1 CS 6910 – Pervasive Computing Spring 2007 Section 3 (Ch.3): Mobile Radio Propagation Prof. Leszek Lilien Department of Computer Science Western Michigan.
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1
CS 6910 – Pervasive ComputingSpring 2007
Section 3 (Ch.3):
Mobile Radio Propagation
Prof. Leszek LilienDepartment of Computer Science
Western Michigan University
Slides based on publisher’s slides for 1st and 2nd edition of: Introduction to Wireless and Mobile Systems by Agrawal & Zeng
© 2003, 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved.
Some original slides were modified by L. Lilien, who strived to make such modifications clearly visible. Some slides were added by L. Lilien, and are © 2006-2007 by Leszek T. Lilien.
Requests to use L. Lilien’s slides for non-profit purposes will be gladly granted upon a written request.
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 2
Chapter 3
Mobile Radio Propagation
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 3
Outline of Chapter 3We skip a lot of detailed information from this Chapter
Introduction Types of Waves
Speed, Wavelength, Frequency Radio Frequency Bands Propagation Mechanisms Radio Propagation Effects Free-Space Propagation Land Propagation Path Loss Fading: Slow Fading / Fast Fading Delay Spread Doppler Shift Co-Channel Interference The Near-Far Problem Digital Wireless Communication System Analog and Digital Signals Modulation Techniques
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 4
3.1. Introduction
This section covers the distinguishing features of mobile radio propagation
Model of wireless mobile channel Time-varying communication path between 2
terminals Fixed BS and mobile MS
Mobility introduces new challenges into radio propagation
© 2007 by Leszek T. Lilien
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 5
Speed, Wavelength, Frequency
System Frequency Wavelength
AC current 60 Hz 5,000 km
FM radio 100 MHz (88-99, 100-108)
3 m
Cellular (original) 800 MHz 37.5 cm
Ka band satellite 20 GHz 15 mm
Ultraviolet light 1015 Hz 10-7 m
Light speed = Wavelength x Frequency = 3 x 108 m/s = 300,000 km/s
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 6
Speed, Wavelength, Frequency – cont.
© 2007 by Leszek T. Lilien
** OPTIONAL ** Broadcast Frequencies (cf.
http://en.wikipedia.org/wiki/Radio_frequencies): AM radio bands:
long waves (now 153–279 kHz, historically up to 413 kHz) medium waves (520–1,710 kHz in the Americas) short waves (2,300–26,100 kHz)
TV Band I (Channels 2 - 6) = 54MHz - 88MHz (VHF) FM Radio Band II = 88MHz - 108MHz (VHF) TV Band III (Channels 7 - 13) = 174MHz - 216MHz
(VHF) TV Bands IV & V (Channels 14 - 69) = 470MHz -
806MHz (UHF) Most common cellular bands now in uses worldwide:
850/900/1800/1900 MHz E.g., China uses yet another
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 7
3.2. Types of Radio Waves
Transmitter Receiver
Earth
Sky wave
Space wave
Ground waveTroposphere
(0 - 12 km)
Stratosphere (12 - 50 km)
Mesosphere (50 - 80 km)
Ionosphere (80 - 720 km)
Ground , space, and sky waves Cellular systems use ground & space
waves
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 8
Radio Frequency BandsClassification Band
Initials Frequency Range Characteristics
Extremely low ELF < 300 Hz
Ground waveInfra low ILF 300 Hz - 3 kHz
Very low VLF 3 kHz - 30 kHz
Low LF 30 kHz - 300 kHz
Medium MF 300 kHz - 3 MHz Ground/Sky wave
High HF 3 MHz - 30 MHz Sky wave
Very high VHF 30 MHz - 300 MHz
Space waveUltra high UHF 300 MHz - 3 GHz
Super high SHF 3 GHz - 30 GHz
Extremely high EHF 30 GHz - 300 GHz
Tremendously high
THF 300 GHz - 3000 GHz
AM long wave
AM med. wave
AM short wave
FM, TV
TV, cellphonesWLAN
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 9
3.3. Propagation Mechanisms Ideal propagation in free space (no obstacles)
Radio signals can penetrate simple walls to some extentLarge structure, a hill – difficult to pass through
Propagation effects due to obstacles Reflection
Propagation wave impinges on an object which is large as compared to wavelength
E.g., the surface of the Earth, buildings, walls, etc. Diffraction
Radio path between transmitter and receiver obstructed by surface with sharp irregular edges
Waves bend around the obstacle, even when LOS (line of sight) does not exist
Scattering Objects smaller than the wavelength of the propagation wave
E.g. foliage, street signs, lamp posts
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 10
Radio Propagation Effectshb – heights of BS antenna, hm - heights of MS antenna
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 11
Quality of signal reaching receiver via different types of radio waves Direct propagation is the best Reflection is 2nd best Diffraction is 3rd best Scattering is 4th best
If no direct-path waves (LOS waves) can reach receiver mainly by reflection or diffraction
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 12
3.4. Free-space Propagation
The received signal power Pr at distance d:
Ae is effective area covered by the transmitter (on the receiver’s side - e.g., receiver’s antenna)
Gt is the transmitting antenna gain (a better antenna has a higher gain)
Pt is transmitting power(Assuming that the radiated power is uniformly distributed over the surface of the sphere.)
