain insights into the performance of GIA in generic wireless-tap networks,it is desirable to characterize how GIA performs in large-scale stochastic wireless-tap networks.A few works have analyzed the performance of stochastic networks with interference control[20],[21].In these works,the interference control policies at different nodes are independent.However,with GIA,the interference control policies at different LTs and LJs become correlated,making it dif?cult to quantify aggregate interference at LRs and ERs.Therefore,charac-terizing the performance of GIA in stochastic networks is challenging.

B.Contribution of This Work

In this work,we will address the challenges listed above. We consider MIMO wireless-tap networks with LJs.To enable the design of effective and scalable GIA algorithms,we?rst decompose the GIA feasibility conditions to a per-node basis. Based on that,we propose an algorithm that generates a fea-sible alignment set by only requiring each legitimate node to communicate with a few nodes,the number of which does not scale with the size of the network.This algorithm,together with the distributive GIA transceiver design algorithm proposed in Part I,construct a GIA algorithm that is applicable to large-scale wireless-tap networks.We then characterize the performance of the proposed algorithm in stochastic wireless-tap networks. We jointly adopt Cauchy-Schwarz inequality,Chebyshev in-equality,and Chernoff inequality to bound the effect of aggre-gate interference from multiple correlated sources,and obtain the performance of GIA.This result demonstrates the contribu-tion of GIA to network secrecy enhancement.It also illustrates how major network parameters,such as node density and an-tenna con?guration,affect the performance of wireless-tap net-works.We also perform various simulations to obtain insights into when and the how GIA technique bene?ts network secrecy.

C.Notations

The notations are consistent with Part I.Additional notations are listed in the following.

1)Functions:Function,and

are the gamma function and incomplete gamma function,re-spectively,denotes the?oor function,and denotes the complex conjugate of a matrix.

2)Probability Theory:The operators,V,and S denote the expectation,variance,and standard deviation of a random variable,and denotes the probability of an event.

represents complex Gaussian distribution,with mean and standard deviation.

II.P ROBLEM F ORMULATION

In this section,we?rst describe the system model of wire-less-tap networks,then illustrate the potential bene?ts of GIA via a case study,and?nally formulate the alignment set design problem of GIA.

A.System Model

Consider a network consisting of LT-LR pairs,LJs and ERs(The LTs and LJs are indexed from1to and from to,respectively.).LT(or LJ,if),LR,and ER are equipped with,,and antennas,respectively. At each time slot,LT(or LJ)sends independent symbols. LT attempts to send con?dential to LR,while ER attempts to intercept these messages.LJ transmits dummy data to generate interference.

The received signals at LR and ER are given by

(1)

where,,are the channel matrices from LT(or LJ)to LR or ER,whose entries are independent random variables drawn from con-tinuous distributions;is the encoded information symbol at LT(or LJ);is the precoder at LT(or LJ);,is the decoder at LR or ER;and,is the white Gaussian noise zero mean and unit variance. The transmission power of LT(or LJ)is given by

.De?ne the con?guration of the legitimate network as,

.

This work Information-theoretic security as the per-formance metric.From[22],[23],under a given transceiver de-sign,the following secrecy rate is achievable for legitimate link:

(2) in which,,is given by

(3)

From[15],when the transmission power at all LTs and LJs are of the same order,i.e.,for some,, ,the secure degree of freedom(sDoF)can be?ned as

(4)

Fig.1.Con ?guration of the example network.

B.Case Study

Example:As illustrated in Fig.1,consider a MIMO wire-less-tap network,as described in Section II-A,with ,

,antenna con ?guration ,,,,,and data stream

con ?guration

,.The entries of all the channel matrices are independent random variables drawn from

.The transmit power at all nodes is 20dB,i.e.,,.

Compare four different strategies:the ?rst two are non-coop-erative,whereas the other two are cooperative:

A.Zero forcing with 2active LTs :LT 1,2use random

precoders

,,2and LR 1,2use zero forcing to cancel interference,i.e.,

and ,where

.To avoid inter-fering with LR 1and 2,LT 3and LJ 4remain silent,i.e.,

,.

B.Zero forcing with 3active LTs :LT 1,2and 3use random

precoders ,

and ,and LR 1,2and 3use zero forcing to cancel interference from LT 2,3and 1,respec-tively,i.e.,

,and .LJ 4remains silent.

C.:LT 1–3IA to design precoders

.Inter-ference at every LR is aligned into a 1-dimensional

subspace.Speci ?cally,is designed to be an eigen-vector of ,,and .,

,and

are designed as in Strategy B.LJ 4still

remains silent.

D.GIA :LT 1–3and LJ 4adopt a coordinated approach to

design their precoders so that interference at every LR is aligned to a 1-dimensional subspace.Speci ?cally,the LTs and LRs design their transceivers as in Strategy C.LJ 4

designs

so that

,

.

This design is feasible as ,are three vectors in .

The signal space at LR 1,2and ER 1,2,as well as the secrecy rate and sDoF of LR 1,2under the above four strategies,are illustrated and compared in Fig.2.3From this ?gure,Strategy

2Small letters are used for all transceivers as they are vectors in this example.

3Because

the cases of LR 3/ER 3are identical to those of LR 2/ER 2under

Strategy B-D,they are omitted in Fig.2for

conciseness.

Fig.2.Signal space at LR 1,2and ER 1,2under different strategies.

C,D perform better than Strategy A,B.This is because the

channel states between LTs and LRs

are independent of those between LTs and ERs

.Therefore,interference that is aligned at the LRs is not aligned at the ERs almost surely.This fact allow the legitimate network to impede ERs without affecting LRs.Strategy D performs best as its jointly exploits the capability of all legitimate partners,i.e.,LTs,LRs,and LJs,to generate desirable interference.

Remark 2.1(Practical Issues):It is worth noting that the GIA technique proposed in the example

?Requires no channel state for the eavesdropping link .The transceivers of the legitimate partners are functions of the channel state of legitimate links,i.e.,.In other words,no channel state information (CSI)of the eaves-dropping link,i.e.,

is required.?Is effective even if ERs have all the CSI .The perfor-mance of Strategy D comes from the unequal dimension of the interference at the ERs and LRs.Since this property is due to the fact that the two sets of channel state and are independent,it is invariant with respect to the amount of CSI at the ERs.

These properties greatly improve the practicality of the pro-posed GIA technique.For instance,the possible leakage of CSI from the legitimate network to ERs does not affect the perfor-mance of the proposed algorithms.

C.Alignment Set Design

In Section II-B,the potential of GIA technique in secrecy enhancement is demonstrated.To cope with the general cases,the following problem is addressed in Part I:

Problem 2.1(GIA Transceiver Design):Design transceivers

,,that satisfy

the constraints:

(5)

(6)

(7) where

is the alignment set.It characterizes the set of interference to be canceled by GIA.

