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Radio Propagation

CSCI 694

24 September 1999Lewis Girod

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17 March 1999 Radio Propagation 2

Outline

Introduction and terminology

Propagation mechanisms

Propagation models

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What is Radio?

Radio Xmitter induces E&M fields

Electrostatic field components 1/d3

Induction field components 1/d2

Radiation field components 1/d

Radiation field has E and B component

Field strength at distance d = EB 1/d2

Surface area of sphere centered at transmitter

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General Intuition

Two main factors affecting signal at receiver

Distance (or delay) Path attenuation

Multipath Phase differences

Green signal travels 1/2 farther thanYellow to reach receiver, who sees Red.

For 2.4 GHz, (wavelength) =12.5cm.

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Objective

Invent models to predict what the field

looks like at the receiver.

Attenuation, absorption, reflection, diffraction...

Motion of receiver and environment

Natural and man-made radio interference...

What does the field look like at the receiver?

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Models are Specialized

Different scales

Large scale (averaged over meters)

Small scale (order of wavelength)

Different environmental characteristics

Outdoor, indoor, land, sea, space, etc.

Different application areas

macrocell (2km), microcell(500m), picocell

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Outline

Introduction and some terminology

Propagation Mechanisms

Propagation models

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Radio Propagation Mechanisms

Free Space propagation

Refraction

Conductors & Dielectric materials (refraction)

Diffraction

Fresnel zones

Scattering

Clutter is small relative to wavelength

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Free Space

Assumes far-field (Fraunhofer region)

d >> D and d >> , where

D is the largest linear dimension of antenna

is the carrier wavelength

No interference, no obstructions

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Free Space Propagation Model

Received power at distance dis

where Pt

is the transmitter power in Watts

a constant factor K depends on antenna gain, a

system loss factor, and the carrier wavelength

Watts)(2

dPKdP tr

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Refraction

Perfect conductors reflect

with no attenuation

Dielectrics reflect a fraction

of incident energy

Grazing angles reflect max*

Steep angles transmit max*

q qr

qt

Reflection induces 180 phase shift

*The exact fraction depends on the materials and frequencies involved

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Diffraction

Diffraction occurs when waves

hit the edge of an obstacle

Secondary waves propagatedinto the shadowed region

Excess path length results in

a phase shiftFresnel zones relate phase shifts

to the positions of obstacles

TR

1st Fresnel zone

Obstruction

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Fresnel Zones

Bounded by elliptical loci of constant delay

Alternate zones differ in phase by 180

Line of sight (LOS) corresponds to 1st zone

If LOS is partially blocked, 2nd zone can

destructively interfere (diffraction loss)

Fresnel zones are ellipses with the T&R at the foci; L1 = L2+

Path 1

Path 2

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Power Propagated into Shadow

How much power is propagated this way?

1st FZ: 5 to 25 dB below free space prop.

Obstruction of Fresnel Zones 1st 2nd

0

-10

-20

-30

-40-50

-60

0o

90

180o

dB

Tip of Shadow

Obstruction

LOS

Rappaport, pp. 97

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Scattering

Rough surfaces

critical height for bumps is f(,incident angle)

scattering loss factor modeled with Gaussiandistribution.

Nearby metal objects (street signs, etc.)

Usually modelled statistically

Large distant objects

Analytical model: Radar Cross Section (RCS)

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Outline



Propagation models

Large scale propagation models

Small scale propagation (fading) models

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Propagation Models: Large

Large scale models predict behavior averaged

over distances >>

Function of distance & significant environmentalfeatures, roughly frequency independent

Breaks down as distance decreases

Useful for modeling the range of a radio systemand rough capacity planning

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Propagation Models: Small

Small scale (fading) models describe signal

variability on a scale of

Multipath effects (phase cancellation)dominate, path attenuation considered constant

Frequency and bandwidth dependent

Focus is on modeling Fading: rapid change insignal over a short distance or length of time.

