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Frequency and Spectrum Types of Waves Propagation Model Free-Space Propagation Path Loss Fading: Slow Fading / Fast Fading Doppler Shift Delay Spread
FIGURE Electromagnetic frequency spectrum.
Wayne Tomasi
Electronic Communications Systems, Fourth Edition
Tomasi
Advanced Electronic Communications
Systems, 6e
FIGURE Electromagnetic wavelength spectrum
Frequency and wave length
= c/f
wave length , speed of light c 3x108m/s, frequency f
1 Mm
300
Hz
10 km
30 kHz
100 m
3 MHz
1 m
300 MHz
10 mm
30 GHz
100
m
3 THz
1 m
300
THz
visible
light
VL
F
LF M
F
HF VHF UHF SHF EHF infrared UV
optical transmission coax cable twisted
pair
Schiller P26
Frequency Name Typical application band (kHz)
3 – 30 Very low frequency Long-distance navigation, (VLF) Underwater comm. Sonar
30 – 300 Low frequency Navigation, underwater comm. (LF) radio beaconing
300 – 3000 Medium frequency Broadcasting, maritime comm. (MF) direction-finding, distress calling, coast guard
Fan P10-11
Frequency Name Typical application band (MHz)
3 – 30 High frequency Long-distance broadcasting, telegraph, (HF) telephone, fax, search and lifesaving,
comm. between aircrafts & ships, and between ship & coast, amateur radio
30 – 300 Very high frequency TV, FM broadcasting, land traffic, air (VHF) traffic, control, taxi, police, avigation,
aircraft communication
300 – 3000 Ultra high frequency TV, cellular phone network, microwave (UHF) link, , radio sounding, navigation, satellite communication, GPS, surveillance radar, radio altimeter
Fan P11
Frequency Name Typical application band (GHz) 3 – 30 Super high frequency Satellite comm., radio altimeter, (SHF) microwave link, aircraft radar, meteorological radar, public land vehicle communication 30 – 300 Extremely high Radar landing system, satellite frequency (EHF) comm., vehicle comm., railway traffic 300 – 3000 Submillimeter wave Experiment, not
designated （0.1 – 1 mm） Fan P11
Frequency Name Typical application band (THz)
43 – 430 Infrared Optical communication (7 – 0.7 m)
430 – 750 Visible light Optical communication (0.7 – 0.4 m) 750 – 3000 Ultraviolet Optical communication
(0.4 – 0.1 m) Note: kHz = 103 Hz, MHz = 106 Hz, GHz = 109 Hz, THz = 1012 Hz, mm = 10-3 m, m = 10-6 m
Fan P11
VHF-/UHF-ranges for mobile radio simple, small antenna for cars
deterministic propagation characteristics, reliable connections
SHF and higher for directed radio links, satellite communication small antenna, beam forming
large bandwidth available
Wireless LANs use frequencies in UHF to SHF range some systems planned up to EHF
limitations due to absorption by, e.g., water (dielectric heating, see microwave oven)
▪ weather dependent fading, signal loss caused by heavy rainfall etc.
Schiller P26-27
Examples Europe USA Japan
Cellular networks GSM 880-915, 925-960, 1710-1785, 1805-1880
UMTS 1920-1980, 2110-2170
LTE 791-821, 832-862, 2500-2690
AMPS, TDMA, CDMA, GSM 824-849, 869-894
TDMA, CDMA, GSM, UMTS 1850-1910, 1930-1990
PDC, FOMA 810-888, 893-958
PDC 1429-1453, 1477-1501
FOMA 1920-1980, 2110-2170
Cordless phones CT1+ 885-887, 930-932
CT2 864-868
DECT 1880-1900
PACS 1850-1910, 1930-1990
PACS-UB 1910-1930
PHS 1895-1918
JCT 245-380
Wireless LANs 802.11b/g 2412-2472 802.11b/g 2412-2462 802.11b 2412-2484
802.11g 2412-2472
Other RF systems 27, 128, 418, 433, 868 315, 915 426, 868
In general: ITU-R holds auctions for new frequencies, manages frequency bands worldwide (WRC, World Radio Conferences); 3GPP specific: see e.g. 3GPP TS 36.101 V11.4.0 (2013-03)
Schiller P28-29
Tomasi
Advanced Electronic Communications
Systems, 6e
TABLE Microwave Radio-Frequency Assignments
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 - 300 kHz
Medium MF 300 kHz - 3 MHz Ground/Shy wave
High HF 3 MHz - 30 MHz Sky wave
Very high VHF 30 MHz - 300 MHz
Space wave
Ultra 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
Agrawal P33
Earth
Ground wave
Space wave
Ionosphere
(80 - 720 km)
Mesosphere
(50 - 80 km)
Stratosphere
(12 - 50 km)
Troposphere
(0 - 12 km)
Agrawal P33
Ground-wave propagation Sky-wave propagation Line-of-sight propagation
Beard P166
Figure Propagation of radio frequencies.