In Part I,the feasibility conditions of Problem2.1are ana-lyzed for given network con?guration and alignment set. In practice,the network con?guration is usually?xed a priori. Hence,to design feasible GIA strategies,the following problem needs to be addressed:

Problem2.2(Alignment Set Design):Design so that GIA is feasible,i.e.,Problem2.1has solutions.

To develop GIA techniques that are applicable to large-scale networks,it is important to design algorithms that can solve Problem2.2distributively.However,this task is dif?cult due to the following technical challenge.

Challenge of Coupled Feasibility Conditions

As Corollary4.3of Part I shows,for GIA to be feasible,it is necessary that the number of variables in transceiver design is no less than the number of constraints for all subsets of GIA constraints in(7).This fact illustrates that GIA feasibility conditions are inherently coupled with each other.Since there are exponentially many subsets of GIA constraints,the design of a feasible alignment set is complicated.

III.A LGORITHM D ESIGN

In this section,a GIA algorithm is proposed to solve Problem 2.2distributively.

De?nition1(Proper Alignment Subsets):Alignment subsets

,and

are proper iff

(8) Theorem3.1(Proper Alignment Subsets Lead to GIA Feasi-bility):Problem2.1is feasible almost surely if the alignment set can be covered by proper alignment subsets,i.e.,

(9) for some proper alignment subsets and.

Proof:Please refer to Appendix A for the proof. Solution to Coupled Feasibility Conditions

Since(8)is a set of per-node constraints,Theorem3.1provides a mechanism to decompose the GIA feasibility constraints to a per-node basis.This result enables legitimate nodes to distributively design the alignment set,while maintaining the GIA feasibility.

Based on Theorem3.1,the following algorithm is adopted to generate alignment set.Algorithm1(Generate Feasible Alignment Set)?Alignment set selection at the transmitter side:LT(or LJ)selects a few LRs such that satis?es(8).4 Notify the selected LRs.

?Alignment set selection at the receiver side:LR selects among the transmitters which do not select LR in the previous step,and make satisfy(8).?Generate alignment set:Set according to(9). Corollary3.1(Feasibility of Algorithm1):In a MIMO wire-less-tap network,when the alignment set is generated by Al-gorithm1,Problem2.1is feasible almost surely.

Proof:This is a direct consequence of Theorem3.1. Remark 3.1(Scalable GIA Algorithm):The freedom in designing the alignment subsets,,in Algo-rithm1enables the legitimate nodes to distributively select the strongest interfering links and hence effectively manage interference.By?rst performing Algorithm1to design a feasible alignment set and then using the algorithm proposed in Part I to design the transceivers,a distributive GIA algorithm is obtained.In this algorithm,the number of nodes that each node needs to exchange messages with are determined by the alignment subsets and hence does not scale with the size of the network.

IV.P ERFORMANCE A NALYSIS

In this work,homogeneous Poisson point process(PPP)[24] will be employed to model the spatial distribution of stochastic wireless networks.

De?nition2(Stochastic Wireless-Tap Network):?Channel Model:The nodes are distributed in a two-dimen-sional in?nite plane.The channel state between two nodes positioned at is given by

where the elements in are independent random variables following complex Gaussian distribution with zero mean and unit variance and the pathloss

(10)

where is the pathloss exponent and is the cutoff threshold.5

?Legitimate user network:The position of the LTs is mod-eled by a homogeneous PPP with density.For an LT located at,the position of the associated LR is given by

,where is drawn from certain probability 4Here node selection criteria is not speci?ed as it does not affect the feasibility of the alignment set.The selection criteria will be speci?ed in the next section to enable performance analysis.

5Suppose the maximum transmit power of nodes in the network is. Then when,the interference that has been ignored by the pathloss cutoff threshold is insigni?cant compared to white noise.In this case, the pathloss model in(10)is a reasonable approximation of the classical one. The two models will be compared via simulation in Fig.7.

distribution in,with.6Each LR and LT is equipped with and number of antennas,respec-tively.Each LT delivers inde-pendent data streams.Denote.?Legitimate jammer network:The position of the LJs is modeled by a PPP with density.Each LJ has

number of antennas and delivers indepen-dent dummy data streams.

?Eavesdropper network:The position of the ER attempting to intercept the information from the LT at position is given by,where is drawn from certain probability distribution in,with.Each ER is equipped with number of antennas and adopts minimum mean square error decoder.Denote. In the following,the position of a node will be used to replace its index.For example,an LT positioned at is denoted by LT.The set of the positions of LTs,LRs,LJs,and ERs are denoted by,,,and,respectively.

To cancel the strongest interference that each LR perceives, the selection criteria in Algorithm1is speci?ed to enable the nodes to select their nearest neighboring nodes,i.e.,?Transmitter side:LT sets,where

,so that

(11)

(12)

where,and for the LTs and LJs,respectively.

?Receiver side:LR sets

where,,so that

(13)

(14)

(15)

where

De?ne the connection density of the legitimate network and the jammer network,,as the expected number of LTs or LJs that may interfere with a receiver,i.e.,

(16)

(17) 6Otherwise,from(10),the channel between the LR and the associated LT is ,which leads to a trivial result.For the same reason,the distance between LT and the corresponding ER is

limited.Fig.3.Illustration of the correlation between alignment subsets of neighboring nodes.Consider two LTs(or LJs)positioned at and,respectively,where ?has a small norm.Events and are correlated

as the two transmitters perceive

where.

This section focuses on analyzing the sDoF achieved by an LR.Firstly,a lemma which relates the sDoF to the dimension of interference at the LRs and ERs is proved.

Lemma4.1(Dimension of Interference):For LR with cor-responding ER,the sDoF de?ned in(4)is given by

(18) where,is a subspace of the receiving signal space of LR or ER,i.e.,or that has no interference.De?ne,,then

(19)

(20)

Proof:Please refer to Appendix B for the proof.

From Lemma4.1,to analyze the network’s sDoF,the charac-terization of is necessary.However,this is challenging for the following reason.

Challenge of Correlated Alignment Set Selection

As illustrated in Fig.3,events and in the?gure,are correlated.This example shows that the random variables in(19)are correlated for different.This correlation makes it dif?cult to characterize .

This challenge is addressed by the following lemma. Lemma4.2(Characterization of):For LR,de?ne

(21)

(22) Then

(23) Moreover,is bounded within,

(24) S

(25)

Proof:Please refer to Appendix C for the proof. Solution to Correlated Alignment Set Selection

From(23),the major randomness of comes from that of.Equations(24)and(25)show that the expectation of scales at,while its uncertainty in expectation and standard deviation both scale at.Therefore,when is large,the randomness in can be ignored compared to its expectation,i.e.,.As will be discussed further in

Remark4.1,this property bounds the effect of correlated alignment set selection and enables an asymptoti-cally accurate characterization of the sDoF performance. Based on Lemma4.2,the following theorem characterizes the sDoF of the GIA algorithm in a stochastic

network.