Transmitter Distance dReceiver
hb
hm
2r
4P
d
PGA tte
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 13
** SKIP ** Antenna Gain For a circular reflector antenna Gain G = ( D / )2
= net efficiency (depends on the electric field distribution over the antenna aperture, losses, ohmic heating , typically 0.55)
D = diameter thus, G = ( D f /c )2, c = f (c is speed of light)
Example: Antenna with diameter = 2 m, frequency = 6 GHz, wavelength = 0.05 m G = 39.4 dB Frequency = 14 GHz, same diameter, wavelength = 0.021 m G = 46.9 dB * The higher the frequency, the higher the gain for the same-size antenna
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 14
Free-space Path Loss
Definition of path loss LP :
Path loss in free space (no obstacles):
where fc is the carrier frequency
The greater the fc , the higher is the loss (see next
slide)
,r
tP P
PL
),(log20)(log2045.32)( 1010 kmdMHzfdBL cPF
Pt is transmitted signal power Pr is received signal power
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 15
Example of Path Loss (Free-space)
Path Loss in Free-space
70
80
90
100
110
120
130
0 5 10 15 20 25 30
Distance d (km)
Path
Los
s Lf
(dB)
fc=150MHz
fc=200MHz
fc=400MHz
fc=800MHz
fc=1000MHz
fc=1500MHz
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 16
3.5. Land Propagation
The received signal power:
where: Gt is the transmitter antenna gain,
Gr is the receiver antenna gain,
L is the propagation loss in the channel,
i.e., L = LP LS LF
L
PGGP trt
r
Fast fading (long-term f.)
Slow fading (short-term f.)
Path loss
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 17
Fast and Slow Fading and Path Loss
Fast fading (short-term fading) – Microscopic aspect of a channel for mobile comm. For a moving MS, it represents fading over its every
step Due to scattering of signal by objects near transmitter
=> Changing wave diffractions
Slow fading (long-term fading) – Variation of propagation loss in a local area (k * 10m) Due to obstacles (e.g., buildings) For an MS, it represents overall average fading over
short distance (e.g., a couple of blocks) traveled by MS Path loss
Propagation loss over long distances (more below)
© 2007 by Leszek T. Lilien
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 18
Schematic Diagram of Propagation Loss (and Fading)
Signal Strength
(dB)
Distance
Path Loss
Slow Fading (Long-term fading)
Fast Fading (Short-term fading)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 19© 2007 by Leszek T. Lilien
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 20
3.6. Path Loss (for Land Propagation)
Path loss as a fcn of distance Lp = A dα
where: A and α: propagation constantsd : distance between transmitter and receiver
Value of : - 2-4 - normally - below 2 in some waveguides - 2 in free space, - 3-4 in typical urban areas - 4 is for relatively lossy environments. - 4-6 in some environments, such as buildings, stadiums & other indoor environments
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 21
Path Loss
Path loss in decreasing order: Urban area (large city) Urban area (medium and small city) Suburban area Open area
Path
loss
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 22
Path Loss (Urban, Suburban and Open areas)
Urban area:
where
Suburban area:
Open area:
)(log)(log55.69.44
)()(log82.13)(log16.2655.69)(
1010
1010
kmdmh
mhmhMHzfdBL
b
mbcPU
citymediumsmallfor
MHzfformh
MHzfformh
cityelforMHzfmhMHzf
mh
cm
cm
cmc
m &,400,97.4)(75.11log2.3
200,1.1)(54.1log29.8
arg,8.0)(log56.1)(7.0)(log1.1
)(2
10
210
1010
4.528
)(log2)()(
2
10
MHzfdBLdBL c
PUPS
94.40)(log33.18)(log78.4)()( 102
10 MHzfMHzfdBLdBL ccPUPO
Notice how LPU is subtracted from in LPS and LPO
-
hb, hm – see slide 20
(Units: MHz, m, etc., in parentheses)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 23
Example of Path Loss (Urban Area: Large City)
Path Loss in Urban Area in Large City
100
110
120
130
140
150
160
170
180
0 10 20 30
Distance d (km)
Pat
h Lo
ss L
pu (
dB)
fc=200MHz
fc=400MHz
fc=800MHz
fc=1000MHz
fc=1500MHz
fc=150MHz Should be on top of this fc list
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 24
