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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Radio TransmissionRadio TransmissionRadio TransmissionRadio Transmission(Large(Large(Large(Large----Scale Fading)Scale Fading)Scale Fading)Scale Fading)
Instructor: Prof. Dr. Noor M. KhanDepartment of Electronic Engineering,Muhammad Ali Jinnah University,Islamabad Campus, Islamabad, PAKISTAN
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 1EE6763 Cellular Mobile Communications
Week 10 Week 10 Week 10 Week 10 ---- 11; Fall 11; Fall 11; Fall 11; Fall ---- 2014201420142014
Islamabad Campus, Islamabad, PAKISTANPh: +92 (51) 111-878787, Ext (Office) 116, Ext (ARWiC Lab) 186 Fax: +92 (51) 2822743 email: [email protected], [email protected] Center for Research in Wireless Communications (ARWiC)www.arwic.com
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Radio Wave Propagation• Mechanisms very diverse
– reflection, diffraction and scattering
• In urban areas where there is no direct LOS, high rise buildings cause severe diffraction loss
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 2EE6763 Cellular Mobile Communications
Week 10 Week 10 Week 10 Week 10 ---- 11; Fall 11; Fall 11; Fall 11; Fall ---- 2014201420142014
• Waves travel along different paths of varying lengths– interaction causes multi-path fading
• Strength decreases as the distance between the transmitter and receiver increases
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Propagation Models
• Have traditionally focused on predicting the average received signal strength in close spatial proximity to a particular location
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 3EE6763 Cellular Mobile Communications
Week 10 Week 10 Week 10 Week 10 ---- 11; Fall 11; Fall 11; Fall 11; Fall ---- 2014201420142014
spatial proximity to a particular location
• Models that predict mean signal strength for an arbitrary transmitter receiver (T-R) separation– Useful for estimating the radio coverage area of
a transmitter -large-scale models
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Propagation Models 2
• Large scale models have T-Rs of several hundred or thousands of meters
• Models that can characterize the rapid
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 4EE6763 Cellular Mobile Communications
Week 10 Week 10 Week 10 Week 10 ---- 11; Fall 11; Fall 11; Fall 11; Fall ---- 2014201420142014
• Models that can characterize the rapid fluctuations of received signal strength over short distances (few wavelengths) or short duration (second) are called small-scale or fading models
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Typical Look
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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 5EE6763 Cellular Mobile Communications
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Free Space Propagation Model
• Predicts received signal strength when Transmitter (T) and Receiver (R) have direct Line of Sight (LOS)
• Satellite & Microwave LOS radio links
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 6EE6763 Cellular Mobile Communications
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• Satellite & Microwave LOS radio links
• As with most large scale models, the free space model predicts that the received power decays as a function of T-R separation raised to some power (power law function)
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Isotropic Antenna
4π=
1=G
λ2
=
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eaAG
2
4
λπ=
πλ4
2
=ea
A
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Free Space Equation
– For a T-R distance ofd
λ)(
2PdP t=
=ravP ⋅Pv
eaAv
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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πλ
π 44)(
2d
PdP t
r=
– Pt - transmitted power,
– Pr(d) - received power,
Isotropic receiver and transmitter antenna used
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Friis Free Space Equation
– For a T-R distance ofd
Ld
GGPdP rtt
r 22
2
)4()(
πλ=
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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– Pt - transmitted power,
– Pr(d) - received power,
– Gt & Gr - transmitter & receiver antenna gains, L - system loss factor not related to propagation (L >= 1), λ - wavelength in meters
Ld)4( π
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Antenna Gain• The gain of an antenna is related to its effective
aperture, Ae, by:
• Ae is related the physical size of the antenna, and λ is related to the carrier frequency by:
eAG
2
4
λπ=
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λ is related to the carrier frequency by:
c
c
f
c
ωπλ 2==
cmms1
sm303.0
/10
/1039
8
==⋅=λ
f - the carrier frequency in Hz, ωc - carrier frequency in radians/sec, c - speed of light in m/sec
→= GHzf 1
EXAMPLE
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Units
• Pt and Pr must be in the same units [W, mW]
• Gt & Gr are dimensionless
• L is due to transmission line attenuation, filter &
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• L is due to transmission line attenuation, filter & antenna losses
• Friis shows that the received power falls off as the square of d - 20 dB/decade
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
EIRP• Isotropic radiator is an ideal antenna which
radiates power with unit gain uniformly in all directions - reference antenna gain in wireless systems
• Effective Isotropic Radiated Power (EIRP) is
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• Effective Isotropic Radiated Power (EIRP) is defined as
EIRP = PtGt
• Represents the maximum radiated power available from the transmitter in the direction of antenna gain as compared to an isotropic radiator
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
ERP
• In practice, effective radiated power (ERP) is used instead to denote the max radiated power as compared to an half-wave-dipole antenna
• Dipole antenna gain = 1.64, ERP will be 2.15dB
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• Dipole antenna gain = 1.64, ERP will be 2.15dB smaller than the EIRP for the same transmission system
• dBi - dB gain wrt to an isotropic source
• dBd - dB gain wrt to a half wave dipole
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Path Loss
• Path Loss represents signal attenuation as a positive quantity measured in dB
−==22
2
log10log10)( GGP
PdBPL rtt
πλ
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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−==22
)4(log10log10)(
dPdBPL
r π
−=22
2
)4(log10)(
ddBPL
πλ
If antenna gains Gr are Gr equal to 1
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Far Field
• Friis model is only valid for received powers, Pr at distances d, which are in the far field or Fraunhofer region.