Fig.4.Illustration of the sDoF per node described by(27). Theorem4.1(Performance of GIA Algorithm):Indicator

?is de?ned in(26)at the bottom of the page.When

and,the sDoF per node is given by

(27) where,are de?ned in(12).

Proof:Please refer to Appendix D for the proof. Remark4.1(Interpretation of Theorem4.1):Fig.4gives an intuitive illustration of the meaning of the sDoF expression in (27).This expression partitions the operation region into three parts according to the value of the indicator.The sDoF per LR is close to the upper bound in the feasible region, whereas it is close to the lower bound0in the infeasible region. Since the width of the transitory region is on,(27) is asymptotically accurate when.This trend will be shown via simulation in Fig.8.

In practice,it is interesting to understand how a stochastic wireless-tap network performs under various network param-eters.However,as data stream numbers,must be in-tegers,and(26)contains the discontinuous function,it is dif?cult to obtain simple insights.To address this issue,a net-work with high connection density,i.e.,,is analyzed in Appendix E.In this scenario,the width of the transitory re-gion is ignorable,and hence sDoF per node when indicator.De?ne the set of feasible data streams as

.Insights obtained from analysis on the feasible set are summarized as follows.

Remark4.2(Operation Modes of GIA):As illustrated in Fig.5,in a wireless-tap network with high connection density,

(26)

Fig.5.Analysis of the feasible region of a stochastic wireless-tap network with high connection density.In this?gure,.

the set of feasible streams is contained by the region above the jamming line and below the aligning curve.The jamming line means that LTs and LJs have generated just enough interfer-ence to occupy the signal space of the ERs,and the aligning curve indicates that the LTs,LJs,and LRs are on the cutting edge of being able to align all interference at the LRs.The slope and the intersection of the jamming line are and ,respectively.The aligning curve is a combination of a horizontal line and two second order curves.In particular, when,the trapezoid with vertices (0,0),,and lies below the aligning curve.From Fig.5,GIA has three operation modes:

?Pure IA mode:When,the LTs and LRs can generate suf?cient interference to jam the ERs and align all interference at the LRs.The LJs can remain idle without losing optimality in the sDoF sense.?Moderate Jamming mode:When

by adopting a small,the LJs can help the LTs to jam the ERs without reducing the sDoF per LR.?Intensive Jamming mode:When

the LJs need to adopt a large to generate suf?cient interference to jam the ERs.As large is adopted,the sDoF per LR needs to be reduced so as to align the interference at the LRs.

Remark4.3(Role of Network Parameters):The effects of network parameters on sDoF are summarized below.

?LJ density:As Fig.6(a)shows,larger leads to a steeper jamming line.This will increase achievable sDoF per LR if GIA is in the intensive jamming mode.

?LT/LR density:As Fig.6(b)shows,larger?

attens both the jamming line and aligning curve,which

reduces achievable sDoF per

LR.Fig.6.Illustration of how the feasible region of changes w.r.t. to network parameters.(a)Larger;(b)Larger;(c)Larger;

(d)Larger.

?LJ antenna:As Fig.6(c)shows,larger pushes the aligning line to the right.This will bene?t achievable sDoF per LR if GIA is in the intensive jamming mode.?Sum of LT and LR antenna:As Fig.6(d)shows,larger pushes up the aligning curve,and hence increases achievable sDoF per LR.

V.S IMULATION R ESULTS

A.Secrecy Rate Under Different Strategies

First compare the secrecy rate(de?ned in(2))achieved by the proposed GIA technique with the following three baselines.?Cooperative jamming(CJ):The LTs and LRs adopt random transceivers,and the LJs adopt zero-forcing(ZF) precoders to cancel their interference with the LRs.?Pure IA(IA):The LTs and LRs adopt IA to cancel inter-ference.The LJs remain idle.

?IA with arti?cial noise(IAN):The LTs and LRs adopt IA to cancel interference.The LJs generate arti?cial noise by adopting random precoders.

To verify the legitimacy of the pathloss model proposed in (10),the secrecy rates under channel models with and without pathloss cutoff are simulated.

Fig.7illustrates that the proposed GIA technique achieves signi?cant performance gain over the baselines.This is because GIA fully exploits the capability of all legitimate partners to create different amounts of interference at the LRs and ERs. From the slope of the secrecy rate under GIA technique,it can be seen that the sDoF per node is around0.9.It is not exactly1 due to the uncertainty term in(27).Also,it can be seen that the secrecy rate under the two types of channel models are reason-ably close.

B.Width of the Transitory Region

Fig.8illustrates the sDoF per node as a function of the indicator under different network densities.If the region in

Fig.7.Secrecy rate as a function of SNR under different schemes.The network parameters are given by,,,,

,,,and.The distance between an LT and the associated LR and ER are given by

and,

respectively.

Fig.8.sDoF per node as a function of the performance indicator under different user densities.The network parameters are given by,, and.The node density is given by,

,and for the three curves,respectively;then?x,,and modify to change the indicator.

which is used to represent the transi-tory region,one can see that the width of this region scales on .This fact?ts the trend described in Remark4.1.

C.Resource Allocation Between Transmitting and Jamming So far,LTs and LJs are assumed to have a?xed prior role. However,their respective roles may overlap.As illustrated in Fig.9,if part of the LRs are deactivated,then from the point of view of the remaining network nodes,the corresponding LTs effectively become LJs.This conversion empowers the pos-sibility

of allocating resources between transmitting and jam-ming.The comparison between the left and right columns of Fig.9sketches the effect of allocating resources between trans-mitting and jamming.This effect can also be interpreted

from Fig.9.Effects of the resource allocation between transmitting and jamming. Fig.6.The operation of turning LTs to LJs is equivalent to an increase and decrease.From Fig.6(a)and(b),this oper-ation enlarges the feasible region and hence increases the sDoF per node at a cost of having less active LRs.

Fig.10illustrates the effect of resource allocation between transmitting and jamming.We?x the sum of the density of the LTs and LJs,i.e.,,and illustrate the sDoF per node,or per unit area as functions of the density of LTs(note that this is also the density of active LRs). Under each active LR density,all the possible stream combina-tions are exhaustively searched to pick out the com-bination that gives the highest.From the right sub-?gure of Fig.10,in terms of sDoF per unit area,one can roughly separate the operation region into two parts,namely the sparse region and the crowded region.In the sparse region,the bene?t from more active LRs dominates,and hence the sDoF per unit area increases under larger.7In the crowded region,the loss from smaller sDoF per node dominates,and hence be-comes a decreasing function of.Therefore,in practice,it is important to control active LR density so that the network op-erates in a favorable region.