Couch P41
Tomasi
Advanced Electronic Communications
Systems, 6e FIGURE Microwave propagation paths
Follows contour of the earth Can Propagate considerable distances
hundreds to thousands of km
Frequencies up to 2 MHz Diffraction Example
AM radio
Fan P11-12
Beard P165
Signal reflected from ionized layer of atmosphere back down to earth
Signal can travel a number of hops, back and forth between ionosphere(60 ~ 400 km) and earth’s surface
One hop max. propagation distance：4000 km Propagation distance by multi-hops: >10000 km Reflection effect caused by refraction Frequency：2 ~ 30 MHz Examples
Amateur radio
CB(Citizens Band) radio
Beard P166
Wayne Tomasi
Electronic Communications Systems, Fourth Edition
FIGURE Critical angle
D layer: 60 ~ 80 km E layer: 100 ~ 120 km F layer: 150 ~ 400 km F1 layer: 140 ~ 200 km F2 layer: 250 ~ 400 km At night: D layer: disappears F1 layer: disappears (Or, F1 and F2 are combined as F layer)
Wayne Tomasi
Electronic Communications Systems, Fourth Edition FIGURE Ionospheric layers
Transmitting and receiving antennas must be within line of sight Satellite communication – signal above 30 MHz not
reflected by ionosphere
Ground communication – antennas within effective line of site due to refraction
Refraction – bending of microwaves by the atmosphere Velocity of electromagnetic wave is a function of the
density of the medium
When wave changes medium, speed changes
Wave bends at the boundary between mediums
Beard P97
Couch P43
2 2 2
2 2
( )
2
d r r h
d rh h
2 2 2d h rh rh
Optical line of sight
Effective, or radio, line of sight
▪ d = distance between antenna and horizon (km)
▪ h = antenna height (m)
▪ K = adjustment factor to account for refraction, rule of thumb K = 4/3
hd 57.3
hd 57.3
Beard P168
FIGURE Space waves and radio horizon
Wayne Tomasi
Electronic Communications Systems, Fourth Edition
Maximum distance between two antennas for LOS propagation: ▪ h1 = height of antenna one
▪ h2 = height of antenna two
2157.3 hh
Beard P168
0 4.12 r td h m h m km
4.12 600 =100.9d km km
Tomasi
Advanced Electronic Communications
Systems, 6e
FIGURE Microwave radio communications link
Transmission range
communication possible
low error rate
Detection range
detection of the signal possible
no communication possible
Interference range
signal may not be detected
signal adds to the background noise
Warning: figure misleading – bizarre shaped, time-varying ranges in reality!
