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Realistic propagation simulation of urban mesh networks

Realistic propagation simulation of urban mesh networks
Realistic propagation simulation of urban mesh networks

Realistic Propagation Simulation of Urban

Mesh Networks

Vinay Sridhara Stephan Bohacek

vsridhara@https://www.doczj.com/doc/633010012.html, bohacek@https://www.doczj.com/doc/633010012.html,

Department of Electrical and Computer Engineering

University of Delaware

Newark,DE19716

Abstract

Simulation plays an important role in the veri?cation of mobile wireless networking protocols.Recently several cities have either begun deploying or are completing plans to deploy large-scale urban mesh networks(LUMNets).

On the other hand,the networking research community has little expertise in simulating such networks.While the protocols are simulated reasonably realistically,the propagation of wireless transmissions and the mobility of nodes are not.Today,simulations typically model propagation with either the free-space model or a"two-ray"

model that includes a ground re?ection.Such models are only valid in open space where there are no hills and no buildings.Since wireless signals at the frequencies used for mobile wireless networking are partly re?ected off of buildings and partly is transmitted into the building,the presence of buildings greatly in?uences propagation.

Consequently,the open-space propagation models are inaccurate in outdoor urban areas.Indoors,the open-space models are not even applicable.This paper presents guidelines for simulating propagation in such urban settings.

Furthermore,extensive background discussion on propagation is also included.The techniques for propagation are validated against propagation measurements.The techniques discussed are implemented in a suite of tools that are compatible with protocol simulators and are freely available for use.

Stephan Bohacek is the corresponding author.His address is University of Delaware,Dept.of Electrical and Computer Engineering,Newark, DE19716,USA,302-831-4274,bohacek@https://www.doczj.com/doc/633010012.html,.

I.I NTRODUCTION

Recently,there has been interest in developing protocols for urban mesh networks such as the ones to be deployed in Philadelphia[1],San Francisco[2],Taipei[3],Minneapolis[4],Anaheim,California,and Tempe, Arizona.Simulation is the common technique to determine the performance of these protocols.However,today, most simulations use the trivial disk propagation model(i.e.,the signal propagates exactly R meters and no further)or a highly idealized propagation model such as the free-space or the two-ray model.Due to the presence of buildings,propagation in urban environments is far more complicated than the propagation presented by these simple models.Consequently,channel variability,which is a key aspect of wireless networking,is not well modeled in today’s simulations.The result is that many insights gained from the free-space environment do not necessarily hold in the urban environment,casting doubt on the applicability of the conclusions drawn from today’s simulations. While the reasons that realistic propagation models are typically not included into network simulations is not well documented,it seems that the typical reasons include the belief that propagation modeling is computationally intractable and that propagation cannot be realistically modeled due to small-scale fading and delay spread.To the contrary,this paper demonstrates the feasibility of including realistic propagation into network simulation.To this end,a simulator has been developed in accordance with the guidelines set forth in this paper[5].This simulator is validated in three scenarios and it is shown that when used with packet level simulation,realistic propagation has a dramatic impact on simulation results.Furthermore,while realistic propagation is computationally intensive,the computational complexity of the approach taken here results in the propagation aspects of the typical simulation taking approximately as long as the processing of the discrete events by the packet simulator.Consequently,this paper provides techniques and methods for greatly improving the quality of simulations.

In order to justify the simulation strategy used,an overview of the key features of propagation in an urban environment is presented.This nonmathematical discussion of propagation also provides networking researchers with an intuition of propagation in urban environments.For example,some of the myths that can be found in the networking literature are dispelled,and issues that are neglected in the networking literature,such as the importance of building materials,are discussed.

The remainder of this paper proceeds as follows.In the next section,stochastic models of propagation are discussed.While stochastic models are often used in communication theory,their applicability to networking is

limited,and,as will be discussed,they should be used with care.In contrast,the propagation simulator discussed here is deterministic.Section III discusses several characteristics of propagation.Speci?cally,the subsections of Section III discuss transmissions through walls,re?ections off of walls,multipath fading,diffraction,scattering,time-varying channels,and delay spread.Section IV discusses computational issues,discusses details of the UDelModels’propagation simulator,and presents validation of the simulator.Section V provides some discussion on the impact that realistic simulation has on the performance of networking protocols.As one might expect,traditional simulations that use random way-point mobility and free-space propagation yield very different results than the simulations carried out using realistic mobility and propagation.It is important to note that realistic simulation of wireless networks is an ongoing effort and that as the computational capabilities increase,more detailed and accurate simulations are possible.Some areas that will bene?t from further effort and improved accuracy are discussed in Section VI.Related work on propagation simulation is provided in Section VII and?nally,concluding remarks can be found in Section VIII.

II.S TOCHASTIC M ODELS OF P ROPAGATION

One of the most important aspects of propagation is the channel gain(other characteristics are discussed below). The objective of propagation simulation is to determine the channel gain(and other channel characteristics).The physical layer model then uses these channel characteristics to determine the probability of transmission error. The relationship between the received signal power P received and transmitter signal power P transmitted is P received= K×H×P transmitter,where K is a constant that depends on the wavelength and the antennas,and H is the channel gain.It is common for this relationship to be speci?ed in dB1and dBm(dB milliWatts),i.e.,

P received[dBm]=10log10K+H[dB]+P transmitter[dBm].