VI.S UMMARY

By creating strong interference at the ERs but little or no in-terference at the LRs,the GIA technique provides an effective tool for wireless secrecy protection.Based on the theoretical framework established in Part I,Part II offers a design for GIA algorithms that is applicable to large-scale networks and char-acterizes the performance of this algorithm in stochastic wire-less-tap networks.Working modes of GIA have been identi?ed and simple insights into how network parameters affect the per-formance of wireless-tap networks have been obtained.Numer-ical results illustrate the contribution of GIA in wireless secrecy protection and con?rm the insights.

7This fact is not always true due to the discrete choices of.For instance,the steep drop indicated in the?gure occurs when changes from 2to1.

Fig.10.sDoF per node/unit area as a function of active LR density.The network parameters are given by,,, ,and.

A PPENDIX A

P ROOF OF T HEOREM3.1

From Theorem4.4of Part I,one only need to show that ma-trix(de?ned in Fig.4of Part I)is full row-rank.Suppose Problem2.1is feasible under alignment subsets and .If the intersection of some alignment subsets are non-empty,e.g.,,then non-overlapping alignment subset can be generated.From Corollary4.1of Part I,since this operation does not change the alignment set,the feasibility of Problem 2.1is preserved.Hence,to prove the theorem,it is suf?cient to consider the case in which

(28) From(9)and(28),every belongs to one and only one alignment subset.Hence,one can reorder the rows of and rewrite the matrix as

(29) where

with

..

.

(30)

..

.

(31)

and the submatrices in are given by

(32) Substituting the condition of proper alignment subset,i.e.,(8), to the expressions of and,i.e.,(9)and(10)of Part I, we get that matrices and in(30)and(31)are full row-rank almost surely.Hence,is full row-rank almost surely.Moreover,from(9)and(10)of Part I,the elements in different submatrices,are independent.Hence(32)assures that is independent of.Therefore,from(29),is full row-rank almost surely.This completes the proof.

A PPENDIX B

P ROOF OF L EMMA4.1

As the entries of the channel matrices are independent random variables drawn from continuous distributions,with probability1,.Substituting this result to(2),

(33) Substituting(33)to(4),(18)is obtained.In the following,the expression of and will be derived.

If a link between LR and LT(or LJ)has zero pathloss,i.e., ,or,there is no interference on this link. Otherwise,the channel state is independent of. In this case,almost surely,where for LTs and for LJs.Hence,with probability1,is given by(19).

Similarly,as the channel state of the eavesdropping network is independent of precoders,(20)is obtained.

A PPENDIX C

P ROOF OF L EMMA4.2

First try to prove(23).Note that

From(13),the sets,,and

do not overlap.Hence,

(34)

where.Substituting(21)and(34)to(19),

(35) where

From(22),.Moreover,from(11)and(14),if,

,which means.With this fact and(35),(23)is obtained. From(15),it is easy to see that is bounded within

.Hence,in the following,the focus is on characterizing the mean and variance of.De?ne

then

(36) To analyze the mean and variance of,?rst analyze those of,.To achieve this task,a characterization the spatial distribution of LRs is needed.

Lemma C.1(Spatial Distribution of LRs):In a stochastic net-work,as described by De?nition2,the position of the LRs is given by a PPP with density.

Proof:From the second item in De?nition2,the position of the LRs is a transformation of that of the LTs,which is a PPP with density.Hence,from[25,Thm.1.3.9],the position of the LRs is also a PPP with density,,where

(37) Here denotes the probability density function of.This completes the proof.

First analyze the expectation.For LR,the positions of the unassociated LTs are given by a homogeneous PPP with density on.Hence

(38) From Lemma C.1,

(39)

(40) Substitute(40)to(38):

(41)

From[26,8.11.2],

(42) By combining(39),(41),and(42),

which is a positive,increasing function of.Hence,when ,is in interval

(43)

Equation(43)is true because,from Stirling’s formula[26, 5.11.7],

(44)

Further noting that is a nonnegative decreasing func-tion of,is in interval

(45)

We next bound the variance of.

Lemma C.2(Bound of the Variance of the Sum of Random Variables):are random variables in.Then

S S(46) Proof:Denote,then

V

(47)

S(48)

where(47)is true due to the Cauchy-Schwarz inequality.This completes the proof.

From Lemma C.2,

S

(49) where function,.

Denote

If,,.Hence V. Otherwise,when,

follows Poisson distribution with mean.Hence,from Chernoff inequality,

(50)

Then S will be bounded by separating the operation region into the following two cases:

Case1:(i.e.,).Substitute(50)into (49),noting that,then

S

(51)

where last inequality is true because of(44).

Case2:(i.e.,).First,prove the following lemma.

Lemma C.3:When,,where

Proof:Since is Poisson random variable with mean,from[27,Thm.2],when

,.This completes the proof. Lemma C.4:When and,

Proof:Note that when,

(52) it can be seen that when,

(53) Noting that,

(54) Substitute(54)to(53),then

This completes the proof.

With the two lemmas proved above,it can be seen that

S

(55)

(56)

(57) where(55)is true because of Lemma C.3and the facts that

(a)is a decreasing function of,

(b)is an increasing function in],

and

(c).

(56)is true because of Lemma C.4and.From(51) and(57),

S

(58) From(36),(45),and(58),(24)and(25)are obtained.

A PPENDIX D

P ROOF OF T HEOREM4.1

From Lemma4.1,to characterize,it is necessary to char-acterize and.Since is addressed by Lemma4.2, the focus here is on.

Lemma D.1(Characterization of):

where

and

V

Proof:The position of LTs and LJs are given by PPPs with density and,respectively.Hence,

and are random variables Poisson distribution, with parameters and,respectively.From the properties of Poisson distribution and(20),Lemma D.1is proved.

Now start the main?ow of the proof of Theorem4.1.When from Lemma D.1and Chebyshev inequality,

(59)

Otherwise,when, noting that,

(60) Similarly,from Lemma4.2and Chebyshev inequality,when

(61) and when,

(62) Substituting(59)–(62)to(18),(27)is obtained.

A PPENDIX E

F EASIBLE R EGION U NDER H IGH C ONNECTION D ENSITY When,the feasible streams

need to satisfy

(63)

(64)

(65) De?ne

(66) Since the quantization error of the function is bounded by (1,0],by substituting(12)to(65),one gets

(67) Hence,the difference between and can be ignored when.Therefore,one can replace by in(63).