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far field or Fraunhofer region.
• Far field of a transmitting antenna is defined as the region beyond the far field distance df, which is related to the largest linear dimension of the antenna aperture and/or carrier wavelength.
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Fraunhofer Distance
• Fraunhofer distance is given by
λ
22l
f
Dd =
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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• Dl is the largest physical liner dimension of the antenna
• To be in the far-field region,df must satisfy
• df >> Dl and df >> λ
λfd =
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Distance d = 0
• The received power equation does not hold for d = 0.
• Large scale models use a close-in distance d - received power reference point
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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• Large scale models use a close-in distance d0 - received power reference point
• The received power at any distance d > d0may be related to Pr(d0 ) at d0
• Pr(d0 ) may be predicted or determined through empirical measurements
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Proportions
dH(d )
Calculating height
of an inaccessible
point
measurable
quantities
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d
d0H(d0 )H(d)
0
)()( 0 dddHdH =
Not
measurable
directly
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Received power Pr(d)
• d must be chosen to be in the far-field region
22
2
)4()(
d
PdP t
r ⋅=πλ
tr P
ddPcon
20
0)( ⋅=2
)(d
PcondP t
r ⋅=20
0)(d
PcondP t
r ⋅=
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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• d0 must be chosen to be in the far-field region
frr ddddd
dPdP ≥≥=
0
2
00)()(
.;log20W001.0
)(log10][)( 0
00f
rr ddd
dddP
dBmdP ≥≥+=
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
measurabl
e
quantities
not
measurabl
e
Received power Pr(d)Pt
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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d
d0
Pr (d0 ) Pr(d)
BSBSBSBS
frr ddddd
dPdP ≥≥=
0
2
00)()(
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Ground Reflection (2-ray) Model
•In a mobile radio channel, a single direct path
between the base station and a mobile is
exception rather then rule
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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exception rather then rule
•Two ray ground reflection model is reasonably
accurate for predicting the large scale signal
strength over distances of several kilometers for
mobile radio systems
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Two Ray Model
ht
hr
d0
d’’
EEEETOTTOTTOTTOT
EEEEOOOO
d’
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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hr
d
−−
−=c
dt
d
dE
c
dt
d
dEtdE CCTOT
''cos
''
'cos
'),( 0000 ωω
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Two Ray Model
)()( 000
fθddd
d
dEdE >>=
d0 – reference
distance
frr ddddd
dPdP ≥≥=
0
2
00)()(
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 23EE6763 Cellular Mobile Communications
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)(cos),( 000 dd
c
dt
d
dEtdE Cθ
>
−= ω
−−
−=c
dt
d
dE
c
dt
d
dEtdE
CCTOT
''cos
''
'cos
'),( 0000 ωω
),''(),'(),( tdEtdEtdEREFLOSTOT
−=
distance
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Two Ray Model Approximations
;rt hhd +>>'''000000
d
dE
d
dE
d
dE ≈≈⇒;2
'''d
hhdd rt≈−⇒
;)('';)(' 2222 dhhddhhd rtrt ++=+−=
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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=dλ
hπh
d
dEdE rt
TOT
2sin2)( 00
''' dddd
rad3.02
for <dλ
hπh rt
2
004
)(d
hh
λ
dπEdE rt
TOT=
4
22
d
hhGGPP rt
trtr =
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Two Ray Model Path Loss
Pt=1;transmitted power[W] Gt=1;trans antenna gain Gr=1;receiver antenna gain 0.15 [m] wavelength 1990 mHz carrier frequency ht=15; hr=1.5;
P
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1/d2 1/d4
Noise level
Large SNRLarge SNRLarge SNRLarge SNR
4
22
d
hhGGPP rt
trtr =
2)(
d
PcondP t
r ⋅=
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Two Ray Model -The Model of ‘Distance Filtering’
1/d2This is
how it
We wish it
was like
this
Pt=1;transmitted power[W] Gt=1;trans antenna gain Gr=1;receiver antenna gain 0.15 [m] wavelength 1990 mHz carrier frequency ht=15; hr=1.5;
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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1/d2
1/d4
how it
is
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Actual Cell Size
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
•D2=[(j·R)2+ (i·R)2 - (i·R) (j·R) cos(120O )]