distance
sender
transmission
detection
interference
Schiller P35-36
Propagation in free space always like light (straight line) Receiving power proportional to 1/d² in vacuum – much more
attenuation in real environments, e.g., d3.5…d4 (d = distance between sender and receiver)
Receiving power additionally influenced by fading (frequency dependent)
shadowing
reflection at large obstacles
refraction depending on the density of a medium
scattering at small obstacles
diffraction at edges
reflection scattering diffraction shadowing refraction Schiller P37-39
Attenuation and attenuation distortion Free space loss Noise Atmospheric absorption Multipath Refraction Thermal noise
Beard P170
Strength of signal falls off with distance over transmission medium
Attenuation factors for unguided media:
Received signal must have sufficient strength so that circuitry in the receiver can interpret the signal
Signal must maintain a level sufficiently higher than noise to be received without error
Attenuation is greater at higher frequencies, causing distortion
Beard P171
Atten
uatio
n
(dB
/km
)
Vapor
Oxygen
Frequency (GHz) (a) Attenuation of oxygen & vapor（concentration 7.5 g/m3）
Atten
uatio
n (d
B/k
m)
Rainfall rate
Frequency (GHz) (b) Attenuation of rainfall Fan P14
The received signal power:
where Pr is the received power,
Pt is the transmitting power,
Gr is the receiver antenna gain,
Gt is the transmitter antenna gain,
L is the propagation loss in the channel, i.e.,
L = LP LS LF
L
PGGP trt
r
Fast fading
Slow fading
Path loss Agrawal P38
If a radio channel’s propagating characteristics are not specified, one usually infers that the signal attenuation versus distance behaves as if propagation takes place over ideal free space. The model of free space treats the region between the transmit and receive antennas as being free of all objects that might absorb or reflect radio frequency (RF) energy. It also assumes that, within this region, the atmosphere behaves as a perfectly uniform and nonabsorbing medium.
Sklar P946
Furthermore, the earth is treated as being infinitely far away from the propagating signal (or, equivalently, as having a reflection coefficient that is negligible). Basically, in this idealized free-space model, the attenuation of RF energy between the transmitter and receiver behaves according to an inverse-square law. The received power expressed in terms of transmitted power is attenuated by a factor , where this factor is called path loss or free space loss.
( )sL dSklar P946
When the receiving antenna is isotropic, this factor is expressed as
where d is the distance between the transmitter and the receiver, and is the wavelength of the propagating signal. For this case of idealized propagation, received signal power is very predictable. For most practical channels, where signal propagation takes place in the atmosphere and near the ground, the free-space propagation model is inadequate to describe the channel behavior and predict system performance.
Sklar P946
Sklar P251
Transmitter Distance d
Receiver
hb
hm
2r
4P
d
PGA tte
The received signal power at distance d:
where Pt is transmitting power, Ae is effective area, and Gt is the transmitting antenna gain. Assuming that the radiated power is uniformly distributed over the surface of the sphere.
Agrawal P35-36
Antenna gain
Power output, in a particular direction, compared to that produced in any direction by a perfect omnidirectional antenna (isotropic antenna)
Effective area
Related to physical size and shape of antenna
Beard P161-162
Relationship between antenna gain and effective area
▪ G = antenna gain
▪ Ae = effective area
▪ f = carrier frequency
▪ c = speed of light (» 3 ´ 108 m/s)
▪ = carrier wavelength
2
2
2
44
c
AfAG ee
RR GA
4
2
Beard P162
Free space loss, ideal isotropic antenna
▪ Pt = signal power at transmitting antenna
▪ Pr = signal power at receiving antenna
▪ = carrier wavelength
▪ d = propagation distance between antennas
▪ c = speed of light (» 3 ´ 10 8 m/s)
where d and are in the same units (e.g., meters)
2
2
2
244
c
fdd
P
P
r
t
H. T. Friis, "A note on a simple transmission formula," Proc.
IRE, vol. 34, pp. 254-256. 1946 Beard P171-172
Free space loss accounting for gain of other antennas
▪ Gt = gain of transmitting antenna
▪ Gr = gain of receiving antenna
▪ At = effective area of transmitting antenna
▪ Ar = effective area of receiving antenna
trtrtrr
t
AAf
cd
AA
d
GG
d
P
P2
22
2
224
Beard P172
Free space loss equation can be recast:
d
P
PL
r
tdB
4log20log10
dB 98.21log20log20 d
dB 56.147log20log204
log20
df
c
fd
Beard P172
Free space loss accounting for gain of other antennas can be recast as
rtdB AAdL log10log20log20
dB54.169log10log20log20 rt AAdf
Beard P172
Path Loss: The signal strength decays exponentially with distance d between transmitter and receiver;
The loss could be proportional to somewhere between d 2 and d 4 depending on the environment.
Definition of path loss LP :
Path Loss in Free-space:
where fc is the carrier frequency.
This shows greater the fc , more is the loss.