To get an idea of common values,consider the typical802.11b transmissions.In this case,the transmission power is15dBm and10log10K=?41dB.Furthermore,the sensitivity of commercially available802.11b receiver cards is approximately-93dBm when receiving at1Mbps.Thus,if the channel gain is lower than-67dB,then it is not possible to decode the transmission with marginal reliability.It is also common to require an extra gain 1For the remainder of the paper,we specify channel gains in dB.

margin to allow for the signal to be decoded reliably(not simply marginally reliability),to account for losses due to connectors and other analogue circuits,and to allow for overly optimistic sensitivity speci?cations.The gain margin depends on the transmitter/receiver manufacturers and system design,and can range from3dB up to9dB, which require the802.11b communication channel gains to be above-64dB and-58dB respectively.

The propagation of wireless signals can be accurately modeled by Maxwell’s Equations.However,it is beyond today’s computational abilities to simulate large urban regions using these equations.For this reason,there has been extensive research effort on developing techniques that provide computationally tractable estimates of the channel gain and other characteristics.In general,the techniques can be classi?ed into deterministic and stochastic models. Furthermore,they can be divided into site speci?c approaches(i.e.,detailed information about the environment is included into the propagation model)and non-site speci?c approaches.As discussed next,for simulation of urban mesh networks,deterministic site speci?c propagation models are appropriate.

We can easily rule-out deterministic non-site speci?c approaches such as the Okumura-Hata model[6]or COST 231[7].Such models provide a relationship between the channel gain and the distance between the receiver and transmitter.However,these models only provide an average behavior and do not model the variability of the channel. On the other hand,non-site speci?c stochastic models can account for channel variability and hence are widely used in communication theory.However,there are many pitfalls to stochastic models which often make them not applicable to urban mesh network simulation.Consider the well established lognormal shadowing model[8].This model speci?es that the received signal power obeys

P received=K

×Y×P transmission,(1)

where K is a constant,d is the distance between the transmitter and receiver,αis the attenuation factor,P transmission is the transmitted power,and Y is a lognormally distributed random variable that accounts for shadowing.This model dictates that if a transmitter and receiver are placed at randomly selected locations,then the relationship between distance,transmitted power and received power obeys(1).While the model has been veri?ed through experimentation,the model focuses only on a single link.On the other hand,in networking,the interest is on a large number of links,speci?cally,the focus is on the graph formed by links.If the relationship between received and transmitted signal strength merely obeys(1),then the graph formed by links would be a type of a random

Strongest signal

Weakest signal

Fig.1.Left,channel gain generated by a correlated lognormal model.Right,channel gains generated by ray-tracing in an urban area.The rectangle shapes are buidlings and the shaded boxes inside the rectangles represent channel gain to locations on the?rst?oor of the building. In both the left and right frames,the star marks the location of the transmitter.

graph,whereas an urban setting induces a graph with deterministic components.Consider the left and right frames in Figure1.The left-hand frame shows the channel gains(including correlations as described in[9]and[10])when a lognormal shadow fading model is used,while the right-hand shows the channel gains in an urban area that is found through the techniques described in the next sections.While it is reasonable to assume that even in the urban setting,if two arbitrary locations are selected,then the signal strength will follow the lognormal distribution(i.e., (1)is valid),it is quite clear that channel gain is not random.Rather,the channel gain is greatly in?uenced by the map of the urban area.For example,the signal propagates far down the streets,while it propagates poorly into or through/over buildings.To see the implication of this,consider the least-hop path shown in Figure2.In this example,only the?rst and last hop are able to propagate between indoor and outdoor,while other hops follow streets(outdoor to outdoor propagation).Thus,we see that the propagation results in routes in urban areas that are not random,but are dependant on the structure of the city.For this reason,we do not use non-site speci?c models, and focus on site-speci?c models where the layout of the city and buildings in?uences the propagation.Currently, the UDelModels’propagation simulator is deterministic.However,future work will include appropriate stochastic elements.

Fig.2.Routing in an Urban ad The shortest hop path travels along the road,it does not follow the shortest geometric route(i.e.,a straight line).

III.C HARACTERISTICS OF U RBAN P ROPAGATION

A.Overview

In the next subsections,several characteristics of propagation are brie?y discussed.The objective is to provide intuition of propagation in urban environments.While there are mathematical models of propagation,we do not provide any mathematical details.An excellent reference that contains mathematical details is[11].

Remark1:We typically focus on the propagation for a particular transmitter and receiver.However,due to reciprocity(e.g.[12]),the channel between two antennas does not depend on which one is the transmitter and which is the receiver.To some degree,the symmetry of channels contradicts the observed asymmetry of links(e.g., [13]and[14]).It is important to note that the observed asymmetry of links is not due to the channel but due to difference in the analogue electronics in the transmitters and receivers.These differences may result in unequal transmit powers and unequal receiver attenuation.In some cases,these differences can be reduced by calibrating the transmit powers.It is also possible that one node experiences more interference than another node.In this case, the probability of error-free packet transmission depends on which node is the transmitter.