After this replacement,(63)is equivalent to the following four inequalities:

(68)

(69)

(70)

(71)

It is easy to see that is a line with slope and intersection,and is a horizontal line with intersection.However,as

and are second order curves,it is dif?cult to give a simple characterization of the feasible region.On the other hand,noting that

?passes through points,,

,and

?passes through points(0,0),, the following proposition summarizes the property of ,and.

Proposition E.1(Properties of the Feasible Region):When

,the points in the interior of trapezoid with vertices(0,0),,

and satisfy(69)–(71).

Proof:Noting that function,with

and is a decreasing function when

(i.e.,),from(66),is an strictly decreasing function of and when.Further noting that(69)–(71) ,if(69)–(71)hold for certain data stream con?gura-tion,then for any satisfying

and,(69)–(71)must hold.Therefore,to prove the proposition,one only need to prove that, for all points on the line segment with end points

and.Since on this line segment,,and thus. This line segment can be expressed as

(72) Substitute(72)into(70)and(71),

Hence,when,

,.This completes the proof.

A CKNOWLEDGMENT

The authors would like to thank A.Conti,R.Cohen,and W.Dai for valuable suggestions and careful reading of the manuscript.

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1994.Liangzhong Ruan (S’10–M’14)received the Ph.D.degree in electrical engineering and computer sci-ence from the Hong Kong University of Science and Technology (HKUST),Clear Water Bay,in 2013,and the B.Eng.degree in electrical engineering from Tsinghua University,Beijing,China,in 2007.

From 2012to 2013,he was with the Laboratory for Information &Decision Systems (LIDS),Massa-chusetts Institute of Technology (MIT),Cambridge,USA,as a visiting graduate student.He is currently a postdoctoral associate at the Wireless Communica-tion and Network Sciences Laboratory,MIT.His research interests include in-terference management,intrinsic wireless secrecy,and quantum entanglement distillation.

Dr.Ruan has served as an area chair for EUSIPCO’16,a session chair for IEEE Globecom’11,and TPC members for IEEE Globecom’15and VTC’15.He also serves as reviewers for multiple transactions,including IEEE J OURNAL ON S ELECTED A REAS IN C OMMUNICATIONS ,IEEE T RANSACTIONS ON S IGNAL P ROCESSING ,and IEEE T RANSACTIONS ON W IRELESS C OMMUNICATIONS

.

Vincent https://www.wendangku.net/doc/aa5559868.html,u (M’98–SM’01–F’11)obtained B.Eng (Distinction 1st Hons)from the department of EEE,University of Hong Kong,in 1992.He joined the Hong Kong Telecom after graduation for 3years as system engineer.He obtained the Sir Edward Youde Memorial Fellowship,Rotoract Scholarship and the Croucher Foundation Scholarship in 1995and studied for Ph.D.at the University of Cambridge,U.K.He completed the Ph.D.degree in 2years and joined the Bell Labs—Lucent Technologies,New Jersey,in 1997.

He joined the department of ECE,Hong Kong University of Science and Technology (HKUST),Clear Water Bay,in 2004and is currently a Chair Pro-fessor.He has been the technology advisor and consultant for a number of companies such as ZTE and Huawei,ASTRI,leading several R&D projects on B3G,WiMAX and Cognitive Radio.He is also the founder and director of

Huawei-HKUST Innovation Lab.His current research interests include inter-ference mitigation,stochastic optimization,and compressive sensing.

Professor Lau has published over 300papers,including around 150IEEE Transaction papers,and contributed to over 40U.S.patents on wireless systems.In addition,he is also the key contributor of 4IEEE standard contributions which are accepted into the IEEE 802.22speci ?cation.He is also a Fellow of IEEE,Fellow of HKIE,Changjiang Chair Professor and the Croucher Senior Research

Fellow.

Moe Z.Win (S’85–M’87–SM’97–F’04)received both the Ph.D.in Electrical Engineering and the M.S.in Applied Mathematics as a Presidential Fellow at the University of Southern California (USC)in 1998.He received the M.S.in Electrical Engineering from USC in 1989and the B.S.(magna cum laude )in Electrical Engineering from Texas A&M University in 1987.

He is a Professor at the Massachusetts Institute of Technology (MIT)and the founding director of the Wireless Communication and Network Sciences

Laboratory.Prior to joining MIT,he was with AT&T Research Laboratories for ?ve years and with the Jet Propulsion Laboratory for seven years.His research encompasses fundamental theories,algorithm design,and experimentation for a broad range of real-world problems.His current research topics include net-work localization and navigation,network interference exploitation,intrinsic wireless secrecy,adaptive diversity techniques,and ultra-wideband systems.Professor Win is an elected Fellow of the AAAS,the IEEE,and the IET,and was an IEEE Distinguished Lecturer.He was honored with two IEEE Tech-nical Field Awards:the IEEE Kiyo Tomiyasu Award (2011)and the IEEE Eric E.Sumner Award (2006,jointly with R.A.Scholtz).Together with students and colleagues,his papers have received numerous awards,including the IEEE Communications Society’s Stephen O.Rice Prize (2012),the IEEE Aerospace and Electronic Systems Society’s M.Barry Carlton Award (2011),the IEEE Communications Society’s Guglielmo Marconi Prize Paper Award (2008),and the IEEE Antennas and Propagation Society’s Sergei A.Schelkunoff Transac-tions Prize Paper Award (2003).Highlights of his international scholarly initia-tives are the Copernicus Fellowship (2011),the Royal Academy of Engineering Distinguished Visiting Fellowship (2009),and the Fulbright Fellowship (2004).Other recognitions include the International Prize for Communications Cristo-foro Colombo (2013),the Laurea Honoris Causa from the University of Ferrara (2008),the Technical Recognition Award of the IEEE ComSoc Radio Commu-nications Committee (2008),and the U.S.Presidential Early Career Award for Scientists and Engineers (2004).

Dr.Win was an elected Member-at-Large on the IEEE Communications So-ciety Board of Governors (2011–2013).He was the Chair (2004–2006)and Secretary (2002–2004)for the Radio Communications Committee of the IEEE Communications Society.Over the last decade,he has organized and chaired numerous international conferences.He is currently an Editor-at-Large for the IEEE W IRELESS C OMMUNICATIONS L ETTERS .He served as Editor (2006–2012)for the IEEE T RANSACTIONS ON W IRELESS C OMMUNICATIONS ,and as Area Editor (2003–2006)and Editor (1998–2006)for the IEEE T RANSACTIONS ON C OMMUNICATIONS .He was Guest-Editor for the P ROCEEDINGS OF THE IEEE (2009)and for the IEEE J OURNAL ON S ELECTED A REAS IN C OMMUNICATIONS (2002).