,r
tP
P
PL
),(log20)(log2045.32)( 1010 kmdMHzfdBL cPF
Agrawal P36
Path Loss in Free-space
70
80
90
100
110
120
130
0 5 10 15 20 25 30
Distance d (km)
Path
Loss L
f (d
B) fc=150MHz
fc=200MHz
fc=400MHz
fc=800MHz
fc=1000MHz
fc=1500MHz
Agrawal P40
Path Loss in Urban Area in Large City
100
110
120
130
140
150
160
170
180
0 10 20 30
Distance d (km)
Pa
th L
oss L
pu
(d
B)
fc=200MHz
fc=400MHz
fc=800MHz
fc=1000MHz
fc=1500MHz
fc=150MHz
Agrawal P40
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)
Path
Loss L
pu (
dB
)
fc=150MHz
fc=200MHz
fc=400MHz
fc=800MHz
fc=1000MHz
fc=1500MHz
Agrawal P40
Path Loss in Suburban Area
90
100
110
120
130
140
150
160
170
0 5 10 15 20 25 30
Distance d (km)
Pa
th L
oss L
ps (
dB
)
fc=150MHz
fc=200MHz
fc=400MHz
fc=800MHz
fc=1000MHz
fc=1500MHz
Agrawal P40
Path Loss in Open Area
80
90
100
110
120
130
140
150
0 5 10 15 20 25 30
Distance d (km)
Pa
th L
oss L
po
(d
B)
fc=150MHz
fc=200MHz
fc=400MHz
fc=800MHz
fc=1000MHz
fc=1500MHz
Agrawal P40
From the website of Science Museum
Mobile phone base station antenna
disguised as a Saguaro cactus,
manufactured by Larson Camouflage, LLC,
Arizona, United States, 2013-2014
Simplest Formula: Lp = A dα
where
A and α: propagation constants
d : distance between transmitter and receiver
α : value of 3 ~ 4 in typical urban area
Agrawal P39
Rappaport P139
Path loss in decreasing order:
Urban area (large city)
Urban area (medium and small city)
Suburban area
Open area
Agrawal P39-40
Okamura, Y. a kol.: Field Strength and its Variability in VHF and UHF Land-Mobile
Radio Service. Rev. Elec. Comm. Lab. No.9-10pp. 825 - 873, 1968.
hb=200m, hm=3m
https://en.wikipedia.org/wiki/Okumura_model
Rappaport P152
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
2
10
1010
4.528
)(log2)()(
2
10
MHzfdBLdBL c
PUPS
94.40)(log33.18)(log78.4)()( 10
2
10 MHzfMHzfdBLdBL ccPUPO
Agrawal P39-40 https://en.wikipedia.org/wiki/Hata_model
% Code for Simulation Of OKUMURA Model % Code By:- Debaraj Rana % mail- [email protected] % Dept. Of Electronics & Telecom. Engg %% VSSUT, Burla,ORISSA clc; clear all; close all; Hte=30:1:100; % Base Station Antenna Height
Hre=input('Enter the receiver antenna height 3m<hre<10m : '); % Mobile Antenna Height d =input('Enter distance from base station 1Km<d<100Km : '); % Distance 30 Km f=input('Enter the frequency 150Mhz<f<1920Mhz : '); c=3*10^8; lamda=(c)/(f*10^6); Lf = 10*log((lamda^2)/((4*pi)^2)*d^2); % Free Space Propagation Loss Amu = 35; % Median Attenuation Relative to Free Space (900 MHz and 30 Km)
Garea = 9; % Gain due to the Type of Environment (Suburban Area) Ghte = 20*log(Hte/200); % Base Station Antenna Height Gain Factor if(Hre>3)
Ghre = 20*log(Hre/3); else Ghre = 10*log(Hre/3); end % Propagation Path Loss L50 = Lf+Amu-Ghte-Ghre-Garea;
display('Propagation pathloss is : '); disp(L50); plot(Hte,L50,'LineWidth',1.5); title('Okumura Model Analysis'); xlabel('Transmitter antenna Height (Km)'); ylabel('Propagation Path loss(dB) at 50 Km'); grid on;
http://www.mathworks.com/matlabcentral/fil
eexchange/28423-okumura-model-
simulation/content/OKUMURA.m
Rappaport P155
J. Walfisch, H. L. Bertoni, "A theoretical model of UHF propagation in urban
environments," IEEE Trans. on Antennas and Propagation, vol. 36, no. 12, pp.