Example of Path Loss (Urban Area: Medium and Small Cities)
Path Loss in Urban Area for Small & Medium Cities
100
110
120
130
140
150
160
170
180
0 10 20 30
Distance d (km)
Pat
h Lo
ss L
pu (
dB) fc=150MHz
fc=200MHz
fc=400MHz
fc=800MHz
fc=1000MHz
fc=1500MHz
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 25
Example of Path Loss (Suburban Area)
Path Loss in Suburban Area
90
100
110
120
130
140
150
160
170
0 5 10 15 20 25 30
Distance d (km)
Path
Los
s Lp
s (d
B)
fc=150MHz
fc=200MHz
fc=400MHz
fc=800MHz
fc=1000MHz
fc=1500MHz
Compare loss for, e.g., 30 km & 1500 MHz with Large/Small Urban
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 26
Example of Path Loss (Open Area)[repeated for completeness]
Path Loss in Open Area
80
90
100
110
120
130
140
150
0 5 10 15 20 25 30
Distance d (km)
Path
Los
s Lp
o (d
B)
fc=150MHz
fc=200MHz
fc=400MHz
fc=800MHz
fc=1000MHz
fc=1500MHz
Compare loss for, e.g., 30 km & 1500 MHz with Large/Small Urban & Suburb.
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 27
3.7. Slow Fading Slow fading (shadowing or log-normal fading) of a signal = long-
term spatial and temporal variations in signal strength over “large enough “ distances Distance is “large enough “ if it produces gross variation in signal strength
for the overall path between the transmitter and receiver
Slow fading obeys log-normal distribution (hence one of its names)
- The pdf of the received signal level is given in decibels (dB) by
where
M is the true received signal level m in dB (i.e., 10log10m) M is the area average signal level (i.e., the mean of M) is the standard deviation in dB
,2
1 2
2
2
MM
eMp
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 28
** SKIP ** Log-normal Distribution
MM
2
p(M)
The pdf of the received signal level(log-normal distribution)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 29
3.8. Fast Fading Fast fading (short-term fading) of a signal = rapid fluctuations in
the spatial and temporal signal characteristics caused by local mulipath Multipath – since scattered, diffracted, and reflected signals gets
to receiver’s antenna over many paths
Fast fading occurs over distances of about half a wavelength Example:
VHF and UHF (30 MHz - 300 MHz & 300 MHz - 3 GHz) Vehicle traveling at 30 mph It passes through several fades in a second
Mobile radio signal consists of: Fast fading signal Superimposed on a local mean value
Local mean value: constant over a small area / varies slowly as the receiver moves
© 2007 by Leszek T. Lilien
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 30
Modeling fast fading: When receiver is far from transmitter
No direct radio waves between transmitter & receiver
Reflected waves stronger
Modeled by the Rayleigh distribution (below) Useful for modeling when no LOS
When receiver is close to transmitter Direct radio wave between transmitter &
receiver is stronger than other waves Stronger than reflected, diffracted, or scattered
Modeled by the Rician distribution (below)
© 2007 by Leszek T. Lilien
Fast Fading - cont. 1
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 31
Rayleigh Distribution
The pdf of the Rayleigh Distribution
r – envelope of the fading signal; - standard deviation
r2 4 6 8 10
P(r)
0
0.2
0.4
0.6
0.8
1.0
=1
=2
=3
rm = 1.777 rm is middle value of envelope signal (i.e. such value that: P(r ≤ rm) = 0.5)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 32
Rician Distribution
r
p(r
)
r86420
0.6
0.5
0.4
0.3
0.2
0.1
0
= 2 = 1
= 0
= 1
= 3
The pdf of the Rician Distribution
r – envelope of the fading signal - amplitude of the direct signal ( = 0 means no direct signal)
= 0 means no direct signal => Rayleigh distr. - see the same shape as for Rayleigh distr. with = 1
For large (= very strong signal), Rician distr. can be approximated by Gaussian distribution
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 33
Modeling fast fading – cont.:
When receiver is far from transmitter Modeled by the Rayleigh distribution
When receiver is close to transmitter Modeled by the Rician distribution
Generalized model for any distance – Nakagami distrib.