B.Transmissions

In urban mesh networks,re?ections off of objects such as buildings and the ground and transmission into buildings play a primary role in the magnitude of the received signal strength.Diffraction and scattering are also important, but from numerical experiments it can be shown that they play a secondary role.When the object that the signal is hitting is much larger than the wavelength,then the behavior of the signal can be accurately modeled as a ray that

is partially re?ected off of the object,partially transmitted through the object,and partially absorbed by the object.

If this ray model is accurate,then there are well known formulas that describe the behavior(e.g.,see[11]).In gen-

eral,the re?ection can be written in terms of six components,H⊥Transmit(θIncidence,εr,ε00r,w,f),H⊥Re?ect(θIncidence,εr,ε00r,w,f),

H⊥Absorb(θIncidence,εr,ε00r,w,f),H k Transmit(θIncidence,εr,ε00r,w,f),H k Re?ect(θIncidence,εr,ε00r,w,f),and H k Absorb(θIncidence,εr,ε00r,w,f) whereθIncidence is the angle between the ray and the material,ε0r andε00r are the real and imaginary part of the

relative dielectric constant of the material,w is the width of the material,f is the frequency of the signal,and the superscript denotes the polarization.

Instead of detailing how each of these factors impacts the propagation,we will consider an example.We examine

the received signal strength on one side of a wall with a transmitter on the other side as shown in left-hand frame

of Figure3.We consider the received signal strength in two locations,speci?cally,one at the same height as the transmitter and one elevated from the transmitter.We assume that the signal strength decays according to free-space propagation and then intersects the wall and suffers insertion loss H k Transmit(where we assume that the wireless

signal is vertically polarized,hence the k superscript).We take the frequency to be2.4GHz,as in802.11b/g.

Three types of wall materials are examined,namely,brick(ε0r=3.9,ε00r=0.001,w=10cm.),concrete(ε0r=5,

ε00r=0.2,w=20cm.),and glass(ε0r=5.8,ε00r=0.003,w=2.5cm.).The behavior for these materials is shown

in the right three frames of Figure3.

Many aspects of transmission through material can be observed in Figure3.First,notice how in the case where

the receiver and transmitter are at the same height,the channel gain increases as the distance between the transmitter

and received decreases.This agrees with the intuition from free-space propagation.The impact of the material can

be seen by noticing the variation in the received signal strength for different materials.For reference purposes,

consider that without the wall,when the transmitter is about5m from the wall,the channel gain is-14dB.from

the wall and a receiver that is at the same height as the transmitter.Thus,when the angle of incidence is0,the wall

reduces the channel gain by0dB(for glass)to6dB(for concrete).The impact of the angle of incidence can be emphasized by considering the channel gain when the transmitter and receiver are not at the same height.As can be

seen,this results in the signal strength?rst increasing and then decreasing as the distance between the transmitter

and receiver increases;this is in con?ict with the behavior in free-space.The key characteristic of propagation at

work here is that when the ray hits the wall at a grazing angle,only a small amount of signal power is transmitted

distance from wall

brick

concrete glass

c

h

a

n

n

e

l

g

a

i

n

(

d

B

)

Fig.3.Transmission through a wall.The?gure depicts the attenuation of the signal when transmitted through walls of different kinds of materials.It also depicts the nature of attenuation due to relative heights of the transmitter and the receiver.

through the wall.The point where the signal strength switches from increasing with the transmitter-receiver distance to decreasing with transmitter-receiver distance depends on the material,the thickness of the material,and the height of the receiver.

Remark2:One interesting implication of Figure3is that if an urban mesh network uses relays mounted on lampposts,then the lamppost are quite close to buildings.Thus,relays mounted on a lamppost on the far side of the street will provide better coverage of a building than a relay mounted on a lamppost on the near side of the street.We concluded that,in some cases,the angle of incidence can be more important than the transmitter-receiver distance.

Figure3shows variation of the channel gain due to the different building materials.The dependence on material poses a serious challenge for simulation.First,walls are typically not made of a single material,but of layers of material.It is,however,possible to extended the method to accommodate layers of different material(e.g.,see[15]) at the expense of computational complexity.A second and more serious problem is that it is not realistic to know the construction material for each building.This dependence on construction materials emphasizes the dif?culty of accurate prediction of channel gains and demonstrates why realistic simulation is more reasonable than accurate simulation.In the UDelModels,it is possible to specify different building materials,but it is assumed that the material is homogeneous for each building.

C.Re?ections

Re?ections are complementary to transmissions.However,it is important to note that some power is absorbed by the material,hence,the power transmitted through a wall and the power re?ected off of a wall do not necessarily

sum to the power of the incident signal and,depending on the material and angle of incidence,a signi?cant amount of energy can be absorbed.