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Large Scale Models

Path loss models

Outdoor models

Indoor models

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Free Space Path Loss

Path Loss is a measure of attenuation based

only on the distance to the transmitter

Free space model only valid in far-field;

Path loss models typically define a close-inpoint d0 and reference other points from there:

2

00)()(

d

ddPdP

rr

dB

dBr

d

ddPLdPdPL

0

0 2)()]([)(

What is dB?

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Log-Distance Path Loss Model

Log-distance generalizes path loss to

account for other environmental factors

Choose a d0 in the far field.

Measure PL(d0) or calculate Free Space Path Loss.

Take measurements and derive empirically.

dBd

ddPLdPL

0

0 )()(

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Log-Distance 2

Value of characterizes different environments

EnvironmentExponent

Free Space 2

Urban area 2.7-3.5

Shadowed urban area 3-5Indoor LOS 1.6-1.8

Indoor no LOS 4-6Rappaport, Table 3.2, pp. 104

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Log-Normal Shadowing Model

Shadowing occurs when objects block LOS

between transmitter and receiver

A simple statistical model can account for

unpredictable shadowing

Add a 0-mean Gaussian RV to Log-Distance PL

Markov model can be used for spatial correlation

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Outdoor Models

2-Ray Ground Reflection model

Diffraction model for hilly terrain

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2-Ray Ground Reflection

For d >> hrht,

low angle of incidence allows the earth to act

as a reflectorthe reflected signal is 180 out of phase

Pr 1/d4 (=4)

RT

ht hr

Phase shift!

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Ground Reflection 2

Intuition: ground blocks 1st Fresnel zone

Reflection causes an instantaneous 180 phase shift

Additional phase offset due to excess path length

If the resulting phase is still close to 180,the gound raywill destructively interfere with the LOS ray.

RT

ht hrp1

p0

180

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Hilly Terrain

Propagation can be LOS or result of

diffraction over one or more ridges

LOS propagation modelled withground reflection: diffraction loss

But if there is no LOS,

diffraction can actually help!

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Indoor Path Loss Models

Indoor models are less generalized

Environment comparatively more dynamic

Significant features are physically smaller

Shorter distances are closer to near-field

More clutter, scattering, less LOS

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Indoor Modeling Techniques

Modeling techniques and approaches:

Log-Normal,

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Outline



Propagation models

Large scale propagation models

Small scale propagation (fading) models

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Recall: Fading Models

Small scale (fading) models describe signal

variability on a scale of

Multipath effects (phase cancellation)dominate, path attenuation considered constant

Frequency and bandwidth dependent

Focus is on modeling Fading: rapid change insignal over a short distance or length of time.

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Factors Influencing Fading

Motion of the receiver: Doppler shift

Transmission bandwidth of signal

Compare to BW of channel

Multipath propagation

Receiver sees multiple instances of signal when

waves follow different paths

Very sensitive to configuration of environment

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Effects of Multipath Signals

Rapid change in signal strength due to

phase cancellation

Frequency modulation due to Doppler shiftsfrom movement of receiver/environment

Echoes caused by multipath propagation

delay

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The Multipath Channel

One approach to small-scale models is to

model the Multipath Channel

Linear time-varying function h(t,)

Basic idea: define a filter that encapsulates

the effects of multipath interference

Measure or calculate the channel impulse response(response to a short pulse at fc):

h(t,) t

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Channel Sounding

Channel sounding is a way to measure the

channel response

transmit impulse, and measure the response to find h(). h() can then be used to model the channel response to

an arbitrary signal: y(t) = x(t)h().

Problem: models the channel at single point in time;

cant account for mobility or environmental changes

h(t,)

SKIP

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Characterizing Fading*

From the impulse response we can

characterize the channel:

Characterizing distortionDelay spread (d): how long does the channel

ring from an impulse?

Coherence bandwidth (Bc): over whatfrequency range is the channel gain flat?

d1/Bc

*Adapted from EE535 Slides, Chugg 99

In time domain, roughly corresponds to the fidelity

of the response; sharper pulse requires wider band

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Effect of Delay Spread*

Does the channel distort the signal?

if W Bc: Frequency Selective Fading

If T < d, inter-symbol interference (ISI) occurs For narrowband systems (W 1/T), FSF ISI.

