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Radio Propagation CSCI 694 24 September 1999 Lewis Girod Outline Introduction and terminology Propagation mechanisms Propagation models What is Radio? Radio Xmitter induces E&M fields Electrostatic field components µ 1/d 3 Induction field components µ 1/d 2

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Radio propagation l.jpg

Radio Propagation

CSCI 694

24 September 1999

Lewis Girod


Outline l.jpg
Outline

  • Introduction and terminology

  • Propagation mechanisms

  • Propagation models

Radio Propagation


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What is Radio?

  • Radio Xmitter induces E&M fields

    • Electrostatic field components µ 1/d3

    • Induction field components µ 1/d2

    • Radiation field components µ 1/d

  • Radiation field has E and B component

    • Field strength at distance d = EB µ 1/d2

    • Surface area of sphere centered at transmitter

Radio Propagation


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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 than Yellow to reach receiver, who sees Red. For 2.4 GHz,  (wavelength) =12.5cm.

Radio Propagation


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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?

Radio Propagation


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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

Radio Propagation


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Outline

  • Introduction and some terminology

  • Propagation Mechanisms

  • Propagation models

Radio Propagation


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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

Radio Propagation


Free space l.jpg
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

Radio Propagation


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Free Space Propagation Model

  • Received power at distance d is

    • where Pt is the transmitter power in Watts

    • a constant factor K depends on antenna gain, a system loss factor, and the carrier wavelength

Radio Propagation


Refraction l.jpg
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

Radio Propagation

*The exact fraction depends on the materials and frequencies involved


Diffraction l.jpg

T

R

1st Fresnel zone

Obstruction

Diffraction

  • Diffraction occurs when waves hit the edge of an obstacle

    • “Secondary” waves propagated into the shadowed region

    • Excess path length results in a phase shift

    • Fresnel zones relate phase shifts to the positions of obstacles

Radio Propagation


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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)

Path 1

Path 2

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

Radio Propagation


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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.

LOS

0

-10

-20

-30

-40

-50

-60

0o

90

180o

dB

Obstruction

Rappaport, pp. 97

Tip of Shadow

1st 2nd

Obstruction of Fresnel Zones 

Radio Propagation


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Scattering

  • Rough surfaces

    • critical height for bumps is f(,incident angle)

    • scattering loss factor modeled with Gaussian distribution.

  • Nearby metal objects (street signs, etc.)

    • Usually modelled statistically

  • Large distant objects

    • Analytical model: Radar Cross Section (RCS)

Radio Propagation


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Outline

  • Introduction and some terminology

  • Propagation Mechanisms

  • Propagation models

    • Large scale propagation models

    • Small scale propagation (fading) models

Radio Propagation


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Propagation Models: Large

  • Large scale models predict behavior averaged over distances >> 

    • Function of distance & significant environmental features, roughly frequency independent

    • Breaks down as distance decreases

    • Useful for modeling the range of a radio system and rough capacity planning

Radio Propagation


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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 in signal over a short distance or length of time.

Radio Propagation


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Large Scale Models

  • Path loss models

  • Outdoor models

  • Indoor models

Radio Propagation


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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-in” point d0 and reference other points from there:

What is dB?

Radio Propagation


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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.

Radio Propagation


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Log-Distance 2

  • Value of  characterizes different environments

Rappaport, Table 3.2, pp. 104

Radio Propagation


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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

Radio Propagation


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Outdoor Models

  • “2-Ray” Ground Reflection model

  • Diffraction model for hilly terrain

Radio Propagation


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T

R

ht

hr

Phase shift!

2-Ray Ground Reflection

  • For d >> hrht,

    • low angle of incidence allows the earth to act as a reflector

    • the reflected signal is 180 out of phase

    • Pr 1/d4 (=4)

Radio Propagation


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T

R

p0

ht

hr

p1

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 ray will destructively interfere with the LOS ray.

180

Radio Propagation


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Hilly Terrain

  • Propagation can be LOS or result of diffraction over one or more ridges

  • LOS propagation modelled with ground reflection: diffraction loss

  • But if there is no LOS, diffraction can actually help!