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University of California, Santa Barbara ME/ECE 141 B Alignment In order to make useful devices the patterns for different lithography steps that belong to a single structure must be aligned to one another. The first pattern transferred to a wafer usually includes a set of alignment marks, which are high precision features that are used as the reference when positioning subsequent patterns, to the first pattern (as shown in figure 1). Often alignment marks are included in other patterns, as the original alignment marks may be obliterated as processing progresses. It is important for each alignment mark on the wafer to be labeled so it may be identified, and for each pattern to specify the alignment mark (and the location thereof) to which it should be aligned. By providing the location of the alignment mark it is easy for the operator to locate the correct feature in a short time. Each pattern layer should have an alignment feature so that it may be registered to the rest of the layers. Figure 1: Use of alignment marks to register subsequent layers Depending on the lithography equipment used, the feature on the mask used for registration of the mask may be transferred to the wafer (as shown in figure 2). In this case, it may be important to locate the alignment marks such that they don't effect subsequent wafer processing or device

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宿舍有个家伙，老不告我一声，就乱动我的东西，比如倒我的开水啊，用我的牙膏啊之类，说他吧，显得我小气吧啦的，不说吧，实在憋得慌。 最近觉得父母很罗嗦，老关心学习啊，上大学之类，好像我不知道学习重要似的，唉，是他们到了更年期，还是我到了更年期了？ 我觉得我不太喜欢问老师问题，喜欢自己解决，但现在有许多题目不会，周围人也没有人问，我真的没有那个勇气。 我们班的某老师讲课太快了，许多人都听得迷迷糊糊的，而且作业留得也多，我都快受不了了。但是他好像没感觉，依然那么投入。 请学生回答、交流。 小结：最终所有的措施都要回归到到一点，就是大胆主动地进行沟通，事情才可能真正得以解决。 任何人都不会无缘无故地喜欢我们、接纳我们。我们首先主动敞开心扉，接纳、肯定、信任他们，保持主动性，这样别人才会同样对待我们。你希望别人怎样对待你，你就应该首先这样对待别人。主动积极的态度，这是人际沟通的首要前提。 二、倾听反馈 情境创设：人际沟通和交流中，是不是胆子大一点，主动一点就行了呢？还需要什么注意事项呢？请一位学生回答。 备用：也可以请学生念下段文字。 上帝给人们两只耳朵，一张嘴，其实就是要我们多听少说。多听少说，善于倾听别人讲话是一种高雅的素养。因为认真倾听别人讲话，表现了对说话者的尊重，人们也往往会把忠实的听众视作可以信赖的知己。而我们许多人的特点是好表现自己，普遍存在着喜欢别人听自己说，而不喜欢听别人说的问题。 那么，如何培养倾听的习惯？即做到：一要专心，无论是听课，还是听同学发言，都要认真听对方说的每一句话，脑子里不想其他事；二要耐心，不随便插嘴，要听完别人的话，才发表自己的意见；三要细心，当别人的话有错时，要求会评价对方，做到不重复他人的意见。四要虚心，当别人提出不同的意见时，要能虚心接受，边听边修正自己的观点；五要用心，在听取他人意见时不能盲从，要有选择地接受。

用心沟通,做客户的贴心人

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监控系统安装流程(视频监控安装教程)

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4、设备散热通风：控制设备的工作环境，要在空调室内，并要清洁，设备间要留的空间，可加装风扇通风。 5、检测对地电压：监控室内，电源的火线、零线、地线，按照规范连接。检测量各设备“外壳”和“视频电缆”对地电压，电压越高，越易造成“摄像机”的损坏，避免“带电拔插”视频线。 C、摄像机的安装 1、监控安装高度：室内摄像机的安装高度以2.5～5米,为宜，室外以3.5～10米为宜;电梯内安装在其顶部。 2. 防雷绝缘：强电磁干扰下，摄像机安装，应与地绝缘;室外安装，要采取防雷措施。 3、选好BNC：BNC头非常关键，差的BNC头，会让你生不如死，一点都不夸张。 4、红外高度：红外线灯安装高度，不超过4米，上下俯角20度为佳，太高或太过，会使反射率低。 5、红外注意：红外灯避免直射光源、避免照射“全黑物、空旷处、水”等，容易吸收红外光，使红外效果大大减弱。 6、云台安装：要牢固，转动时无晃动，检查“云台的转动范围”，是否正常，解码器安装在云台附近。

用心与学生沟通

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用心沟通作文

用心沟通作文 用心沟通作文1： 沟通这两个字对我们每个人来说都很熟悉，它不仅是人和人之间连接心的桥梁，也是人与外界交流的纽带。正是因为某些人忽略了它，所以觉得人生乏味，变得孤独，缺乏自信。 我妈妈就是一个这样的人。在我读大班时，她为了能够更好地照顾我，辞去了工作，专心辅导我的功课和生活起居，每次我在学习 上碰到困难的时候，她都会耐心的给我讲解，晚上我和爸爸回来更 是还有一桌丰盛的晚餐等着我们。她还经常和我们聊天、谈心。 因此我们需要沟通，沟通能带给我们快乐和幸福，能够拯救一个孤独的灵魂，一个孤独的人生。 用心沟通作文2： 威廉·费尔普八岁的时候，和父母一同去林兹莉姑妈家中度假。 一天晚上，有位客人来访。客人看上去非常喜欢他，于是问：“告诉我，你最喜欢什么?” 于是客人就和他谈笑风生，大谈特谈船的知识。客人临走时，威廉依依不舍地和他道别。 虽然客人走了，但威廉意犹未尽，兴高采烈地对姑妈说：“您发现没有，林兹莉姑妈，这位先生真是好得没治了，没想到他和我一样，也喜欢船。” “可是为什么他说的话全都和船有关啊?”威廉有些糊涂了。 姑妈意味深长地说：“那是凶为他人格高尚，他见你对船感兴趣，所以就专门谈能够使你高兴的话题，以便得到你真心的欢迎。” 到什么山头唱什么歌，选对了话题，就等于友好地握住了对方的手，不是吗?