To get an understanding of the impact of re?ections,we consider propagation down a building lined street,as shown in Figure4.Here the signal is repeatedly re?ected off of walls and,in a sense,focused down the street.This effect is sometimes referred to as propagation down an urban canyon.A similar effect can also arise in hallways and tunnels.The result is that the received signal strength is stronger when propagating down a street than it would be with the same transmitter-receiver distance but in free-space.

Figure4shows the channel gain down an urban canyon for the same set of materials considered above and the free-space approximation.Note that free-space predicts a substantially smaller received signal strength than the simulated received signal.For example,when the receiver-transmitter distance is300m.,the difference between the free-space and the model that accounts for re?ection ranges from13dB to5dB,depending on the material and the distance between the walls.Figure4also shows approximations of the channel gain given by1/dα,where, for a canyon width of7m.,α=1.38and a canyon width of35m.,α=1.47.It should be pointed out that it is often assumed thatα∈[2,4],however,as this simple example demonstrates,it is possible that for some paths we haveα<2.That is,while buildings may block communication,they may also enhance communication.

Note the lack of smoothness when the walls are made of brick and the width is35m(e.g.d=50).This is due to the wide variation in the re?ection coef?cient as the angle of incidence varies.Indeed,depending on the material and the width of the material,there may be some angles of incidence where no signal is re?ected.Such angles are called Brewster angles.In some settings,the wide variation of the re?ected signals strength as a function of incident angle results in large?uctuations in the total received signal strength for small movements of the receiver or transmitter antenna.This amounts to further sensitivity of communication on building materials.

D.Multipath Fading

It is well known that wireless signals can experience small-scale fading or multipath fading.Such fading results from the constructive and destructive interference of signals that follow different paths from the transmitter to the receiver.As a result,when the wavelength is small,a small displacement of the transmitter or the receiver will cause a change in the interference and hence a change in the received signal strength.While fast-fading is a signi?cant problem in many wireless systems,it is typically not relevant in wide bandwidth communications such as those often

010*******

010*******d c h a n n e l g a i n (d B )width = 7 m

width = 35 m Fig.4.Propagation down a street.The ?gure depicts the effect of propagation down an urban canyon for different wall materials,different attenuation exponents,and for the free space

used for data communications (e.g.,802.11).The reason is that the received signal strength is essentially averaged over the bandwidth,which,by de ?nition,is wide.The left-hand frame in Figure 5shows an example of the signal strength at various frequencies.Note that at some frequencies,the signal strength is quite low,even 40dB less than the mean signal strength of 0dB.A narrow bandwidth communication will experience such degradations in signal strength.However,when averaged over a suf ?ciently wide bandwidth,the average signal does not experience degradation.For example,the middle frame in Figure 5shows how the signal strength varies for small changes in position.Note that the narrow bandwidth signal experiences rapid and large ?uctuations,while the wide bandwidth case experiences much smaller variations.

In general,the wider the bandwidth,the less susceptible to fast fading.However,variation in signal strength also depends on the environment.The right-hand frame of Figure 5shows the variance of the received signal strength over a circle with one meter radius as a function of the bandwidth.Each curve is for a slightly different environment,but in all cases it is for propagating down the urban canyon as shown in the left-hand frame of Figure 4.Note that in general,the variance decreases as the bandwidth increases.However,the variance of the narrow bandwidth case and the rate that the variation decreases with the bandwidth depends on the environment.In all cases,the variance is quite small when the bandwidth exceeds 10MHz,while 802.11b has a bandwidth of 22MHz.It should be noted that there are other factors besides multipath re ?ections that could cause large changes in signal strength over small

020*********

-50-30-10

10Frequency ?2.4 GHz (MHz)

024680123

S i g n a l S t r e n g t h Position (m)V a r i a n c e o f S i g n a l S t r e n g t h

d=300 m width = 7 m d=100 m width = 7 m Narrow band Bandwidth (MHz)

Fig.5.Fast fading in narrow band and wide band communication scenarios.Left:the signal strength as a function of frequency for a narrow band signal propagating down an urban canyon.Middle:signal strength of a narrow and wide band signal as a function of receiver position perturbation when propagating down an urban canyon.Right:variance in signal strength due to change in receiver position as a function of bandwidth for when propagating down a urban canyon as shown in Figure 4.

changes in position,e.g.changes in antenna orientation.

E.Diffraction

While re ?ections and transmission play an important role in propagation,diffraction is also signi ?cant and should not be neglected.Diffraction allows the signal to "bend"around corners and over/around buildings.However,the diffracted signal will not be as strong as the original signal;the sharper the bend,the weaker the signal.Consider the examples in Figure 6,which use the Uniform Diffraction Theory [16],[17].The left-hand frames show the diffraction around a corner.The second from the left frame compares free-space propagation around the corner to free-space propagation with the added loss due to diffraction.The right-hand frames show diffraction over a building where two diffractions are required.In both cases,as h increases,the signal must make a sharper bend (i.e.,the diffraction angle increases)and,hence,more loss is incurred.It is important to note that the signal strength decreases quickly as h increases.From the right-hand frames in Figure 6,it can be seen that diffracting over a building that is only 5m.higher than the transmitter and receiver results in a channel gain that is too small for typical 802.11communication (recall the discussion in Section II),while diffracting around a single corner (left hand plots of Figure 6)might result in a suf ?ciently large channel gains for most 802.11communications.Indeed,our simulations indicate that for 802.11,diffracting around two corners results in loss that is typically too great for 802.11.

