Diffraction, Scattering, Long-Distance Path Loss Model, Log-Normal Shadowing

$Page 1: Diffraction, Scattering, Long-Distance Path Loss Model, Log-Normal Shadowing$
Wireless Communications(and Networks)


EE 552/452 Spring 2007

OutlineOutline Review

– Free space propagation Received power is a function of transmit power times gains

of transmitter and receiver antennas Signal strength is proportional to distance to the power of -2

– Reflection: Cause the signal to decay faster. Depends on the height of transmitter and receiver antennas

Homework

Conference, moving of classes

Project, TI toolboxes

Diffraction

Scattering

Practical link budget model

DAYANANDA SAGAR COLLEGE OF ENGINEERING, BANGALORE


EE 552/452 Spring 2007

Diffraction

Diffraction occurs when waves hit the edge of an obstacle– “Secondary” waves propagated into the shadowed region

– Water wave example

– Diffraction is caused by the propagation of secondary wavelets into a shadowed region.

– Excess path length results in a phase shift

– The field strength of a diffracted wave in the shadowed region is the vector sum of the electric field components of all the secondary wavelets in the space around the obstacle.

– Huygen’s principle: all points on a wavefront can be considered as point sources for the production of secondary wavelets, and that these wavelets combine to produce a new wavefront in the direction of propagation.



EE 552/452 Spring 2007

Diffraction geometry

Derive of equation 4.54-4.57



EE 552/452 Spring 2007




EE 552/452 Spring 2007


Fresnel-Kirchoff distraction parameters, 4.56



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Fresnel Screens

Fresnel zones relate phase shifts to the positions of obstacles

Equation 4.58

A rule of thumb used for line-of-sight microwave links 55% of the first Fresnel zone is kept clear.



EE 552/452 Spring 2007

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)

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



EE 552/452 Spring 2007

Fresnel diffraction geometry



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Knife-edge diffraction

Fresnel integral, 4.59



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Knife-edge diffraction loss

Gain

Exam. 4.7

Exam. 4.8



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Multiple knife-edge diffraction



EE 552/452 Spring 2007

Scattering

Rough surfaces– Lamp posts and trees, scatter all directions

– Critical height for bumps is f(,incident angle), 4.62

– Smooth if its minimum to maximum protuberance h is less than critical height.

– Scattering loss factor modeled with Gaussian distribution, 4.63, 4.64.

Nearby metal objects (street signs, etc.)– Usually modeled statistically

Large distant objects– Analytical model: Radar Cross Section (RCS)

– Bistatic radar equation, 4.66



EE 552/452 Spring 2007

Measured results



EE 552/452 Spring 2007

Measured results



EE 552/452 Spring 2007

Propagation Models

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, – Experimental rather than the theoretical for previous three models– Path loss models, Outdoor models, Indoor 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.



EE 552/452 Spring 2007

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:

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.

2

00 )()(

d

ddPdP rr

dB

dBr d

ddPLdPdPL

00 2)()]([)(

dBd

ddPLdPL

00 )()(



EE 552/452 Spring 2007

Typical large-scale path loss



EE 552/452 Spring 2007

Log-Normal Shadowing Model

Shadowing occurs when objects block LOS between transmitter and receiver

A simple statistical model can account for unpredictable “shadowing” – PL(d)(dB)=PL(d)+X0,

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

– Variance is usually from 3 to 12.

– Reason for Gaussian



EE 552/452 Spring 2007

Measured large-scale path loss

Determine n and by mean and variance

Equ. 4.70

Equ. 4.72

Basic of Gaussian

distribution



EE 552/452 Spring 2007

Area versus Distance coverage model with shadowing model

Percentage for

SNR larger than

a threshold

Equ. 4.79

Exam. 4.9




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Diffraction, Scattering, Long-Distance Path Loss Model, Log-Normal Shadowing