introductory radiowave propagation.ppt
TRANSCRIPT
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Introduction to Radiowave
PropagationDr Costas Constantinou
School of Electronic, Electrical & Computer Engineering
University of BirminghamW: www.eee.bham.ac.uk/ConstantinouCC/
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Introduction
For an overview, see Chapters 14 of L.W. Barclay
(Ed.), Propagation of Radiowaves, 2ndEd., London:
The IEE, 2003
The main textbook supporting these lectures is: R.E.Collin, Antennas and Radiowave Propagation, New
York: McGraw-Hill, 1985
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Introduction (cont.)
Simple free-space propagation occurs only rarely
For most radio links we need to study the influence
of the presence of the earth, buildings, vegetation,
the atmosphere, hydrometeors and the ionosphere In this lectures we will concentrate on simple
terrestrial propagation models only
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Radio Spectrum
Symbol Frequency range Wavelength, Comments
ELF < 300 Hz > 1000 km Earth-ionosphere waveguide
propagationULF 300 Hz3 kHz 1000100 km
VLF 3 kHz30 kHz 10010 km
LF 30300 kHz 101 km Ground wave propagation
MF 300 kHz3 MHz 1 km100 m
HF 330 MHz 10010 m Ionospheric sky-wave propagation
VHF 30300 MHz 101 m Space waves, scattering by objects
similarly sized to, or bigger than, a free-
space wavelength, increasingly affected
by tropospheric phenomena
UHF 300 MHz3 GHz 1 m100 mmSHF 330 GHz 10010 mm
EHF 30300 GHz 101 mm
8 1; 3 10 msc f c
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Electromagnetic waves
Spherical waves
Intensity (time-average)
Conservation of energy; the inverse square law
HES
212Wm
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Electromagnetic waves
Conservation of energy; the inverse square law
Energy cannot flow perpendicularly to, but flows along
light rays
2
dtransmitte
2
steradiansofsectorangularanindtransmitte
2
22112
2
2
1
2
1
1
2
4
11
21
r
P
rl
P
rr
PAAPrr
AA
l
AA
r
r
rEr
rrr
r
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Free-space propagation
Transmitted power
EIPR(equivalent isotropically radiated power)
Power density at receiver
Received power
Friis power transmission formula
txP
txtxPG
2
txtxrx
4 RPG
S
4;
4
2
rx
rxrx
2
txtxrx GAA
R
PGP ee
2
rxtx
tx
rx
4
RGG
P
P
Tx Rx
R
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Free-space propagation (cont.)
Taking logarithms gives
where is the free-space path loss, measured in decibels
Maths reminder
RGGPP
4log20log10log10log10log10 10rx10tx10tx10rx10
cbcb aaa logloglog ,loglog bcba
c
a
dBdBidBidBWdBW 0rxtxtxrx LGGPP
0L
dB4
log20 100
RL
kmdfL 10MHz100 log20log204.32dB
,log
loglog
a
bb
c
c
a
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Basic calculations
Example: Two vertical dipoles, each with gain 2dBi, separated
in free space by 100m, the transmitting one radiating a power
of 10mW at 2.4GHz
This corresponds to 0.4nW (or an electric field strength of
0.12mVm-1)
The important quantity though is the signal to noise ratio atthe receiver. In most instances antenna noise is dominated by
electronic equipment thermal noise, given by
where is Boltzmans constant, B is the
receiver bandwidth and T is the room temperature in Kelvin
0.801.0log202400log204.32dB 10100 L
0.940.802log102log1010log10dBW 10102
10rx P
TBkN B123 JK1038.1 Bk
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Basic calculations (cont.)
The noise power output by a receiver with a Noise FigureF=
10dB, and bandwidth B = 200kHz at room temperature (T =
300K) is calculated as follows
Thus the signal to noise ratio(SNR) is given by
FTBkN B 1010 log10log10dBW 10log10102003001038.1log10dBW 10
323
10 N
dBm8.110dBW8.140 N
8.1400.94dBWdBWdB NPSNR
dB8.46SNR
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Basic calculations (cont.)