Radio Propagation


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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

Radio Propagation


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Indoor Modeling Techniques

  • Modeling techniques and approaches:

    • Log-Normal, <2 for LOS down corridor

    • Log-Normal shadowing model if no LOS

    • Partition and floor attenuation factors

    • Computationally intensive “ray-tracing” based on 3-D model of building and attenuation factors for materials

Radio Propagation


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Outline

  • Introduction and some terminology

  • Propagation Mechanisms

  • Propagation models

    • Large scale propagation models

    • Small scale propagation (fading) models

Radio Propagation


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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 in signal over a short distance or length of time.

Radio Propagation


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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

Radio Propagation


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Effects of Multipath Signals

  • Rapid change in signal strength due to phase cancellation

  • Frequency modulation due to Doppler shifts from movement of receiver/environment

  • Echoes caused by multipath propagation delay

Radio Propagation


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h(t,)

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):

t

Radio Propagation


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SKIP

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; can’t account for mobility or environmental changes

h(t,)

Radio Propagation


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Characterizing Fading*

*Adapted from EE535 Slides, Chugg ‘99

  • From the impulse response we can characterize the channel:

  • Characterizing distortion

    • Delay spread (d): how long does the channel ring from an impulse?

    • Coherence bandwidth (Bc): over what frequency range is the channel gain flat?

    • d1/Bc

In time domain, roughly corresponds to the “fidelity” of the response; sharper pulse requires wider band

Radio Propagation


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Effect of Delay Spread*

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

  • Does the channel distort the signal?

    • if W << Bc: “Flat Fading”

      • Amplitude and phase distortion only

    • 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)

Radio Propagation


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RMS Delay spread ()

Mean excess delay

Qualitative Delay Spread

Typical values for  :

Indoor: 10-100 ns

Outdoor: 0.1-10 s

Noise threshold

Power(dB)

Delay

Radio Propagation


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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  are responses 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?

    • fd1/tc

Radio Propagation


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Effect of Coherence Time*

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

  • Is the channel constant over many uses?

    • if T << tc: “Slow fading”

      • Slow adaptation required

    • if T > tc: “Fast fading”

      • Frequent adaptation required

      • For typical systems, symbol rate is high compared to channel evolution

Radio Propagation


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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

Radio Propagation


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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

Radio Propagation


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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 multipaths

    • parameter K (dB) defines strength of dominant component; for K=-, equivalent to Rayleigh

Radio Propagation


Application of wssus l.jpg

s(t)

R1

r(t)

R2

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

Rappaport, Fig. 4.24, pp. 185.

Radio Propagation


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Saleh & Valenzuela (1987)

Rappaport, pp. 188

  • Measured same-floor indoor characteristics

    • Found that, with a fixed receiver, indoor channel is very slowly time-varying

    • RMS 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 correlated multipath components.

Radio Propagation


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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 Rayleigh variables, decay exponentially with cluster delay and with intra-cluster delay

Radio Propagation


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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. Stüber, 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.

Radio Propagation


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The End

Radio Propagation


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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:

Radio Propagation


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Free Space 2a

  • Free space power flux density (W/m2)

    • power radiated over surface area of sphere

    • where Gt is transmitter antenna gain

  • By covering some of this area, receiver’s antenna “catches” some of this flux

Radio Propagation


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Free Space 2b

  • Fraunhofer distance: d > 2D2/

  • Antenna gain and antenna aperture

    • Ae is the antenna aperture, intuitively the area of 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

Radio Propagation


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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

Radio Propagation


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LNSM 2

  • PL(d)[dB] = PL(d0) +10nlog(d/d0)+ X

    • where X is a zero-mean Gaussian RV (dB)

  •  and n computed from measured data, based on linear regression

Radio Propagation


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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  2hthr/

    • where hr and ht are the receiver and transmitter antenna heights

Radio Propagation


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Convolution Integral

  • Convolution is defined by this integral:

Indexes relevant portion of impulse response

Scales past input signal

Radio Propagation


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Partition Losses

  • Partition losses: same floor

    • Walls, furniture, equipment

    • Highly dependent on type of material, frequency

  • Hard partitions vs soft partitions

    • hard partitions are structural

    • soft partitions do not reach ceiling

      • “open plan” buildings

Radio Propagation


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Partition Losses 2

  • Partition losses: between floors

    • Depends on building construction, frequency

    • “Floor attenuation factor” diminishes with successive 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

Radio Propagation


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Materials

  • Attenuation values for different materials

Radio Propagation


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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

Radio Propagation


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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

Radio Propagation


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dB 3

  • dB can express ratios, but what about absolute quantities?

