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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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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 = EB µ 1/d2
- Surface area of sphere centered at transmitter

Radio Propagation

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

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

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

Outline

- Introduction and some terminology
- Propagation Mechanisms
- Propagation models

Radio Propagation

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

- Assumes far-field (Fraunhofer region)
- d >> D and d >> , where
- D is the largest linear dimension of antenna
- is the carrier wavelength

- d >> D and d >> , where
- No interference, no obstructions

Radio Propagation

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

- 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

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

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

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

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

Outline

- Introduction and some terminology
- Propagation Mechanisms
- Propagation models
- Large scale propagation models
- Small scale propagation (fading) models

Radio Propagation

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

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

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

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

Log-Distance 2

- Value of characterizes different environments

Rappaport, Table 3.2, pp. 104

Radio Propagation

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

Outdoor Models

- “2-Ray” Ground Reflection model
- Diffraction model for hilly terrain

Radio Propagation

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

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

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

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

- Environment comparatively more dynamic

Radio Propagation

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

Outline

- Introduction and some terminology
- Propagation Mechanisms
- Propagation models
- Large scale propagation models
- Small scale propagation (fading) models

Radio Propagation

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

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

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

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

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

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?
- d1/Bc

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

Radio Propagation

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)

- if W << Bc: “Flat Fading”

Radio Propagation

Mean excess delay

Qualitative Delay SpreadTypical values for :

Indoor: 10-100 ns

Outdoor: 0.1-10 s

Noise threshold

Power(dB)

Delay

Radio Propagation

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

Radio Propagation

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

- if T << tc: “Slow fading”

Radio Propagation

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

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

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

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

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

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

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

The End

Radio Propagation

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

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

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

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

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

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

Radio Propagation

Convolution Integral

- Convolution is defined by this integral:

Indexes relevant portion of impulse response

Scales past input signal

Radio Propagation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

- 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

Review

- Object of radio propagation models:
- predict signal quality at receiver

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

Radio Propagation

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

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

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

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

- 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

Radio Propagation

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.

- Statistical models (Rice/Rayleigh/Log Normal)

Radio Propagation

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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