用心沟通作文3： 在闲暇之中，翻开散着墨香的书页，端一杯水，营造出淡淡的书香味，细细地回顾过去，其实与书沟通，乐趣也是妙不可言的。 习惯了人与人之间的沟通，就想拥有一份宁静的交流，你可以与书交流。让它点亮你心中的那灯吧! 我喜欢与书沟通，它让我明白‘一日无书，百事荒芜。’的习惯，让我品味到‘问渠哪得清如许，唯有源头活水来’。的读书之乐。 有一次，我边吃饭，边看书，看得十分投入，仿佛自己也身临其境了，天意弄人，我阴差阳错地夹起一片姜，把我辣得满头大汗。 但从此以后我变得更加爱看书了。 书给予我的，不单单是体会，更多是人生的启迪。 我失败时，书教我勇敢地面对，勇往直前，把失败看作成功的起点，它把我带到成功的彼岸。当我成功时，他叫我再接再厉。与书 沟通，你的生活会更美好。书像一个无声的世界，让我辨清善，恶，美，丑。

用心沟通 平等对话

用心沟通平等对话 ——英语课堂突发案例剖析 【事件回放】 期中考试后的第一个星期三，上午第二节课铃声响起时，作为英语老师的我，站在教室的讲台前，准备上课。上课铃音乐结束后，我和同学们打完招呼，便准备开始今天40分钟的英语学习。因为考虑到现在的孩子们英语学习中有投机主义思想存在，在上次英语课下课时布置作业，我只是强调了上次课堂上学习的两篇小短文要会背诵，但是没有告诉学生，今天的课一定会抽查。为了检查学生课下英语的复习情况，我抽查了近10位同学。在我看来，这10位同学在班级里算是对英语学科学习很感兴趣的。但是抽查的结果令我很意外，只有3位同学顺利的背诵了出来，有一位同学还是在老师每句话第一个单词都给出提示的情况下，才基本背诵出来。我的心里顿时也觉得很失望、很难过，但我还是强压着心里的不满，在第10个同学坐下后，说道：“我们有的学生很虚伪，在老师面前摆出很上进很要学习的样子，但是，只要老师一离开他们的视线，便把学习的事情远远地抛在了脑后。”说完，我便开始继续上课。突然，一位男生高举着手，站了起来。我一开始看见他站起来的时候，还以为是他要上洗手间，心里想：毕竟这是第一节课，和早自习、早操连在一起，没时间上厕所也情有可原，所以心里这样想着，便打算说：“好的，你去吧！”可我的话还没说出口，同学Z便开口道：“老师，你真的觉得我虚伪吗？我觉得我不虚伪的啊……”看着他那张委屈的脸、听着他颤抖的声音，我知道，我的话对他产生了很大的伤害。他继续说着：“其实，我上初中的时候，老师就说过我说瞎话（撒谎）……”哽咽的太厉害了，再加上其他同学都在劝他：“别哭了，别哭了！”此时的他，边嘟哝着边拿着纸擦眼泪，整个人已经不是站在那里，而是扒在课桌上。那时的我，其实心里的感受不知道该如何描述：内疚？感动？欣慰？……真的找不词来形容，但有一点是肯定的，我的眼睛是热热的，但全班人的课堂还是要继续，所谓我安慰到：“快坐下吧，真的很对不起，老师说的话让你这么难过，真的对不起！老师的意思是，不但要有学习的决心，更要有学习的行动。对不起了，可能是老师措辞不当，好好听课吧！”说着，我满脸微笑向他道了歉，希望他能静下来继续认真听课。 【策略措施】 1、放下师道尊严，真诚道歉。“人非圣贤，孰能无过？”承担着当代教育使命的教师，我 们更要有承认错误的勇气，这也是用教师自身的实际行动来教育着现在的孩子们。成长的过程，总是伴随着一次又一次失败的体验，也正是从失败的体验中，我们才从呱呱坠地的那刻起，收获着成长。所以，错了并不是关键，关键在于敢于不敢于承认错误、认真对待并改正错误。所以，作为教师的我，在学生Z反应出情绪的时候，便意识到自己的言语已经触动甚至是伤害了孩子。于是，我很虔诚地跟学生Z连续说了不少于三个对不起，真心地对不起。因为我知道，此时老师的对不起，一定会让孩子的内心得以舒缓，敢于面对他的内心世界。 2、尊重学生人格，细心呵护。不论年龄，不论智商，不论家庭背景，不论健康与否……， 我们身边的每一个人，都应该是一个大写的“人”字，特别是在青少年时期，这个大写的“人”必须被高度的重视，也只有这样，作为教育工作者的我们，才能培养将来合格甚至是优秀的社会人。在学生Z身上，我看到了美好的一面。他坦率而真诚，从他的泪水里，我感觉到他的是非观，知道“虚伪”不是一件值得倡导的事情。那时候，我的脑海里又想起拉那个身背13条人命的杀人狂成瑞龙，他青少年时期被“暴力”开除、不得不走入社会大染缸的事实，让我明白这个时期的孩子太需要人格的尊重、需要我们用心呵护。当然，我知道，学生Z不至于那样，但我也不希望这课堂里的一个小小事件折射出的一系列问题，被我轻易忽视，不希望他这样的心理在将来走向的社会生活中，被

沟通从用心开始

沟通从用心开始 初入学校，新接班级，遇到46个活泼可爱的孩子。在跌跌撞撞中，我也慢慢转换角色，在上课、执勤、备课、午休等事情中忙忙碌碌着，体会着教师生活的充实和精神上的满足。二年级的孩子认知上还不成熟，所以他们在心理上会更多的依赖老师，怎么跟孩子都沟通，到底是严多一点还是柔多一点，我一时有点拿捏不好。 刚开学的第一周，整体感觉孩子们大部分很乖，上课瞪着小眼睛看着老师，几乎没有交头接耳的孩子，我私下很高兴，想到接了一个很好管教的班级应该是件幸福的事。可是在批改孩子们的练习和作业中，我慢慢发现孩子们只是一味的听课，并没有多动脑筋去思考，学过的知识在做题的时候除了几个基础好一点的孩子会举一反三，大部分孩子还是不能做到。了解到这一点，在后面的上课中，我有意引导孩子去思考去自己发掘，但是大部分孩子表现的很一般，表现的兴趣也很淡，也许他们已经习惯被动接受，我内心压力很大，在冷静思考和寻求班主任了解情况后，我决定平静下火气和急躁的心来，用心沟通试试，我拿着练习册和作业找到相关孩子，一个个地聊，了解到他们的心里怎么想的，然后加以开导和鼓励。慢慢第二周我发现，班里许多孩子在不做一些拓展思路或者动脑筋的题，惩罚他们的效果远不如加以鼓励的效果，经过我单聊的孩子在课堂上明显提升了积极思考积极性，在做作业时，做题的正确率也提高了很多。初步掌握住感觉后，我尝试在课堂上和课下利用课间操回来和吃饭前的时间，开始抓

班中基础较弱的孩子，这些孩子本身上课有些注意力不集中，课下做作业也是不太上心。多给他们一些时间和耐心，用心给他们讲解，这些基础弱的孩子进步较慢，但是这些孩子态度慢慢上来了。 沟通从用心开始，相信每个孩子都有自己的闪光点，只是有些孩子基础好，有些孩子基础弱。让孩子在一种轻松的环境中能主动学习这要比简单的教学要艰难的多。培养起孩子们这种习惯，靠简单的急躁和发火只会让孩子离老师越来越远，所以用心沟通，让孩子愿意靠近老师，也更愿意听老师的教导，愿意去主动学习，赢得老师的表扬。