NRijijRD 33 22 =⋅++=
Distance between interfering cells
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D
j=2
NRD 3=
R – cell radius
N- cluster size
D – distance between interfering cells
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Simpler SIR
– Considering only the first layer of interfering cells & if all these BS are equidistant
)3()/( NRDS nn
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– i0 - number of neighboring/interfering co-channel cells
00
)3()/(
i
N
i
RD
I
S nn
==
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
1 → 6
2 → 12
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3 → 18
k → 6k
…
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Interference Limitation
=nNS )3(
∑=
−
−
=0
1
)(i
i
ni
n
D
R
I
SNkRD K 3<
−nRS
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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∑=
−⋅= K
k
nk
N
I
S
0
16
)3(
∑=
−⋅
−= K
k
nNkRk
nR
I
S
0)3(6
k – circle of interfering cels
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Interference Limitation
∑=
−⋅= K
k
n
n
k
N
I
S
0
16
)3(
© Dr. Noor M KhanDr. Noor M KhanDr. Noor M KhanDr. Noor M Khan
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– Considering K layers of interfering cells
– For N fixed, n=2 and the number of layers K→∞; S/I →0
∞== ∑=∞→
)1
(lim0
K
k kOI
K
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Log-distance Path Loss Model• Average received power decreases as the n-th power of the
relative distance between the transmitter and the receiver
• The average large scale path loss for an arbitrary T-R separation is expressed as function of distance using a path-loss exponent
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path-loss exponent
n
d
ddPL
∝
0
)(
+=
00 log10)(][
d
dndPLdBPL
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Log-distance Path Loss Model
• n - the rate at which the path loss increases– For free space n=2
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– For free space n=2
• d0 – close-in reference distance
• The value of n depends on the specific propagation environment
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Example
Environment Path Loss Exponent, n
Free space 2
Urban area cellular radio 2.7 to 3.5
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Urban area cellular radio 2.7 to 3.5
Shadowed urban cellularradio
3 to 5
Inbuilding LOS 1.6 to 1.8
Obstructed in building 4 to 6
Obstructed in factories 2 to 3
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Log-normal Shadowing 1
• The log distance Model does not consider the effects of environmental clutter– Large discrepancies
• It has been shown that path loss at a
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• It has been shown that path loss at a particular location is random, and distributed log-normally
σσ Xd
dndPLXdPLdPL +
+=+=
00 log10)()()(
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Log-normal Shadowing 2
• Xσ - zero mean Gaussian distributed random σ
)(dPLPP tr −=
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σvariable (dB) with standard deviation σ(dB)
• d0, n and σ statistically describe the path loss model for an arbitrary location
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Log-normal Shadowing 3
• n and σ are in practice computed from measured data using linear regression (fitting)
• PL(d0) is based either on close-in measurements or on a free space assumption from transmitter to d
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0
on a free space assumption from transmitter to d0
• A number of practical models exist for predicting path loss in “real” propagation conditions
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
A Cell Design Problem
A GSM-1800 operator provides cellular coverage in Karachi (Area: 2500 km2) with 49 microcells of similar hexagonal geometry. If a mobile unit is considered to be located at the edge of a cell, find the Signal to Noise Ratio (SNR) that is ensured for 90% of the time at the mobile unit.
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the mobile unit.
Assume the following: The close-in reference distance d0 = 1 km. Transmitter power Pt = 10W, the receiver and the transmitter antenna gains are Gt=3 dB and Gr=0 dB, respectively. The propagation beyond the close-in distance occurs with a path loss exponent n=4 and follows a log-normal distribution with standard deviation σ=6.5dB. Normal temperature in Karachi is 27O C and the noise figure of the mobile unit is 10dB.
Radio Transmission 39EE6763 Cellular Mobile CommunicationsEE6763 Cellular Mobile CommunicationsEE6763 Cellular Mobile CommunicationsEE6763 Cellular Mobile Communications
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