Not so for wideband systems (W >> 1/T)

For a system with bw W and symbol time T...

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Qualitative Delay Spread

RMS Delay spread ()

Mean excess delay

Noise threshold

Delay

Power(dB)

Typical values for :

Indoor: 10-100 nsOutdoor: 0.1-10 s

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Characterizing Fading 2*

Characterizing Time-variation: How does

the impulse response change with time?

Coherence time (tc): for what value of areresponses at t and t+ uncorrelated? (How

quickly is the channel changing)

Doppler Spread (fd): How much will the

spectrum of the input be spread in frequency?

fd1/tc

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Effect of Coherence Time*

Is the channel constant over many uses?

if T tc: Fast fading

Frequent adaptation required For typical systems, symbol rate is high compared to

channel evolution

For a system with bw W and symbol time T...

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Statistical Fading Models

Fading models model the probability of a

fade occurring at a particular location Used to generate an impulse response

In fixed receivers, channel is slowly time-varying; the

fading model is reevaluated at a rate related to motion

Simplest models are based on the WSSUS

principle

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WSSUS*

Wide Sense Stationary (WSS) Statistics are independent of small perturbations in time

and position I.e. fixed statistical parameters for stationary nodes

Uncorrelated Scatter (US) Separate paths are not correlated in phase or attenuation

I.e. multipath components can be independent RVs

Statistics modeled as Gaussian RVs

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Common Distributions

Rayleigh fading distribution

Models a flat fading signal

Used for individual multipath components

Ricean fading distribution

Used when there is a dominant signal

component, e.g. LOS + weaker multipathsparameter K (dB) defines strength of dominant

component; for K=-, equivalent to Rayleigh

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Application of WSSUS

Multi-ray Rayleigh fading:

The Rayleigh distribution does not model

multipath time delay (frequency selective)Multi-ray model is the sum of two or more

independent time-delayed Rayleigh variables

s(t)

R1

R2 r(t)

Rappaport, Fig. 4.24, pp. 185.

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Saleh & Valenzuela (1987)

Measured same-floor indoor characteristics

Found that, with a fixed receiver, indoor

channel is very slowly time-varyingRMS delay spread: mean 25ns, max 50ns

With no LOS, path loss varied over 60dB range

and obeyed log distance power law, 3 > n > 4

Model assumes a structure and models

correlatedmultipath components.

Rappaport, pp. 188

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Saleh & Valenzuela 2

Multipath model Multipath components arrive in clusters, follow Poisson

distribution. Clusters relate to building structures. Within cluster, individual components also follow

Poisson distribution. Cluster components relate to

reflecting objects near the TX or RX.

Amplitudes of components are independent Rayleighvariables, decay exponentially with cluster delay and

with intra-cluster delay

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References

Wireless Communications: Principles and Practice, Chapters 3 and 4,

T. Rappaport, Prentice Hall, 1996.

Principles of Mobile Communication, Chapter 2, G. Stber, Kluwer

Academic Publishers, 1996. Slides for EE535, K. Chugg, 1999.

Spread Spectrum Systems, Chapter 7, R. Dixon, Wiley, 1985 (there is a

newer edition).

Wideband CDMA for Third Generation Mobile Communications,

Chapter 4, T. Ojanpera, R. Prasad, Artech, House 1998. Propagation Measurements and Models for Wireless Communications

Channels, Andersen, Rappaport, Yoshida,IEEE Communications,

January 1995.

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The End

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Scattering 2

hc is the critical height of a protrusion to

result in scattering.