While diffracting around two or more corners leads to large losses,802.11might be able to communicate

70605040302002040

12090

6030

h (m)C h a n n e l g a i n (d B )With diffraction

Free-space only h (m)C h a n n e l g a i n (d B )0102030

40Fig.6.Diffraction around a corner (left)and over a building (right).As h increases,the signal strength decreases.The dashed lines show the signal strength if the loss was only due to free space propagation while the solid line shows the signal strength when the loss due to diffraction is also included.

effectively around a single corner.Consequently,a signi ?cant portion of the coverage area of 802.11is due to https://www.doczj.com/doc/633010012.html,ing the UDelModels’propagation simulator,it is possible to quantify the impact of diffraction.Table I shows the number of locations to which a particular transmitter is able to communicate when only line-of-sight is used,when line-of-sight and re ?ections/transmissions are used,and when all the components are used,namely,line-of-sight,re ?ections/transmissions and diffraction.The table also shows the difference in the coverage when different numbers of iterations are used.By the number of iterations,we mean the maximum number of re ?ections,transmissions,or diffractions that each ray may experience.We see that about 22%of the locations are missed if diffraction is not used.However,if only line-of-sight is considered,then 78%of the locations are missed.For these calculations,a map of the Paddington area of London was used and the transmitter and receivers were located

1.5m above the ground or above the ?oor.If the transmitter was higher (e.g.,a mobile phone base station),or transmissions with smaller channel gains can be received,then it is possible that diffraction could play a larger role than is illustrated in this example.

F .Scattering

Scattering is often used to refer to the impact of smaller unmodeled objects on the propagation,e.g.,lampposts,trees,vehicles,people,and of ?ce furniture.Scattering also accounts for the unevenness of building walls (e.g.,windows,doors,or facades).Without detailed knowledge of the location and dimension of small objects and without details of building walls,it is dif ?cult to include the effects of these types of scatterers into propagation simulation.Furthermore,the inclusion of such details greatly increases the computational complexity of propagation

TABLE I

C OVERAGE AN

D COMPUTATION TIME

simulation.As a result,relatively little work has focused on including scattering into propagation prediction.One exception is[18]where the impact of scatterers was examined.It was found that in dense urban environments,such scattering does not dominate.More speci?cally,at short distances,scatterers have little impact,but may have a some impact at greater distances(e.g.,in some cases the difference between prediction and measurements decreased from6dB to3dB when scatterers were included).On the other hand,in areas where building density is low(e.g., suburban areas),scatterers such as lampposts,tress,and vehicles may dominate the propagation.This is one reason why this paper focuses on the urban setting.

Scattering can also occur when a wireless signal propagates through vegetation.Indeed,if the vegetation is large and dense,the scattered signal dominates over the direct,non-scattered signal.Even when the vegetation is thin,as it usually is in urban areas,the vegetation can cause loss.At2.4GHz,vegetation causes a loss of approximately

0.2dB per meter of vegetation[19].It is also common to model diffraction over vegetation[20].

G.Time-Varying Channel Gain

While the variability of channel gain is greatly affected by the movement of the transmitter or receiver,the channel gain can also change when the transmitter and receiver are?xed,but objects in the environment move. The right-hand frame of Figure7shows the channel gain as a function of time for a receiver and transmitter as observed along a sidewalk during rush-hour in the city center of Philadelphia.As shown in the left-hand frame of Figure7,the transmitter was5.4m above the sidewalk,while the receiver was only1.2m above the sidewalk. While time-varying propagation is dif?cult to model,in[21],a diffusion-based model was developed that accurately models the variability shown in Figure7.However,more work is required to develop models in general settings.

30405060050100

observed data Time (s)

-C h a n n e l G a i n (d B

)

Fig.7.Left,experimental setup for measuring the time varying nature of propagation in a busy street in Philadelphia.Right,an observed time-series of the channel gain.

It should be noted that the time-varying propagation is due to mobility in the environment.

H.Delay Spread

As noted in sections III-B,III-C and III-E,the wireless signal may follow several different paths from the transmitter to the receiver.While one impact of multiple paths is that the signal may experience multipath fading,another result is that the multiple copies of the wireless transmission will be received at different points of time.Essentially,these multiple copies will interfere with each other.When this self-interference is considered as noise,it is clear that the effective SNR is decreased by the presence of these delayed copies.Since the traditional calculation of SNR considers delayed copies of the transmission as useful signal power,the traditional SNR might not be a good indicator of probability of transmission error.

