1. Chapter 3 Mobile Radio Propagation
Prof. Chih-Cheng Tseng
EE of NIU
Chih-Cheng Tseng

2. Speed, Wavelength, Frequency
Light Speed (c) = Wavelength (l) x Frequency (f)
= 3  108 m/s
System
Frequency
Wavelength
AC current
60 Hz
5,000 km
FM radio
100 MHz
3 m
Cellular
800 MHz
37.5 cm
Ka band satellite
20 GHz
15 mm
Ultraviolet light
1015 Hz
10-7 m
EE of NIU
Chih-Cheng Tseng

3. Types of Radio Waves Ionosphere (80 - 720 km) Sky wave
Transmitter
Receiver
Earth
Sky wave
Space wave (LOS)
Ground wave
Troposphere ( km)
Stratosphere ( km)
Mesosphere ( km)
Ionosphere ( km)
電離層
中氣層
平流層
對流層
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Chih-Cheng Tseng

4. Radio Frequency Bands Classification Band Initials Frequency Range
Characteristics
Extremely low
ELF
< 300 Hz
Ground wave
Infra low
ILF
300 Hz - 3 kHz
Very low
VLF
3 kHz - 30 kHz
Low LF
30 kHz kHz
Medium MF
300 kHz - 3 MHz
Ground/Sky wave
High HF
3 MHz - 30 MHz
Sky wave
Very high
VHF
30 MHz MHz
Space wave (LOS)
Ultra high
UHF
300 MHz - 3 GHz
Super high
SHF
3 GHz - 30 GHz
Extremely high
EHF
30 GHz GHz
Tremendously high
THF
300 GHz GHz
EE of NIU
Chih-Cheng Tseng

5. Propagation Mechanisms
Reflection (反射)
Propagation wave impinges on an object which is large as compared to wavelength, e.g., the surface of the Earth, buildings, walls, etc.
Diffraction (繞射)
Radio path between transmitter and receiver obstructed by surface with sharp irregular edges, e.g., waves bend around the obstacle, even when LOS (line of sight) does not exist.
Scattering (散射)
Objects smaller than the wavelength of the propagation wave, e.g. foliage, street signs, lamp posts.
EE of NIU
Chih-Cheng Tseng

6. Radio Propagation Effects
Building
STOP
Scattered
Reflected Signal
Direct Signal
Diffracted Signal hb hm d
Transmitter
Receiver
EE of NIU
Chih-Cheng Tseng

7. Free-Space Propagation
Assuming that the radiated power is uniformly distributed over the surface of the sphere.
The received signal power at distance d:
Pt is transmitting power
Ae is effective area covered by the sender
Gt is the transmitting antenna gain
EE of NIU
Chih-Cheng Tseng

8. Antenna Gain For a circular reflector antenna, the antenna gain
 is the net efficiency (typically 0.55)
D is the diameter
c is the speed of light 3108 m/s
Example:
If the antenna diameter = 2 m and frequency = 6 GHz, then, wavelength = 0.05 m and G = 39.4 dB.
If the frequency = 14 GHz and diameter = 2 m , then, the wavelength = m and G = 46.9 dB
Higher the frequency, higher the gain for the same size antenna.
EE of NIU
Chih-Cheng Tseng

9. Land Propagation The received signal power:
Gr is the receiver antenna gain,
L is the propagation loss in the channel, i.e.,
L = LP LS LF
Fast fading
Slow fading
Path loss
EE of NIU
Chih-Cheng Tseng

10. Path Loss (Free-Space)
Definition of path loss LP :
The signal strength decays exponentially with distance d between transmitter and receiver;
The loss could be proportional to somewhere between d2 and d4 depending on the environment.
Path Loss in Free-space:
fc is the carrier frequency.
This shows greater the fc, more is the loss.
EE of NIU
Chih-Cheng Tseng

11. Path Loss (Land Propagation)
Simplest Formula:
A and α are the propagation constants
d is the distance between transmitter and receiver
α is the value of 3 ~ 4 in typical urban area
EE of NIU
Chih-Cheng Tseng

12. Example of Path Loss (Free-space)
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Chih-Cheng Tseng

13. Path Loss in Different Areas (1)
Path loss in decreasing order:
Urban area (large city)
Urban area (medium and small city)
Suburban area
Open area
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Chih-Cheng Tseng

14. Path Loss in Different Areas (2)
Urban Area
where
For a large city, the path loss is the same as the that for small- and medium cities under hb=50m and hm=1.65m.
correction factor for the mobile antenna height
EE of NIU
Chih-Cheng Tseng

15. Concept Used for Calculating a(hm)
Transmitter
Distance d
Receiver hb hm
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Chih-Cheng Tseng

16. Path Loss in Different Areas (3)
Suburban
Open area
課本(3.14)式有誤
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Chih-Cheng Tseng

17. Path Loss --- Urban: Large City
hb=50m and hm=1.65m
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Chih-Cheng Tseng

18. Path Loss --- Urban: Medium and Small Cities
hb=50m and hm=1.65m
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19. Path Loss --- Suburban Area
hb=50m and hm=1.65m
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Chih-Cheng Tseng

20. Path Loss --- Open Area
hb=50m and hm=1.65m
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21. Fading Fast Fading (Short-term fading) Slow Fading (Long-term fading)
Signal Strength
(dB)
Distance
Path Loss
Slow Fading
(Long-term fading)
Fast Fading
(Short-term fading)
EE of NIU
Chih-Cheng Tseng