1788-1796, Dec. 1988
Intermodulation noise – occurs if signals with different frequencies share the same medium
Interference caused by a signal produced at a frequency that is the sum or difference of original frequencies
Crosstalk – unwanted coupling between signal paths
Impulse noise – irregular pulses or noise spikes
Short duration and of relatively high amplitude
Caused by external electromagnetic disturbances, or faults and flaws in the communications system
Beard P177-178
Ratio of signal energy per bit to noise power density per Hertz
The bit error rate for digital data is a function of Eb/N0 Given a value for Eb/N0 to achieve a desired error rate,
parameters of this formula can be selected
As bit rate R increases, transmitted signal power must increase to maintain required Eb/N0
TR
S
N
RS
N
Eb
k
/
00
Stallings P111
Atmospheric absorption – water vapor and oxygen contribute to attenuation
Multipath – obstacles reflect signals so that multiple copies with varying delays are received
Refraction – bending of radio waves as they propagate through the atmosphere
Beard P180-182
Tomasi
Advanced Electronic Communications
Systems, 6e FIGURE Median duration of fast fading
Transmitter d
Receiver
hb
hm
Diffracted
Signal
Reflected Signal
Building
STOP Scattered
Agrawal P35
Signal can take many different paths between sender and receiver due to reflection, scattering, diffraction
Time dispersion: signal is dispersed over time
interference with “neighbor” symbols, Inter Symbol Interference (ISI)
The signal reaches a receiver directly and phase shifted
distorted signal depending on the phases of the different parts
signal at sender
signal at receiver
LOS pulses multipath
pulses
LOS
(line-of-sight)
Schiller P39
Multiple copies of a signal may arrive at different phases If phases add destructively, the signal level
relative to noise declines, making detection more difficult
Intersymbol interference (ISI) One or more delayed copies of a pulse may arrive
at the same time as the primary pulse for a subsequent bit
Beard P183
Sketch of Three Important Propagation
Mechanisms Beard P183
Figure Illustrating the mechanism of radio propagation
in urban areas. (From Parsons, 1992, with permission.) Haykin P532
Reflection - occurs when signal encounters a surface that is large relative to the wavelength of the signal
Diffraction - occurs at the edge of an impenetrable body that is large compared to wavelength of radio wave
Scattering – occurs when incoming signal hits an object whose size in the order of the wavelength of the signal or less
Beard P182-183
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
Agrawal P34-35
Rappaport P121
Rappaport P122
Rappaport P128
Rappaport P129
Figure 4.12 Illustration of Fresnel zones for different knife-edge diffraction scenarios. Rappaport P130
Ionosphere scattering
Frequency: 30 ~ 60 MHz
Troposphere scattering
Frequency: 100 ~ 4000 MHz
Meteor-tail scattering
Frequency: 30 ~ 100 MHz
Effective
scattering region
Transmitting
antenna Earth Receiving
antenna
Figure Troposphere scattering
communication
Ground
Figure Meteor-tail scattering
communication
Fan P15
Channel characteristics change over time and location signal paths change
different delay variations of different signal parts
different phases of signal parts
quick changes in the power received (short term fading)
Additional changes in distance to sender
obstacles further away
slow changes in the average power received (long term fading)
short term fading
long term
fading
t
power
Schiller P40
Fast fading Slow fading
Flat fading Selective fading
Rayleigh fading Rician fading
Beard P185
Figure Small-scale and large-scale fading. Rappaport P106
Slow fading is caused by movement over distances large enough to produce gross variations in the overall path between transmitter and receiver.
The long-term variation in the mean level is known as slow fading (shadowing or log-normal fading). This fading caused by shadowing.
Agrawal P41
Shadowing: Often there are millions of tiny obstructions in the channel, such as water droplets if it is raining or the individual leaves of trees. Because it is too cumbersome to take into account all the obstructions in the channel, these effects are typically lumped together into a random power loss.