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Propagation over a flat earth
The two ray model (homogeneous ground)
Valid in the VHF, band and above (i.e. f 30MHz whereground/surface wave effects are negligible)
Valid for flat ground (i.e. r.m.s. roughness z< , typically f 30GHz)
Valid for short ranges where the earths curvature is negligible (i.e. d 0 path obstraction)(u0< 0 path clearance)
u
a
Site shielding
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Site sheilding
The Kirchhoff integral describing the summing of secondary
wavefronts in the Huygens-Fresnel principle yields the field at
the receiver
where k1describes the transmitter power, polarisation and
radiation pattern,f(r)describes the amplitude spreading
factor for the secondary waves (2D cylindrical wavef(r) = r1/2,
3D spherical wavef(r) = r) and u1is a large positive value of u
to describe a distant upper bound on the wavefront
1
0
1
expu
u
jkrE R k du
f r
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Site shielding
Stationary phase arguments (since the exponent is oscillatory,
especially for high frequencies) show that only the fields in
the vicinity of the point O contribute significantly to the field
at R
If point O is obstructed by the knife-edge, then only the fields
in the vicinity of the tip of the knife-edge contribute
significantly to the field at R
Using the cosine rule on the triangle TPR, gives
2 2 22
2 2 2
2 1 2 1 1 2 1
1
2 cos
2 cos
r PR TP TR TP TR
ud d d d d d d
d
a
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Site shielding
If we assume that d1, d2>> , u(stationary phase and far-field
approximations), then u/d1, a
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Site shielding
Since , we make the substitution
which simplifies the integral to the form,
where we have used the stationary phase argument to makethe upper limit
Using the definition of the complex Fresnel integral,
21 21 2
d dk u ud d
21 22
1 2 2
2&
2
d d du k u k du
d d k
0
1 2 2
2 2
expexp 2
k jkd E R j d
k f d
20
exp 2
x
F x j d
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Site shielding
To determine k3we let and useF()=F() and
the fact that in this case we have free-space propagation (i.e.
E(R) =E0(R)) , to get,
1 2
3
2 2
3 0
3 0
exp
12
k jkd k
k f d
E R k F F
jE R k F
0 3
0 0
3
1
11 2
E R k j
E R E Rk j
j
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Site shielding
Therefore,
where,
The path-gain factor,F, is given by,
Useful engineering approximations:
0
0 21 exp 22
E RE R j j d
1 2
0 0
1 2
2 d du
d d
0
2
0
1exp 2
2
E RF j d
E R
10 10 0 0
2
10 0 0 0
2
10 0 0 0
20log 13 20log 2.4
20log 6.02 9.11 1.27 0 2.4
20log 6.02 9.0 1.65 0.8 0
F
F v
F v
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Site shielding
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Multipath propagation
Mobile radio channels are predominantly in the VHF
and UHF bands
VHF band (30 MHz f 300 MHz, or 1 m 10 m)
UHF band (300 MHz f 3 GHz, or 10 cm 1 m) In an outdoor environment electromagnetic signals
can travel from the transmitter to the receiver along
many paths
Reflection
Diffraction
Transmission
Scattering
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Multipath propagation
Narrowband signal
(continuous wave
CW) envelope
Area mean or path
loss (deterministic or
empirical)
Local mean, or shadowing, or slowfading (deterministic or statistical)
Fast or multipathfading (statistical)
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Multipath propagation The total signal consists of
many components
Each componentcorresponds to a signalwhich has a variableamplitude and phase
The power received variesrapidly as the componentphasors add with rapidlychanging phases
Averaging the phase angles results in the local meansignal over areas of the order of 102
Averaging the length (i.e. power) over manylocations/obstructions results in the area mean
The signals at the receiver can be expressed interms of delay, and depend on polarisation, angle
of arrival, Doppler shift, etc.
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Area mean models
We will only cover the Hata-Okumura model, which
derives from extensive measurements made by
Okumura in 1968 in and around Tokyo between 200
MHz and 2 GHz The measurements were approximated in a set of
simple median path loss formulae by Hata
The model has been standardised by the ITU as
recommendation ITU-R P.529-2
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Area mean models
The model applies to three clutter and terrain
categories
Urban area: built-up city or large town with large buildings
and houses with two or more storeys, or larger villages
with closely built houses and tall, thickly grown trees
Suburban area: village or highway scattered with trees and
houses, some obstacles being near the mobile, but not
very congested
Open area: open space, no tall trees or buildings in path,
plot of land cleared for 300400 m ahead, e.g. farmland,
rice fields, open fields
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Area mean models
where
citiessmalltomediumfor8.0log56.17.0log1.1
MHz300cities,largefor1.154.1log29.8
MHz300cities,largefor97.475.11log2.394.40log33.18log78.4
4.528log2
log55.69.44
log82.13log16.2655.69
2
2
2
2
cmc
cm
cm
cc
c
b
bc
fhfE
fhE
fhEffD
fC
hB
hfA
DRBAL
CRBALERBAL
logdB:areasopen
logdB:areassuburbanlogdB:areasurban
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Area mean models
The Hata-Okumura model is only valid for:
Carrier frequencies: 150 MHz fc1500 MHz
Base station/transmitter heights: 30 m hb200 m
Mobile station/receiver heights: 1 m hm10 m Communication range:R> 1 km
A large city is defined as having an average building height
in excess of 15 m
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Local mean model
The departure of the local mean power from the area meanprediction, or equivalently the deviation of the area meanmodel is described by a log-normal distribution
In the same manner that the theorem of large numbers states
that the probability density function of the sum of manyrandom processes obeys a normal distribution, the product ofa large number of random processes obeys a log-normaldistribution
Here the product characterises the many cascaded
interactions of electromagnetic waves in reaching the receiver The theoretical basis for this model is questionable over
short-ranges, but it is the best available that fits observations
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Local mean model
Working in logarithmic units (decibels, dB), the total path lossis given by
whereXis a random variable obeying a lognormal
distribution with standard deviation (again measured indB)
Ifxis measured in linear units (e.g. Volts)
where mxis the mean value of the signal given by the areamean model
XdLdPL
2dB2dB
2exp2
1
XXp
2
dBdB2
lnlnexp2
1
xmxx
xp
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Local mean model
Cumulative probability density function
This can be used to calculate the probability that the signal-to-
noise ratio will never be lower than a desired threshold value.
