Radio propagation

Radio Propagation

CSCI 694

24 September 1999

Lewis Girod

17 March 1999 Radio Propagation 2

Outline

• Introduction and terminology

• Propagation mechanisms

• Propagation models


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


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.


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?


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


Outline

• Introduction and some terminology

• Propagation Mechanisms

• Propagation models


Radio Propagation Mechanisms

• Free Space propagation

• Refraction– Conductors & Dielectric materials (refraction)

• Diffraction– Fresnel zones

• Scattering– “Clutter” is small relative to wavelength


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


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

Watts)(2d

PKdP t

r


Refraction

• Perfect conductors reflect with no attenuation

• Dielectrics reflect a fraction of incident energy– “Grazing angles” reflect max*– Steep angles transmit max*

r

t

• Reflection induces 180 phase shift

*The exact fraction depends on the materials and frequencies involved


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

TR

1st Fresnel zone

Obstruction


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


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


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)


Outline



• Propagation models– Large scale propagation models– Small scale propagation (fading) models


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


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.


Large Scale Models

• Path loss models

• Outdoor models

• Indoor models


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:

2

00 )()(

d

ddPdP rr

dB

dBr d

ddPLdPdPL

00 2)()]([)(

What is dB?


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

00 )()(


Log-Distance 2

• Value of characterizes different environments

Environment Exponent

Free Space 2Urban area 2.7-3.5Shadowed urban area 3-5Indoor LOS 1.6-1.8Indoor no LOS 4-6

Rappaport, Table 3.2, pp. 104


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


Outdoor Models

• “2-Ray” Ground Reflection model

• Diffraction model for hilly terrain


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)

RT

ht hr

Phase shift!


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.

RT

ht hrp1

p0

180


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!


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


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


Outline



• Propagation models– Large scale propagation models– Small scale propagation (fading) models


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.


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


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


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


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,)

SKIP


Characterizing Fading*

• 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?

d1/Bc

*Adapted from EE535 Slides, Chugg ‘99

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


Effect of Delay Spread*

• 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)

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


Qualitative Delay Spread

RMS Delay spread ()

Mean excess delay

Noise threshold

Delay

Pow

er(d

B)

Typical values for :Indoor: 10-100 nsOutdoor: 0.1-10 s


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?

– fd1/tc


Effect of Coherence Time*

• 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

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


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


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


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


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.


Saleh & Valenzuela (1987)

• 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.

Rappaport, pp. 188


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


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.


The End


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(θ 8

λ

i

ch

)log(20)log(20)π4log(30

]dB[)λlog(20)dBi()dBm()dBm( 2

RT

TTR

dd

mRCSGPP


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

2π4 d

GPP tt

d


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

2λ

π4 eAG

π4

λ 2GAe


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)π(4

λ 1)(

2

2

2 L

GGP

ddP rtt

r


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


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


Convolution Integral

• Convolution is defined by this integral:

τ)τ()τ()(

)()()(

dthxty

thtxty

Indexes relevant portion of impulse response

Scales past input signal


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


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


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


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

210

dB1

2 PPP

P


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


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


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


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


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


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)


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


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.


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*hand integrate over

and Store y(t)

y(t)

y(t)

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


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.


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)


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”


Flat Fading

• T >> d and W << BC minimal ISI

0 Ts 0 0 Ts+

fc fcfc

t t t

f f f

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

Time domain(convolve)

Freq domain(filter)

=

=

Delay spread

Coherence BW


Frequency Selective Fading

• T << d and W >> 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


Review

• Object of radio propagation models:– predict signal quality at receiver

• Radio propagation mechanisms– Free space (1/d2)– Diffraction– Refraction– Scattering


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


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


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?


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


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.


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

Engineering