RCS: ratio of power density scattered to receiver

to power density incident on the scattering object Wave radiated through free space to scatterer and reradiated:

)sin(8

i

ch

)log(20)log(20)4log(30

]dB[)log(20)dBi()dBm()dBm( 2

RT

TTR

dd

mRCSGPP

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Free Space 2a

Free space power flux density (W/m2)

power radiated over surface area of sphere

where Gtis transmitter antenna gain

By covering some of this area, receivers

antenna catches some of this flux

24 d

GPP

tt

d

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Free Space 2b

Fraunhofer distance: d > 2D2/

Antenna gain and antenna aperture

Ae is the antenna aperture, intuitively the areaof the antenna perpendicular to the flux

Gr is the antenna gain for a receiver. It is related to Ae.

Received power (Pr) = Power flux density (Pd) * Ae

2

4e

AG 4

2

GAe

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Free Space 2c

where L is a system loss factor

Pt is the transmitter power

Gt and Gr are antenna gains is the carrier wavelength

Watts)(4

1)(

2

2

2L

GGP

ddP rttr

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LNSM 2

PL(d)[dB] = PL(d0) +10nlog(d/d0)+ Xwhere X is a zero-mean Gaussian RV (dB)

and n computed from measured data,based on linear regression

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Ground Reflection 1.5

The power at the receiver in this model is

derivation calculates E field;

Pr = |E|2Ae; Ae is ant. aperture

The breakpoint at which the model

changes from 1/d2

to 1/d4

is 2hthr/where hr and ht are the receiver and transmitter

antenna heights

4

22

d

hhGGPP

rt

rttr

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Convolution Integral

Convolution is defined by this integral:

)()()(

)()()(

dthxty

thtxty

Indexes relevant portionof impulse response

Scales past input signal

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Partition Losses

Partition losses: same floor

Walls, furniture, equipment

Highly dependent on type ofmaterial, frequency

Hard partitions vs soft partitions

hard partitions are structural

soft partitions do not reach ceiling open plan buildings

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Partition Losses 2

Partition losses: between floors

Depends on building construction, frequency

Floor attenuation factor diminishes withsuccessive floors

typical values:

15 dB for 1st floor

6-10 dB per floor for floors 2-5

1-2 dB per floor beyond 5 floors

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Materials

Attenuation values for different materialsMaterial Loss (dB) Frequency

Concrete block 13-20 1.3 GHz

Plywood (3/4) 2 9.6 GHz

Plywood (2 sheets) 4 9.6 GHz

Plywood (2 sheets) 6 28.8 GHz

Aluminum siding 20.4 815 MHz

Sheetrock (3/4) 2 9.6 GHz

Sheetrock (3/4) 5 57.6 GHz

Turn corner in corridor 10-15 1.3 GHz

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What does dB mean?

dB stands for deciBel or 1/10 of a Bel

The Bel is a dimensionless unit for

expressing ratios and gains on a log scale

Gains add rather than multiply

Easier to handle large dynamic ranges

))log()(log(10log10P

P12

1

2

10

dB1

2PP

P

P

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dB 2

Ex: Attenuation from transmitter to receiver.

PT=100, PR=10

attenuation is ratio of PT to PR[PT/PR]dB = 10 log(PT/PR) = 10 log(10) = 10 dB

Useful numbers:

[1/2]dB -3 dB

[1/1000]dB = -30 dB

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dB 3

dB can express ratios, but what about

absolute quantities?

Similar units reference an absolute quantityagainst a defined reference.

[n mW]dBm = [n/mW]dB

[n W]dBW = [n/W]dB

Ex: [1 mW]dBW = -30 dBW

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Channel Sounding 2

Several Channel Sounding techniques can

measure the channel response directly:Direct RF pulse (we hinted at this approach)

Sliding correlator

Frequency domain sounding

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Channel Sounding 3

Direct RF Pulse

Xmit pulse, scope displays response at receiver

Can be done with off-the-shelf hardwareProblems: hard to reject noise in the channel

If no LOS

must trigger scope on weaker multipath component may fail to trigger

lose delay and phase information

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Channel Sounding 4

Sliding correlator

Xmit PseudoNoise sequence

Rcvr correlates signal with its PN generatorRcvr clock slightly slower; PN sequences slide

Delayed components cause delayed correlations

Good resolution, good noise rejection

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Channel Sounding 5

Frequency domain sounding

Sweep frequency range

Compute inverse Fourier transform of responseProblems

not instantaneous measurement

Tradeoff between resolution (number of frequency

steps) and real-time measurement (i.e. duration as

short as possible)

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Digression: Convolutions

The impulse response box notation

implies the convolution operator,

Convolution operates on a signal and animpulse response to produce a new signal.