A channel where multiple copies of the signal arrive at different times is said to have delay-spread.While there is no ideal metric of delay-spread,two common measures are the mean delay spread and the RMS delay spread (see

[8]page 199for de ?nitions).To explore the impact of delay-spread,consider Figure 8,which shows the relationship between SNR and bit-error probability for different amounts of delay spread for a simple 802.11b receiver and for a 802.11a receiver.Note that the bit-error probability of 802.11b is greatly affected by the delay-spread.Also,it is can be seen that for an RMS delay-spread of above 60ns.,which is quite common in an urban setting,the impact of the delay is quite severe.From measurements,it has been found that indoors,the RMS delay-spread is typically less than 50ns.,but outdoors,it can exceed 500ns.The dependence of delay-spread on the communication environment has been widely observed (e.g,[13]and [22]).It should be noted that the delay-spread typically increases with the distance between the transmitter and receiver [23].And therefore,roof-top con ?gurations such as those studied

in[13],which are able to propagate considerable distances due to the lack of obstructions at higher heights,are likely to experience large delay-spread values.As pointed out in[13],to predict the transmission error probability, in some cases,both delay-spread and SNR are required.

Incorporating the effects of delay-spread into wireless simulation poses signi?cant dif?culties.First,the mapping from RMS or mean delay-spread to transmission error probability is not well de?ned.It is possible to have a channel with high RMS delay-spread that yields lower transmission error probability than the one that has a lower RMS delay-spread and conversely.Second,RAKE receivers can be incorporated into receivers that can greatly mitigate the effects of delay-spread.However,the implementation of the RAKE receiver has a signi?cant impact on the performance.For example,[24]shows that high performance RAKE receivers can mitigate the impact of delay-spread,while less effective RAKE receivers will perform poorly when the delay-spread is large.Thus,it is dif?cult to make any conclusions about the effect of delay-spread on future mesh networks based on current receivers.

In anticipation of receivers more suitable for outdoor use,another alternative is to neglect delay-spread.Not only is such an approach reasonable when the inclusion of algorithms that mitigate the effect of delay-spread into802.11b receivers is anticipated,but also because other physical layers based on OFDM greatly mitigate the impact of delay-spread.Consider Figure8,which shows the relationship between SNR and bit-error probability for different values of RMS delay-spread when802.11a is used.Note that the impact of delay-spread is not discernible.Schemes such as802.11g and802.16use OFDM and hence are also relatively immune to delay-spread.In summary,while delay-spread can have a signi?cant impact on transmission error,there are a number of physical layer schemes that can mitigate these effects,and,considering the rapid migration between physical layers(e.g.,from802.11b to802.11g), it seems likely that when there is a need(i.e.,when outdoor mesh networks are?nally deployed)such schemes will become wide-spread.Therefore,depending on the assumptions made about the network being simulated,realistic simulation of future urban mesh networks does not necessarily require consideration of delay-spread.

IV.C OMPUTATIONAL T ECHNIQUES

A.Overview

While much is known about propagation,a major obstacle to simulation of propagation is the computational complexity.This complexity forces a trade-off between computational complexity and accuracy.The dif?culty to

-20-100102030

10-610-4

10-2100

Es/No (dB)B i t E r r o r P r o b a b i l i t y 802.11b -0.7ns 802.11b -13ns 802.11b -26.4ns 802.11b -58ns 802.11a -0.7ns to 220ns

Fig.8.Bit-error probabilities as a function of delay-spread and SNR.Simulation of 802.11b at 1Mbps (without a RAKE receiver)and 802.11a at 6Mbps.The different curves for 802.11b correspond to different RMS-delay spreads.For a delay-spread of 7ns to 220ns,802.11a gave the same relationship between SNR and bit-error rate,hence this relationship is shown with a single curve.

specify the details of the environment (e.g.,wall materials and exact dimensions and structure of buildings)also forces a trade-off with accuracy.It is important to note that the propagation must be determined from every location that a transmitter/receiver could be located to every other possible location that a transmitter/receiver could be located.The simulation of a 1km ×1km urban region often requires hundreds of thousands of locations.Hence,the computation to determine the signal strength from a single location,which is in itself computationally dif ?cult,must be repeated hundred of thousands of times.In this section,techniques to ef ?ciently simulate propagation are discussed.The techniques described are part of the UDelModels simulation package.In the next subsection,outdoor propagation is discussed,and is followed by a discussion on indoor propagation simulation.

B.Outdoor Propagation

Once the map of buildings,bandwidth,and building materials have been de ?ned,propagation can be estimated.As noted above,extreme care must be taken to reduce the computation.A signi ?cant computational savings can be achieved if it is assumed that all walls are vertical.In this case,the 3-D ray tracing problem reduces to a two stage problem,each of which are much smaller than the 3-D problem.The ?rst stage is illustrated in the left-hand plot in Figure 9,where two vertical plane paths are shown (the path that diffracts around the smaller building is not shown).The ?rst stage is a 2-D ray-tracing.Once the vertical plane paths are found,the 3-D ray paths restricted to the vertical plane paths can easily be computed.The right-hand frame in Figure 9shows the paths of rays in the vertical planes.One vertical plane path has three ray paths,one that diffracts over a building,one

