Workshop on Small-Angle X-ray Scattering and Diffraction Studies
Diffraction, Scattering, Long-Distance Path Loss Model, Log-Normal Shadowing
Transcript of 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
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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.
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EE 552/452 Spring 2007
Diffraction geometry
Derive of equation 4.54-4.57
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EE 552/452 Spring 2007
Diffraction geometry
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Diffraction geometry
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.
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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
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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
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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
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EE 552/452 Spring 2007
Measured results
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EE 552/452 Spring 2007
Measured results
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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.
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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 )()(
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EE 552/452 Spring 2007
Typical large-scale path loss
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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” – 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
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Measured large-scale path loss
Determine n and by mean and variance
Equ. 4.70
Equ. 4.72
Basic of Gaussian
distribution
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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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Questions?Questions?