Rayleigh distribution is its special case Rician distribution can be closely approximated
by it “Can often be better” than Rician
© 2007 by Leszek T. Lilien
Fast Fading - cont. 2
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 34
Characteristics of Instantaneous Amplitude Instantaneous amplitude => potentially fast changing
signal
Characteristics of instantaneous amplitude Level crossing rate at a specified threshold (signal level)
Average number of times per second that the signal envelope crosses the threshold in positive-going direction
Fading rate Number of times that the signal envelope crosses the middle
value rm in positive-going direction per unit time Depth of fading
Ratio of mean square value of fading signal and minimum value of fading signal
Average depth of fading often used instead Fading duration
Duration for which signal is below a given threshold
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 35
3.9. Doppler Effect (Doppler Shift) Doppler effect - occurs when a wave source and a receiver are
moving towards or away from each other When they are moving toward each other, the frequency of the
received signal is higher than the source frequency When they are moving away from each other, the frequency is
lower than the source frequency
Received signal frequency is
where: fC - source frequency ,
fD - the Doppler shift in frequency
Doppler shift is
where: v - the moving speed - the wavelength of the carrier of the source signal
cosv
fD
DCR fff
MS
Signal from source
Moving direction of the receiver (MS)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 36
*** SKIP *** Moving Speed Effect[LTL:] This textbook figure is not consistent with text referring to it. It is confusing in the context of the Doppler effect (which has to do with signal frequency not signal strength, as the figure suggests).
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 37
3.10. Delay Spread When a signal propagates from a transmitter to a receiver, it can
suffer one or more reflections [Agrawal & Zeng]
Now, instead of single-path direct signal we have a multipath reflected signal reaching the receiver
More descriptively: Each reflection of the original signal produces a new (fainter) “child” signal that follows its own path
The path followed by the “child” signal is determined by reflection parameters
When all “children” signals are put together, we have multiple reflected signals (all originating from the original signal) following a multipath towards the receiver
Some of the “children” signals may be too faint to reach the receiver
Some of the “children” signals may be reflected in wrong direction(s) and never reach the receiver
© 2007 by Leszek T. Lilien
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 38
Delay Spread – cont.
Different paths in the multipath have different lengths, so the time of arrival for each of many reflected “child” signals is different
This spreads out the received signal
=> is called “delay spread” If we had direct signal only, there would be one signal
path, no children signals, and no delay spread
See Figure (next)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 39
Delay Spread
Delay
Sig
nal S
tren
gth
The signals reflected from nearby reflectors
The signals reflected from intermediate reflectors
The signals reflected from distant reflectors
Q1: A signal reflected by a nearby reflector arrives sooner than a signal reflected by a more distant reflector. Why?
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 40
Delay Spread – cont. 1
© 2007 by Leszek T. Lilien
Q1: A signal reflected by a nearby reflector arrives sooner than a signal reflected by a more distant reflector. Why?
A: First note that the direct path is the shortest path from the xmitter to the receiver.
A signal reflected by a nearby reflector already traveled most of the distance d as a direct signal. In other words, such signal already traveled most of the distance d along the shortest path to the receiver.
A signal reflected further away from the receiver was reflected earlier, so it traveled more of the distance d as a multipath reflected signal, i.e., its components (children signals) traveled more of the distance d along a longer (not the shortest) path to the receiver.
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 41
Delay Spread (again)
Delay
Sig
nal S
tren
gth
The signals reflected from nearby reflectors
The signals reflected from intermediate reflectors
The signals reflected from distant reflectors
Q2: A signal reflected by a nearby reflector is stronger than a signal reflected by a more distant reflector. Why?
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 42
Delay Spread – cont. 2
© 2007 by Leszek T. Lilien
Q2: A signal reflected by a nearby reflector is stronger than a signal reflected by a more distant reflector. Why?
A: A signal reflected by a nearby reflector already traveled most of the distance d as the strongest (single-path & direct) signal.
A signal reflected further away from the receiver was reflected earlier, and traveled more of the distance d as a weaker (multipath & reflected) signal. To be precise, it traveled as a multipath collection of reflected children signals, collectively weaker than the original single-path & direct signal would be.