This is called an outage calculation Typical values of dB= 10 dBare encountered in urban
outdoor environments, with a de-correlation distance
between 2080 mwith a median value of 40 m
2erfc
211
2exp2
1cdf 2dB
2
dB
Threshold
dLL
dXXLPL
T
dLLT
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Fast fading models Constructive and destructive
interference
In spatial domain
In frequency domain
In time domain (scatterers, tx and rx inrelative motion)
Azimuth dependent Doppler shifts
Each multipath component travelscorresponds to a different path length.
Plot of power carried by eachcomponent against delay is called the
power delay profile (PDP )of thechannel.
2ndcentral moment of PDP is called thedelay spread
P
Im
Re
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Fast fading models
The relation of the radio system channel bandwidthBchto the
delay spread is very important
Narrowband channel(flat fading, negligible inter-symbol interference
(ISI), diversity antennas useful)
Wideband channel(frequency selective fading, need equalisation(RAKE receiver) or spread spectrum techniques (W-CDMA, OFDM,
etc.) to avoid/limit ISI)
Fast fading refers to very rapid variations in signal strength (20
to in excess of 50 dBin magnitude) typically in an analogue
narrowband channel
Dominant LOS component Rician fading
NLOS components of similar magnitude Rayleigh fading
1 chB
1 chB
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Fast fading models
Working in logarithmic units (decibels, dB), the total path loss
is given by
where Y is random variable which describes the fast fading
and it obeys the distribution
for Rayleigh fading, where the mean value of Yis
YXdLdPL 10log20
80.012 Y
0,0
0,2
exp2
2
2
Y
YYY
Yp
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Fast fading models
For Rician fading
whereysis the amplitude of the dominant (LOS) componentwith power . The ratio is called the RicianK-factor. The mean value of Yis
The Rician K-factor can vary considerably across small areas inindoor environments
0,0
0,I2
exp202
22
2
Y
YYyyYY
Ypss
22
sy22
Rice 2syK
2exp2I2I12 10 KKKKKY
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Fading models
Similar but much more complicated outage calculations
E.g. Rayleigh and log-normal distributions combine to give a Suzuki
distribution
The spatial distribution of fades is such that the length of a
fade depends on the number of dB below the local meansignal we are concerned with
Fade depth (dB) Average fade length ()
0 0.479
-10 0.108
-20 0.033
-30 0.010
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Tropospheric propagation
Over long-distances, more than a few tens of km,
and heights of up to 10 km above the earths surface,
clear air effects in the troposphere become non-
negligible The dielectric constant of the air at the earths
surface of (approx.) 1.0003 falls to 1.0000 at great
heights where the density of the air tends to zero
A consequence of Snells law of refraction is that
radiowaves follow curved, rather than straight-line
trajectories
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Tropospheric propagation
The variation of the ray
curvature with refractive index is
derived:
AA: wavefront at time t
BB: wavefront at time t + dtABand AB: rays normal to the
wavefronts
: radius of curvature of AB
A
A
BB
O
d
d dh
n + dn
n
c dt
A B d v dt n
c dtAB d d v dv dt
n dn
d c c
dt n n dn d
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Tropospheric propagation
Retaining only terms which are correct to first order in small
quantities,
But this is the curvature, C, of the ray AB, by definition.
Furthermore,
For rays propagating along the earths surfaceis very small
and we may take cos= 1. Moreover, n11.
n n nd dn dnd
1 1
dn nd
dn
n d
cosdh d
1 1cos
dnC
n dh
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Tropospheric propagation
If n= constant, dn/dh= 0 C= 0and the ray has zero
curvature, i.e. the ray path is a straight line
A ray propagating horizontally above the earth must have a
curvature C= (earths radius)1= a1in order to remain
parallel with the earths surface. But its actual curvature is
given by Cand not C.
The difference between the two curvatures gives the
curvature of an equivalent earth for which dn/dh= 0andwhich has an effective radius ae,
dnCdh
1 1 1
e
dn
a a dh ka
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Tropospheric propagation
kis known as the k-factor for the earth
Typically, dn/dh0.039106m11/(25,600 km)
Therefore,
The k-factor of the earth is k= 4/3
The effective radius of the earth is ae= 4a/3
These values are used in the standard earth model which
explains why the radio horizon is bigger than the radio horizon
1 1 1 1
6,400 km 25,600 km 6,400 kme
a k
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Tropospheric propagation
Problem: Find the radio horizon of an elevated antenna at a
height htabove the earth
Answer: 2 e tR a h