  • Similar units reference an absolute quantity against a defined reference.

    • [n mW]dBm = [n/mW]dB

    • [n W]dBW = [n/W]dB

  • Ex: [1 mW]dBW= -30 dBW

Radio Propagation


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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

Radio Propagation


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Channel Sounding 3

  • Direct RF Pulse

    • Xmit pulse, scope displays response at receiver

    • Can be done with off-the-shelf hardware

    • Problems: 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

Radio Propagation


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Channel Sounding 4

  • Sliding correlator

    • Xmit PseudoNoise sequence

    • Rcvr correlates signal with its PN generator

    • Rcvr clock slightly slower; PN sequences slide

    • Delayed components cause delayed correlations

    • Good resolution, good noise rejection

Radio Propagation


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Channel Sounding 5

  • Frequency domain sounding

    • Sweep frequency range

    • Compute inverse Fourier transform of response

    • Problems

      • not instantaneous measurement

      • Tradeoff between resolution (number of frequency steps) and real-time measurement (i.e. duration as short as possible)

Radio Propagation


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Digression: Convolutions

  • The impulse response “box” notation implies the convolution operator, 

    • Convolution operates on a signal and an impulse response to produce a new signal.

    • The new signal is the superposition of the response to past values of the signal.

    • Commutative, associative

Radio Propagation


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y(t)

h(t)

y(t)

Convolutions 2

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

x(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.

+

Radio Propagation


Convolutions 3 l.jpg

y(t)

h(t-)

h(t-)

h(t-)

h(t-)

h(t-)

h(t)

Flip & Slide: h(t-)

Flip & Slide: h(t-)

Flip & Slide: h(t-)

Flip & Slide: h(t-)

Flip & Slide: h(t-)

Convolutions 3

  • Graphical method: “Flip & Slide”

x(t)

=

Pairwise multiply x*h

and integrate over 

x()

y(t)

and Store y(t)

Radio Propagation


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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.

Radio Propagation


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Frequency Domain

  • Functions of frequency

    • usually capitalized and take the parameter “f”

    • where f is the frequency in radians/sec

    • and the value of the function is the amplitude of the component of frequency f.

  • Convolution in time domain translates into multiplication in the frequency domain:

    • y(t) = x(t)h(t)  Y(f) = X(f)H(f)

Radio Propagation


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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 the same signal are “duals”

Radio Propagation


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Flat Fading

  • T >> d and W<< BC  minimal ISI

r(t)

s(t)

h(t,)

Delay spread

=

Time domain

(convolve)

t

t

t

0

0

Ts

0

Ts+

Coherence BW

Freq domain

(filter)

=

f

f

f

fc

fc

fc

Radio Propagation


Frequency selective fading l.jpg
Frequency Selective Fading

  • T << d and W>> BC  ISI

r(t)

s(t)

h(t,)

Delay spread

=

Time domain

(convolve)

t

t

0

0

Ts

0

Ts

Ts+

Coherence BW

Freq domain

(filter)

=

f

f

f

fc

fc

fc

Radio Propagation


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Review

  • Object of radio propagation models:

    • predict signal quality at receiver

  • Radio propagation mechanisms

    • Free space (1/d2)

    • Diffraction

    • Refraction

    • Scattering

Radio Propagation


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Review 2

  • Factors influencing received signal

    • Path loss: distance, obstructions

    • Multipath interference: phase cancellation due to excess path length and other sources of phase distortion

    • Doppler shift

    • Other radio interference

Radio Propagation


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Review 3

  • Approaches to Modelling

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

    • large scale models: concerned with gross behavior as a function of distance

    • small scale (fading) models: concerned with behavior during perturbations around a particular distance

Radio Propagation


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Relevance to Micronets

  • Micronets may require different models than most of the work featured here

    • Smaller transmit range

    • Likely 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?

Radio Propagation


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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 distance away 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

Radio Propagation


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Relevance 3

  • Relevant modelling tools:

    • Statistical models (Rice/Rayleigh/Log Normal)

      • Statistical fading assumes particular dynamics, this depends 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.

Radio Propagation


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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?

Radio Propagation


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