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 43
Delay Spread – cont. 3
© 2007 by Leszek T. Lilien
Typical delay spread: 3 microsec. in a city area 10 microsec. in a hilly terrain
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 44© 2007 by Leszek T. Lilien
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 45
3.11. Intersymbol Interference (ISI) Intersymbol Interference (ISI) - caused by delay spread
Example of ISI: 101… digital signal sent from xmitter to rcver
4 multipaths due to reflections Single-path direct signal 4 multipath reflected children
signals Each child generated by another reflection of the
original signal
See figures in the next 2 slides
Observation – case of ISI: In Slide +2 multipath components for symbol “1” arrive at
the time when only multipath components for symbol “0” should be arriving => symbol “1” interferes with symbol “0”
© 2007 by Leszek T. Lilien
[Agrawal&Zeng]
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 46
Intersymbol Interference (ISI) Example
Modified by LTL
Figure: Xmitter and receiver are synchronized
Red broken-line arrows show synchronization “Short delay”: all 4 delayed multipath signals showing
NULL1 arrive within duration of their “time slot “
Time
Time
Transmission signal
Received signal (Short delay)
1
0
1
Propagation time
Delayed multipathsignals
NULL
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 47
Intersymbol Interference (ISI) Example
Modified by LTL
Figure Xmitter and receiver are synchronized
Red broken-line arrows show synchronization “Long delay”: only 1 delayed multipath signal showing
NULL1 arrives within duration of its “time slot” 3 delayed multipath signals arrive too late (within the next “time slot”)
Time
Time
Transmission signal
Received signal (Long delay)
1
0
1
Delayed multipathsignalsPropagation time
NULL
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 48
Burst error– a contiguous sequence of symbols, received over a data transmission channel, such that:(a) the first symbol and the last symbol are in error,
and (b) there exists no contiguous subsequence of m
correctly received symbols within the error burst The last symbol in a burst and the first symbol in
the following burst are separated by m correct bits or more
The length of a burst of errors in a frame is defined as the number of bits from the first error to the last, inclusive
Error burst – occurrence of burst errors Burst error rate – measures the rate of burst errors
ISI can cause burst errors=> ISI has impact on the burst error rate of a channel
3.11. Intersymbol Interference (ISI) – cont. 1
© 2007 by Leszek T. Lilien
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 49
3.11. Intersymbol Interference (ISI) – cont. 2
To assure low bit-error rate (BER), digital transmission rate R must be limited by delay spread d as follows:
dR
21
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 50
3.12. Coherence Bandwidth Gain [cf. http://en.wikipedia.org/wiki/Gain]
= the mean ratio of the signal output of a system to the signal input of the system
Gain has wide use to characterize amplifiers
Linear phase channel (or filter) [cf. http://en.wikipedia.org/wiki/Linear_phase]
= channel with no distortion due to the frequency-selective delays
All frequency components have equal delay times
In contrast, in a filter/channel with non-linear phase, delay varies with frequency, resulting in phase distortion
Flat channel Passes all frequencies (“spectral components”) with
approxi-mately equal gain and linear phase
© 2007 by Leszek T. Lilien
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 51
3.12. Coherence Bandwidth – cont.1
Coherence bandwidth Bc
= channel frequency range over which the channel can be considered “flat”
In other words: the frequency interval over which two different frequencies f1 and f2 of a signal are likely to experience correlated (amplitude) fading [cf. http://en.wikipedia.org/wiki/Coherence_bandwidth]
*** SKIP this bullet *** - NOT EXPLAINED WELL – SEEMS INCONSISTENT WITH THE REST Bc represents the correlation between 2 fading signal envelopes at
frequencies f1 and f2 Correlation => a statistical measure
Bc is a function of delay spread Bigger delay spread => lower correlation
Two frequencies that are larger than their coherence bandwidth Bc fade independently
Concept of coherence bandwidth useful in diversity reception Diversity reception = multiple copies of same message are sent using
different frequencies
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 52
3.12. Coherence Bandwidth – cont.2
Let S = transmitted signalB = bandwidth of SBc = channels’ coherence bandwidth
If B < Bc => linear transmission of S Only gain and phase of S are changed
=> S not distorted Intuitively, whole B for S is flat (whole B within Bc)
If B > Bc => non-linear transmission of S Part of S truncated
=> S severely distorted Intuitively, only part of B for S is flat (part of B outside of Bc)
© 2007 by Leszek T. Lilien
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 53
3.13. Cochannel Interference
Cells reuse frequencies Same freq assigned to different cells
=> cells using the same frequency interfere with each other
Let: rd - the desired signal
ru - the interfering undesired signal
- the protection ratio for which rd ru (so that interference of ru is limited by )
(Probability of) cochannel interference between cells reusing a frequency
Pco = P(rd ru )
where P(rd ru ) = probability that rd ru
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 54
3.13. Cochannel Interference
Cells having the same frequency interfere with each other rd is the desired signal
ru is the interfering undesired signal is the protection ratio for which rd ru (so that interference of ru
is limited by )
Cochannel interference between cells using the same frequency
Pco = P(rd ru )
where P(rd ru ) = probability that rd ru
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 55
The End of Section 3
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