Fading
Kevin Bolding
Electrical Engineering
Seattle Pacific University
Seattle Pacific University
Fading
No. 1
Signals fade
• Received Signal Strength (RSS) varies over time and space
• Slow Fading caused by large obstacles and terrain impairments
• Appears as local rises/falls in RSS around a logarithmic curve
Free Space Attentuation
Free Space Attenuation of 90dBm Signal at 100MHz
FSA with Slow Fading
40
35
RSS (dBm)
30
25
20
15
10
5
0
0
500
1000
1500
2000
2500
Distance (m)
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Fading
No. 2
Multipath fading
• Reflections and diffraction cause radio signals to follow
different paths to the receiver
• The received signals are summed at the receiver
• The signal components will have various phases and
amplitudes
• This will cause positive and negative interference that varies
based on the relative locations of the:
• Source
• Objects in the path
• Receiver
• As these objects move around, the interference pattern will
change
• The signal strength will vary significantly over small variations in
the placement of these objects
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Fading
No. 3
Fading due to reflections
• Multiple signal paths will result in multiple received signals
• Each reflection path is longer than the direct path – a change in
the path length results in a phase difference
• Reflections off of the earth usually introduce a 180 degree
phase shift
• In the absence of reflecting objects other than the earth, the
relationship of the various reflected signal depends on
• The location and height of the transmitter and receiver
• The wavelength (frequency) of the signal
• Multiple reflections cause the RSS to vary with frequency
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Fading
No. 4
Fading due to multipath Doppler shift
• If the receiver is moving relative to the transmitter, there will be a
shift in frequency – Doppler shift
• Frequency increases if moving closer
• Frequency decreases if moving apart
• At typical vehicle velocities, the Doppler shift is under 100Hz,
which is not itself a problem
• In a multipath situation, the relative velocity of the receiver varies
depending on the geometry of the paths
•  Different paths have different Doppler shifts, leading to slightly
different frequencies
• The received signal strength will vary over time as the alignment
of the various signals changes
• Multipath Doppler shift causes the RSS to vary over time
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No. 5
Doppler Shift
• For E/M waves, the change in frequency (Doppler
shift) is computed by:
• vs,r is the relative speed of the
receiver w.r.t. the transmitter. vs,r is
positive when the receiver is moving
away from the transmitter.
• f0 is the frequency and 0 is the
wavelength of the E/M wave.
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Fading
No. 6
Fading varies with time and frequency
Amplitude of the channel attenuation in dB versus carrier frequency (in MHz)
and time (in milliseconds).
Normalized delay spread tm = 0.05 and normalized Doppler spread fD = 0.05.
A time selective and frequency selective Rayleigh fading channel
From: http://www.wirelesscommunication.nl/reference/chaptr03/channel.htm
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Fading
No. 7
Multipath fading
http://en.wikipedia.org/wiki/Image:Rayleigh_fading_doppler_10Hz.svg
Average RSS
Fades
“Deep” Fades
An example of multipath fading from a moving receiver.
Seattle Pacific University
Fading
No. 8
Multipath Fading Analysis
• Some environments have a large number of
scatterers
• Ionosphere
• Urban environments
• If there are a large number of scattering objects, the
received signal has phase and amplitude
represented by a complex vector z with:
• Randomly distributed Real part (Normal dist.)
• Randomly distributed Imaginary part (Normal dist.)
• Note: This assumes that only scattered rays are
received. If scattered and the direct ray are both
received, a different model applies.
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Fading
No. 9
Complex plane
Im
y
z = x + iy
phase
x
Re
• Amplitude = sqrt (x2+y2)
See http://www.wirelesscommunication.nl/reference/chaptr03/rayjava/rayjava.htm
for an animation tool
Seattle Pacific University
Fading
No. 10
Rayleigh Distribution
• A random variable follows the Rayleigh distribution
if it is a vector with its orthogonal components
normally and independently distributed
• The Real (x) and Imaginary (y) parts of the received
signal are both normally distributed
• The amplitude has a Rayleigh distribution
PDF of a Rayleigh
Distribution with various
Variances
Mean
Power < Mean
Power > Mean
Tail goes to infinity
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Fading
No. 11
Rayleigh Fading with Moving Receiver
•
•
•
•
Rayleigh PDF
Rayleigh fading describes the change in RSS at
various locations
A Rayleigh faded channel has significant RSS
variations over very small distances
A moving receiver experiences this as RSS
changes over a short period of time
A moving receiver also experiences Doppler
shift, which increases the rate of fading
RSS, 4 MPH
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RSS, 40 MPH
Fading
No. 12
Analysis using Rayleigh Model
Assume fade margin is set
to some level.
(Example: -15dB)
 = ratio of margin to RMS
mean (Example: -15dB =
1/31.6 = 0.032)
fd=Maximum Doppler shift
(Example: 10Hz)
How often do fades exceed
the fade margin?
Analytically, compute the
Level Crossing Rate (Hz):
RSS, 4 MPH, Max Doppler = 10Hz
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Fading
How long is the average
fade duration for fades
beyond the fade margin?
Analytically, compute
the Average Fade Duration (s):
No. 13
Rician Fading
• If the received signal is a combination of a single line-of-sight
(dominant) ray and scattered rays, the RSS follows the Rice
distribution
• The Rice distribution has a parameter, v, that represents the
degree of dominance of the primary ray
• At v=0, the Ricean distribution is the same as the Rayleigh
distribution
v=0, Rayleigh
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Note that the mean
changes with v
Fading
No. 14
Fading Summary
• Obstructions cause fading through blockages,
reflections and diffraction
• Slow fading refers to deviations from free-space
fading that occur over longer distances
• Caused by large obstructions
• Characterized by log-normal distribution
• Fast fading refers to deviations that occur over very
short distances
• Caused by multipath
• Characterized by Rayleigh or Ricean distributions
Seattle Pacific University
Fading
No. 15