Fig.9.Left:a top-view of the scene on the right.The lines shown are found from2-D ray-tracing.Right::Two vertical plane paths(found from2-D ray-tracing)and5ray paths.

that re?ects off of the ground and passes through a building,and one that passes straight through a building.The other vertical plane path has two ray paths,one re?ecting off of the wall of a building and one re?ecting off of the wall of building and undergoing a ground re?ection.While Figure9shows each vertical plane paths having two or three ray paths,in general,in one vertical plane path there are many ray paths that may include re?ection off of the ground,and transmissions through buildings or diffractions over buildings.The UDelModels’propagation simulator only considers three types of ray paths,direct paths(no ground re?ections and no diffractions over buildings),ground re?ected paths with no diffraction,and paths that include no transmissions through buildings but rather diffract over buildings.Note that diffractions and transmissions through buildings result in signi?cant loss, and hence neglecting ray paths with multiple diffractions or diffractions and transmissions into buildings has little impact on accuracy.This method of3-D ray-tracing is known as vertical plane launching[25],and is known to yield accurate propagation estimates in real cities,where all walls are not necessarily vertical[26].

A straightforward implementation of even2-D ray-tracing is computationally dif?cult.Instead,a technique that is more appropriately called beam tracing can be performed.Like ray tracing,the goal of beam tracing is to determine the paths from the transmitter to receiver.Beam tracing begins with the source broadcasting the signal in all directions.This transmission is not modeled as a large number of rays,but as a small number of beams.When a beam intersects a building,two beams are generated,one is re?ected off of the building and one is transmitted into the building.If only a part of the beam intersects the building,then multiple beams are generated,in particular, one that re?ects off of the building,one that transmits into the building,one that passes by the building,as well

as several beams that account for the diffracted signal.Each diffracted beam models a particular range of angles of diffraction.The strength of the diffracted beam is the average strength for the diffraction angles that the beam models.Note that smaller the range of angles for each beam,the more accurate the diffraction model is.But this generates more beams,increasing the computational complexity of the process.Finally,if the receiver is found to be included within the span of a beam,the vertical plane path is found and the3-D rays from transmitter to receiver are determined.Once a3-D ray is found,the3-D ray information,speci?cally,signal strength,phase,delay,angle of departure from the transmitter,and angle of arrival at the receiver are recorded.

The beam tracing computation can be further simpli?ed by dividing the2-D space into a grid and the determining the propagation between the center points of each square.Each square of the grid is called a?oor-tile.Outdoors and indoors are discretized in this manner.To reduce the number of?oor tiles,the entire space is not discretized. Rather,?oor-tiles are placed only along the center-lines of sidewalks,roads,and hallways.For rooms,?oor tiles are placed in every location that a mobile node can be located.Similarly,the walls of buildings are also divided into wall-tiles.Since the beam tracing is in2-D,the wall-tiles are segments(1-D tiles).The smaller the size of these tiles(?oor-tiles and wall-tiles)more accurate the simulation results,but also the more computationally expensive. The computation is divided into two parts,preprocessing and beam tracing.During preprocessing,ray neighbors for each tile are found.A tile’s ray neighbors are all the tiles that could be directly reached(i.e.,without re?ection, transmission through a wall,or diffraction)by a ray emanating from the tile.Once the ray neighbors are found, beam tracing can be performed ef?ciently.Figure10illustrates how the beam tracing with wall tiles is performed. The process of beam tracing Figure10is carried out in a breadth?rst manner2with each beam continued to be re?ected,transmitted until either the beam exits the modeled area or until the estimated channel gain of the beam falls below a threshold.Each time a beam is generated,the?oor-tiles it covers are determined and the3-D ray information is recorded.Note that the3-D ray information allows one to interpolate the signal strength between grid points as well as determine the delay-spread,the Doppler spread(once velocity is known),as well as simulate directional antennas.It is possible to determine the receiver power over a particular bandwidth by integrating the signal strengths in a way that accounts for phase(i.e.,accounting for constructive/destructive interference).The 3-D ray information requires a signi?cant amount of information be saved.A considerable amount of savings is 2Here,breadth?rst means that all the k th re?ections are found before the(k+1)th re?ections are found.

Fig.10.Beam Tracing.Suppose a beam strikes the wall tile marked A.The re?ection of this beam is modeled as a beam emanating from the virtual source as shown.This beam is between and is de?ned by the two rays marked1and2.These rays are used to select the?oor tile ray-neighbors that this beam strikes(since ray-neighbors are precomputed,this selection is computationally ef?cient).Similarly,the rays1and 2are used to select the set of A’s wall tile ray-neighbors that the beam strikes.One such wall tile is shown in the upper right and is marked B.The beam that strikes tile B is de?ned by the rays marked3and4.These rays de?ne the beam that is transmitted through tile B and can be used to?nd the beam that is re?ected off of B.This process of re?ection and transmission is repeated until the beam’s strength is small enough that it can be neglected(e.g.,-110dB).

achieved by simply recording the received power over a bandwidth and RMS delay-spread(which is merely two integers).Of course,this approach cannot be used if directional antennas are simulated or Doppler spread included. Another important computational saving is achieved by recognizing that the communication is not possible between most locations,hence the propagation matrix is https://www.doczj.com/doc/633010012.html,putational savings are possible by using techniques to store sparse matrices.However,since the resulting data is large,and since simulation requires the determination of a large number of channel gains,it is important that the sparse matrix techniques support fast access.