The new signal is the superposition of the

response to past values of the signal.

Commutative, associative

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y(t)

y(t)

Convolutions 2

y(t) is the sum of scaled, time-delayed responses

x(t) h(t) =

+

h(t)

Each component of the sum is scaled

by the x(t)dt at that point; in this

example, the response is scaled to 0

where x(t) = 0.

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Flip & Slide: h(t-)h(t-) Flip & Slide: h(t-)h(t-) Flip & Slide: h(t-)h(t-)

Convolutions 3

Graphical method: Flip & Slide

x(t)

x()

h(t) =

Pairwise multiply x*h

and integrate over

and Store y(t)

y(t)

y(t)

Flip & Slide: h(t-)h(t-) Flip & Slide: h(t-)h(t-)

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Frequency and Time Domains

The channel impulse response is f(time)

It describes the channel in the time domain

Functions of frequency are often very useful; Space of such functions is frequency domain

Often a particular characteristic is easier to

handle in one domain or the other.

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Frequency Domain

Functions of frequency

usually capitalized and take the parameter f

where f is the frequency in radians/secand the value of the function is the amplitude of

the component of frequency f.

Convolution in time domain translates intomultiplication in the frequency domain:

y(t) = x(t)h(t) Y(f) = X(f)H(f)

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Frequency Domain 2

Based on Fourier theorem:

any periodic signal can be decomposed into a

sum of (possibly infinite number of) cosines The Fourier Transform and inverse FT

Convert between time and frequency domains.

The frequency and time representations of thesame signal are duals

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Flat Fading

T >> d and W

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Frequency Selective Fading

T > BC ISI

0 Ts 0 0 Ts+

fc fcfc

t t

f f f

s(t) r(t)h(t,)

Time domain(convolve)

Freq domain(filter)

=

=

Delay spread

Coherence BW

Ts

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Review

Object of radio propagation models:

predict signal quality at receiver

Radio propagation mechanismsFree space (1/d2)

Diffraction

RefractionScattering

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Review 2

Factors influencing received signal

Path loss: distance, obstructions

Multipath interference: phase cancellation dueto excess path length and other sources of phase

distortion

Doppler shift

Other radio interference

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Review 3

Approaches to Modelling

Models valid for far-field, apply to a range of

distanceslarge scale models: concerned with gross

behavior as a function of distance

small scale (fading) models: concerned with

behavior during perturbations around a

particular distance

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Relevance to Micronets

Micronets may require different models

than most of the work featured here

Smaller transmit rangeLikely to be near reflectors: on desk or floor.

On the other hand, at smaller scales things are less

smooth: ground reflection may turn into scattering

Outdoors, throwing sensors on ground may not

work. Deployable tripods?

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Relevance 2

Consequences of Fading

You can be in a place that has no signal, but

where a signal can be picked up a short distanceaway in any direction

Ability to move? Switch frequencies/antennas? Call

for help moving or for more nodes to be added?

If stuck, may not be worth transmitting at all

Reachability topology may be completely

irrelevant to location relationships

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Relevance 3

Relevant modelling tools:

Statistical models (Rice/Rayleigh/Log Normal)

Statistical fading assumes particular dynamics, thisdepends on mobility of receivers and environment

CAD modelling of physical environment and

ray tracing approaches.

For nodes in fixed positions this is only done once.

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Relevance 4

An approach to modelling? Characterize wireless system interactions with

different materials, compare to published data

Assess the effect of mobility in environment on fixed

topologies, relate to statistical models

Try to determine what environmental structures and

parameters are most important:

Scattering vs. ground reflection?

can a simple CAD model help?

694 radio

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