22. Slow Fading What is slow fading?
Long-term variation in the mean level of received signals.
The channel impulse response changes at a rate much slower than the transmitted baseband signal.
Slow fading is also called shadowing or log-normal fading because its amplitude has a log-normal pdf.
The amplitude change caused by shadowing is often modeled using a log-normal distribution.
EE of NIU
Chih-Cheng Tseng

23. Log-normal distribution
Shadowing
Log-normal distribution
The pdf of the received signal level is given in decibels by
M is the true received signal level m in decibels, i.e., 10log10m.
is the area average signal level, i.e., the mean of M.
 is the standard deviation in decibels.
EE of NIU
Chih-Cheng Tseng

24. Log-normal Distribution2
p(M) M M
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Chih-Cheng Tseng

25. Fast Fading What is fast fading?
Short-term fading due to fast spatial variation.
The channel impulse response changes rapidly than the transmitted baseband signal.
EE of NIU
Chih-Cheng Tseng

26. Fast Fading --- Receiver Far From the Transmitter
Assume
There are no direct radio waves between transmitter and receiver.
The prob. distribution of signal amplitude of every path is a Gaussian distribution.
The phase distribution of every path is uniformly distributed over (0,2p) radians.
The prob. distribution of the envelope for the composite signals is a Rayleigh distribution.
EE of NIU
Chih-Cheng Tseng

27. Rayleigh Distribution2 4 6 8 10
P(r)
0.2
0.4
0.6
0.8
1.0
=1
=2
=3
r is the envelope of the fading signal
s is the standard deviation
EE of NIU
Chih-Cheng Tseng

28. Fast Fading --- Receiver Close to the Transmitter
Assume
The direct radio wave between transmitter and receiver is stronger than other radio waves.
The prob. distribution of signal amplitude of every path is a Gaussian distribution.
The phase distribution of every path is uniformly distributed over (0,2p) radians.
The prob. distribution of the envelope for the composite signals is a Rician distribution.
EE of NIU
Chih-Cheng Tseng

29. Rician Distribution r is the envelope of the fading signal
Pdf p(r)
b = 2
b = 1
b= 0 (Rayleigh)
 = 1
b = 3
r is the envelope of the fading signal
s is the standard deviation
b is the amplitude of the direct signal
I0(x) is the zero-order Bessel function of the first kind
EE of NIU
Chih-Cheng Tseng

30. General Model of Fading Channel --- Nakagami
For Nakagami distribution, the pdf of the received signal envelop is
is the Gamma function
is the average power, i.e., the 2nd moment of the fading signal
is the fading term, where m≥ 0.5
If m=1, Nakagami distribution becomes to Rayleigh distribution
If m approach to infinity, the distribution becomes to an impulse, i.e., no fading.
Nakagami is used to replace Rician since Bessel function is not required
EE of NIU
Chih-Cheng Tseng

31. Characteristics of Instantaneous Amplitude
Level Crossing Rate:
Average number of times per second that the signal envelope crosses a specified level in positive going direction.
Fading Rate:
Number of times signal envelope crosses middle value in positive going direction per unit time.
Depth of Fading:
Ratio of mean square value and minimum value of fading signal.
Fading Duration:
Time for which signal is below given threshold.
EE of NIU
Chih-Cheng Tseng

32. Doppler Effect
When a wave source and a receiver are moving, the frequency of the received signal will not be the same as the source.
When they are moving toward each other, the frequency of the received signal is higher than the source.
When they are opposing each other, the frequency decreases.
The frequency of the received signal is
fC is the frequency of source carrier,
fD is the Doppler frequency.
EE of NIU
Chih-Cheng Tseng

33. Doppler frequency (or Doppler shift)
v is the moving speed,
 is the wavelength of carrier MS
Signal from sender
Moving direction of receiver with speed v q
EE of NIU
Chih-Cheng Tseng

34. Moving Speed Effect V1 V2 V3 V4 Signal strength Time EE of NIU
Chih-Cheng Tseng

35. Delay Spread
When a signal propagates from a transmitter to a receiver, signal suffers one or more reflections.
This forces signal to follow different paths.
Each path has different path length, so the time of arrival for each path is different.
This effect which spreads out the signal is called “Delay Spread”, td.
EE of NIU
Chih-Cheng Tseng

36. Delay Spread Signal Strength Delay
The signals from close by reflectors
The signals from intermediate reflectors
Signal Strength
The signals from far away reflectors
Delay
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Chih-Cheng Tseng

37. Inter-Symbol Interference (ISI)
Caused by time delayed multipath signals
Has impact on burst error rate of the channel
If the transmission rate is R, a low bit-error-rate (BER) can be obtained when
EE of NIU
Chih-Cheng Tseng

38. Inter-Symbol Interference (ISI)
Time
Transmission signal
Received signal (short delay)
Received signal (long delay) 1
Propagation time
Delayed signals
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Chih-Cheng Tseng

39. Coherence Bandwidth Coherence bandwidth Bc≈ 1/(2πd) Flat fading
A statistical measure of the range of frequencies over which the channel can be considered as “flat”.
Flat fading
If the bandwidth of Tx signal is lower than the channel coherent bandwidth, nonlinear transformation could no occur.
Frequency-selective fading
If the bandwidth of Tx signal is higher than the channel coherent bandwidth, nonlinearity is present.
EE of NIU
Chih-Cheng Tseng

40. Cochannel Interference
Cells having the same frequency interfere with each other.
In a cellular system, to reuse the frequencies, the same frequency is assigned to different cells.
EE of NIU
Chih-Cheng Tseng

41. Homework
P3.7
P3.11
P3.12
P3.18
P3.20
EE of NIU
Chih-Cheng Tseng