C.Indoor Propagation

Beam tracing can be performed indoors as well as outdoors.However,the computational complexity depends on the number of walls.Since building interiors have a large number of walls,beam tracing inside all the buildings within a large region of a city exceeds today’s computational abilities.Fortunately,it has been found that a realistic estimate of indoor propagation can be performed without using beam tracing.Speci?cally,the attenuation factor (AF)model has been shown to provide realistic channel gain estimates,with the error found to be within4dB[8]. The AF model assumes that communication indoors takes a straight line path(i.e.,no re?ections off of interior walls). Furthermore,transmissions through each interior wall and transmissions through each?oor result in attenuation. While the amount of attenuation depends on the building,a value of4dB per wall(for an of?ce building)has been shown to work well[8].Realistic attenuation for passing through1?oor is30dB,passing through2?oors is35dB,

passing through3?oors is39dB and passing through4or more?oors is40dB[8].In summary,outdoors,rays make re?ections off of buildings,diffractions over and around buildings,and transmissions into buildings.Once inside a building,the ray will continue in the same direction,experiencing further attenuation for any interior wall or?oor that it passes through.When a ray strikes an exterior wall from the inside,it is both re?ected back inside and transmitted outside.

https://www.doczj.com/doc/633010012.html,putational Complexity

Determining the propagation matrix of a region of an urban area is a feasible but highly computationally complex task.The complexity is both in terms of memory usage and processing time.Processing times for a1km×1km urban region is often on the order of tens of processor days.But the process is highly parallelizable and nearly scales with the number of processors used(i.e.,75processor days takes about5days on15processors).Of course,the entire channel gain matrix for each city only needs to be found once.Table II outlines the memory requirements and the processing time for two cities.These two cities represent two ends of the spectrum.Paddington is a dense city with relatively small buildings,whereas the University of Delaware campus has much more open space and larger buildings.Note that the campus map is signi?cantly larger than Paddington,but only has slightly more buildings. The memory requirement is dominated by the lists of ray neighbors.In Table II,the wall tiles were2meters long and?oor tiles were1m×1m.While the number of wall and?oor tiles scales linearly with the reciprocal of the size of the tiles(i.e.,if the wall tiles are twice as long,there are half as many)3,the total ray neighbors scale quadratically.For the simulations shown in Table II,there are between20,000to40,000exterior?oor tiles,and 80,000to100,000interior?oor tiles.As expected,sidewalks and roads utilize little area outdoors,but indoors, hallways and of?ces?ll large areas.

As shown in Table II,there are on the order of10to100million ray neighbors for a city of size about1km×1km. Since each list entry requires40B,the memory requirement approaches4GB.Assuming suf?cient memory resources, the computation time for the preprocessing stage is relatively short;the cities shown in Table II took a single day on an AMD Athlon64FX55with8GB RAM.

Once the ray neighbors are found,the propagation characteristics between each pair of?oor tiles can be found. From a single source,the propagation characteristics to all destinations can be found at the same time.Table 3Recall that the?oor tiles cover sidewalks,roads,hallways,and of?ces only.

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公司简称(英文):GRAND 企业法人(中文):刘铭华 企业法人(英文):Minghua Liu 电话:86-25-23501213 传真:86-25-23500638 邮政编码:210005 网址:https://www.doczj.com/doc/633010012.html, 公司地址(中文):南京市北京西路嘉发大厦2501室 公司地址(英文):Room2501,Jiafa Mansion, Beijing West road, Nanjing 210005, P.R.China 公司介绍:我们是一家专营食品的公司,长期以来致力于提高产品质量,信誉卓著,欢迎来函与我公司洽谈业务! 可自由添加图片 注意事项:最好使用GIF或JPG格式的图片,尺寸建议在120*120(像素)左右。 填写完毕后,点"确定"; 3 以同样方法登陆其他四个角色(进口商、工厂、出口地及进口地银行),分别创建基本资料。 (1)进口商资料如: 公司全称:Carters Trading Company, LLC 公司简称:Carters 企业法人:Carter 电话:0016137893503 传真:0016137895107 网址:https://www.doczj.com/doc/633010012.html, 公司地址(注意应根据所属国家来填写):P.O.Box8935,New Terminal, Lata. Vista, Ottawa, Canada 公司介绍:We are importers in all items enjoying good reputation! (2)工厂资料如: 公司全称:冠驰股份有限公司 公司简称:冠驰 企业法人:张弛 电话:86-25-29072727 传真:86-25-29072626 邮政编码:210016 网址:https://www.doczj.com/doc/633010012.html, 公司地址:南京市中正路651号3楼 公司介绍:我公司为信誉卓著的厂商,产品深受客户喜爱,欢迎与我公司洽谈业务,我们

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