用心沟通

沟通从心开始——用一颗真诚的心去待人处事 “沟通”代表人相互之间理解和信任。“从心开始”表明用真心和真诚筑起心与心之间的桥梁。“从心开始”是沟通的基石和最高境界，只有用真心、用真诚去传情达意，才能使彼此的交流更为顺畅、更为精彩。 在我们日常生活于工作中，做人要用心，用心去感受别人做的事，用心去对待他人。当看到你的朋友产生误解的时候，走上前去把误会解除；当朋友在生活中资源紧缺、生活拮据时，尽自己所能对他施以援手，助其度过难关；当同事焦头烂额的忙于棘手的事情时，不是有句老话叫：“三个臭皮匠抵过一个诸葛亮”，及时帮他出谋划策，他将对你感激不尽。这些我们在生活中处处可见的事实，都是用心去沟通最好的例证。 大家在广告中常见到这样的标语——沟通从心开始。这是中国移动的企业定位，“沟通从心开始”，既是对中国移动历史和现实的写照，也是对未来发展的牵引；既是一种经营方式，也是对社会风尚的倡导。这简简单单的六个字同样可以作为我公司每位员工的警示牌，只要我们每个人从内心去沟通，去做事，才能被领导认可，让领导在第一时间掌握工作进展状态，尽早得到领导的帮助和指点，及时发现工作中存在的问题和不足，并提出指导性的意见。只有有效的沟通，才能上下一致、齐心协力，提升工作效率，把公司越办越强。 那么我们日常工作中有哪些不当的沟通例子？怎样做才是有效的沟通呢？ “如果您的意思正是这样，那又为何不这么说？” “我希望他们把话说明白点。” “我不敢肯定自己该做什么。” “他（她）开玩笑时，我希望能明白。” “我实在没听明白。”“恩，应该是这样”等等，这样的一些例子，我们耳熟能详。当我们意识到某件事情没做好时，我们总会把它归因于“思维混乱”所致，可是，却忽略了“沟通”的重要性，是无效的沟通让我们词不达意，语焉不详。要铭记：别人不理解你的话是你没表述清楚而非他人不理解，如果你表述的很清楚，都不是三岁小孩，又有谁理解不了呢？有了问题，请“自省、反思”，这也是我们工作中应当时刻注意的。 同时防止沟通障碍，也是我们需要注意的。那么我们就应当树立正确的印象，一要注意外表：着装时不拘礼节表明您要么对交流沟通的另一方漠不关心，要么您想先声夺人。破烂的牛仔裤和邋里邋遢的运动鞋与笔挺气派的西装给人以截然不同的印象。根据场合的不同，两种着装风格都会给人以完全错误的信息。二要注意措辞：不假思索地使用乡言俚语会得罪他人，也会扭曲信息。举个例说，私下里把顾客或主顾叫作“伙计”似乎给人以一种哥们义气的感觉。但它也不知不觉地传达出对别人的轻慢。三要注意拖沓：不准时赴约表明您不把别人当回事。如果某人守时，别人就会认为他很在意，把别人放在心上，但如果总是迟到，就会给人这样的印象，即沟通的内容是不重要的。 所以要做到有效的沟通，首先注意着装，准确用语，具备正确的时间观，其次与人交流要控制自身情绪，不能意气用事。同时不可主观臆断，完全的不主观是不可能的，但要尽全力避免。再次就是要善于聆听，要用心去考虑对方的感受，做到换位思考，也就是俗话说的：“要是换了你怎么办”。当然最重要的就是要建立良好的沟通氛围，不是有句老话叫：“伸手不打笑脸人”，只要我们时时微笑待人，那么我们将会领略别人的善意。

视频监控系统控件安装(从IE访问)

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The Lifetime Reliability Solutions Certificate Course in Maintenance and Reliability Module 4 – Precision Maintenance Techniques for Machinery Session 18 Machine Installation – Shaft Alignment 1. Introduction There is no dispute between vibration and reliability trainers, practitioners and commentators that misalignment, and related problems, is the principal cause of problems in rotating machinery. It is generally accepted that this is in the order of 50% of adverse vibration cases, it will of course vary from industry to industry. Attention to alignment issues alone would be a very productive place to start any reliability programme. Unlike bearings, there are no published standards for alignment tolerances. Those that have been prepared have been by industry interest groups, such as API, or by trainers who have had access to a wide input from industry as to what is effective and produces worthwhile results. A popular misconception is that flexible couplings will accommodate misalignment without detriment to other components in the machine, and adopt those criteria. The criteria given for couplings is related to the transmission of the rated torque, they give no consideration to the bearings or seals etc. There are numerous problems which have an influence upon the final alignment result and it is important to address these. Where these other issues have not been attended to an alignment task can take many hours longer than one where they have been, and the final result is most probably not so good or enduring. There is a truth that correcting the contributory problems is probably more important, and ultimately profitable, than the actual alignment itself. This session will look at these related problems and at the techniques of alignment. 30-40

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子讨论并评价这些事情，站在各个角度去分析这些事情。这样时间长了，就会提高孩子判断问题和分析问题的能力，并且还能养成善于观察的习惯，另一方面还锻炼了他的语言表达能力。只要这样坚持经常和孩子谈话，他会觉得你很关心他学校的生活，他会把他在学校的喜怒哀乐都告诉你，你也就可以对他进行适时的指导。我觉得对自己的孩子要做到“三个知道，一个跟上”即知道孩子在干什么、怎么干的、干的怎么样，表扬要跟上。 二、做好与孩子的学校、老师的沟通，共同做好孩子的教育 我们家长的如何配合学校和老师做好对孩子的教育工作，是相当重要的。首先我们家长对孩子的教育问题要有一个正确的认识，对孩子的教育不能单纯依靠学校教育来完成，而必须同时依靠学校教育、家庭教育和社会教育的通力合作。学校教育是一对多的教育，一门课的老师在课堂上对几十个孩子讲课，努力想让讲的内容使每个孩子都能理解，但是，不可能说老师对每个孩子都面面俱到地了解和帮助，这需要时间，这样我们就不能对老师过分苛求，应该努力在孩子心目中树立老师的形象，这一点非常重要。如果我们能够坚持这样树立老师在孩子心目中的地位，孩子就会觉得他的老师很了不起，他就会认真地接受老师的教育，学习成绩也就会更好。家长们可能都有体会，老师说一句话，胜于家长说十句。而且家长的文化程度各不相同，即使文化程度高的家长，但我们小时候受的教育和现在的孩子不同，有时孩子的题目连家长一时都做不出来，所以孩子文化知识的教育主要还得依靠老师和学校。然而家庭教育又有学校教育无法替代的优势。家庭教育是多对一的教育，而且孩子在家里的时间也更长，所以