Log-normal distribution: - The pdf of the received signal level is given in decibels by
where M is the true received signal level m in decibels, i.e., 10log10m, M is the area average signal level, i.e., the mean of M,
is the standard deviation in decibels
,2
1 2
2
2
MM
eMp
Agrawal P42
M
2
p(M)
M
The pdf of the received signal level Agrawal P42
The signal from the transmitter may be reflected from objects such as hills, buildings, or vehicles. Fast fading is due to scattering of the signal by object near transmitter. When MS far from BS, the envelope distribution of received signal is
Rayleigh distribution with b=0. The pdf is where is the standard deviation, r is the envelope of
fading signal, b is the amplitude of direct signal, and I0 is the zero order Basel Function. Middle value rm of envelope signal within sample range to be
satisfied by
We have rm = 1.777
0),(20
22
2
22
rr
Ier
rp
r
.5.0)( mrrP
Agrawal P43
r 2 4 6 8 10
P(r)
0
0.2
0.4
0.6
0.8
1.0
=1
=2
=3
The pdf of the envelope variation Agrawal P43
Rappaport P211
When MS is not far from BS, the envelope distribution of received signal is called a Rician distribution. The pdf is
where
is the standard deviation,
I0(x) is the zero-order Bessel function of the first kind,
is the amplitude of the direct signal
0,02
2
2
22
rr
Ier
rp
r
Agrawal P44
r
p(r
)
r86420
0.6
0.5
0.4
0.3
0.2
0.1
0
= 2
= 1
= 1
= 3
= 0 (Rayleigh)
The pdf of the envelope variation Agrawal P45
Rappaport P214
Level Crossing Rate:
Average number of times per second that the signal envelope crosses the 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.
Agrawal P46-47
Doppler Effect: When a wave source and a receiver are moving towards each other, 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.
Thus, the frequency of the received signal is
where fC is the frequency of source carrier,
fD is the Doppler frequency.
Doppler Shift in frequency:
where v is the moving speed,
is the wavelength of carrier.
DCR fff
cosv
fD Signal
MS Moving speed v
Agrawal P48-49
RappaportP180
Rappaport P219
Rappaport P219
Time
V1 V2 V3 V4
Sig
nal
str
eng
th
Different moving speed
Agrawal P48
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”.
Agrawal P50
Delay
Sig
nal
Str
eng
th
The signals from close by reflectors
The signals from intermediate reflectors
The signals from far away reflectors
Agrawal P50
Time
Time
Time
Received signal (short delay)
Received signal (long delay)
1
0
1
Propagation time Delayed signals
Transmission signal
Agrawal P51
Caused by time delayed multipath signals Has impact on the burst error rate of channel Second multipath is delayed and is received
during next symbol For low bit-error-rate (BER)
R (digital transmission rate) limited by delay
spread d.
d
R2
1
Agrawal P51
Coherence bandwidth Bc:
Represents correlation between two fading signal envelopes at frequencies f1 and f2.
Is a function of delay spread.
Two frequencies that are larger than coherence bandwidth fade independently.
Concept useful in diversity reception
▪ Multiple copies of the same message are sent using different frequencies.
Agrawal P52
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 the signals interfere the least)
If P(rd ru ) is the probability that rd ru ,
Cochannel probability Pco = P(rd ru )
Agrawal P52-53
Tomasi
Advanced Electronic Communications
Systems, 6e
FIGURE Co-channel interference
Tomasi
Advanced Electronic Communications
Systems, 6e FIGURE Adjacent-channel interference
Forward error correction Adaptive equalization Diversity techniques
Beard P189-192
Transmitter adds error-correcting code to data block
Code is a function of the data bits
Receiver calculates error-correcting code from incoming data bits
If calculated code matches incoming code, no error occurred
If error-correcting codes don’t match, receiver attempts to determine bits in error and correct
Beard P189
Can be applied to transmissions that carry analog or digital information Analog voice or video
Digital data, digitized voice or video Used to combat intersymbol interference Involves gathering dispersed symbol energy back
into its original time interval Techniques Lumped analog circuits
Sophisticated digital signal processing algorithms
Beard P190
Diversity is based on the fact that individual channels experience independent fading events Space diversity – techniques involving physical
transmission path
Frequency diversity – techniques where the signal is spread out over a larger frequency bandwidth or carried on multiple frequency carriers
Time diversity – techniques aimed at spreading the data out over time
Beard P191-192
Frequency and Spectrum Types of Waves Free-Space Propagation Path Loss Propagation Model Fading Doppler Shift Delay Spread
Stalling’s book P125 5.13 5.14
