radio transmission - arwic · muhammad ali jinnah university, islamabad campus, pakistan radio...
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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
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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
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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
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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 2EE6763 Cellular Mobile Communications
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• Waves travel along different paths of varying lengths– interaction causes multi-path fading
• Strength decreases as the distance between the transmitter and receiver increases
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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
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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 3EE6763 Cellular Mobile Communications
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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
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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
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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 4EE6763 Cellular Mobile Communications
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• 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
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Typical Look
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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
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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)
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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
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Free Space Equation
– For a T-R distance ofd
λ)(
2PdP t=
=ravP ⋅Pv
eaAv
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πλ
π 44)(
2d
PdP t
r=
– Pt - transmitted power,
– Pr(d) - received power,
Isotropic receiver and transmitter antenna used
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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=
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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
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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
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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
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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
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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
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Path Loss
• Path Loss represents signal attenuation as a positive quantity measured in dB
−==22
2
log10log10)( GGP
PdBPL rtt
πλ
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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
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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.
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Fraunhofer Distance
• Fraunhofer distance is given by
λ
22l
f
Dd =
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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 =
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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
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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
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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
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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 ⋅=
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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 ≥≥+=
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
measurabl
e
quantities
not
measurabl
e
Received power Pr(d)Pt
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d
d0
Pr (d0 ) Pr(d)
BSBSBSBS
frr ddddd
dPdP ≥≥=
0
2
00)()(
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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
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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
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Two Ray Model
ht
hr
d0
d’’
EEEETOTTOTTOTTOT
EEEEOOOO
d’
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hr
d
−−
−=c
dt
d
dE
c
dt
d
dEtdE CCTOT
''cos
''
'cos
'),( 0000 ωω
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Two Ray Model
)()( 000
fθddd
d
dEdE >>=
d0 – reference
distance
frr ddddd
dPdP ≥≥=
0
2
00)()(
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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
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Two Ray Model Approximations
;rt hhd +>>'''000000
d
dE
d
dE
d
dE ≈≈⇒;2
'''d
hhdd rt≈−⇒
;)('';)(' 2222 dhhddhhd rtrt ++=+−=
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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 =
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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 ⋅=
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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;
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1/d2
1/d4
how it
is
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Actual Cell Size
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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 27EE6763 Cellular Mobile Communications
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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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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 28EE6763 Cellular Mobile Communications
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D
j=2
NRD 3=
R – cell radius
N- cluster size
D – distance between interfering cells
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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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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 29EE6763 Cellular Mobile Communications
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– i0 - number of neighboring/interfering co-channel cells
00
)3()/(
i
N
i
RD
I
S nn
==
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
1 → 6
2 → 12
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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 30EE6763 Cellular Mobile Communications
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3 → 18
k → 6k
…
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Interference Limitation
=nNS )3(
∑=
−
−
=0
1
)(i
i
ni
n
D
R
I
SNkRD K 3<
−nRS
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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 31EE6763 Cellular Mobile Communications
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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
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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
EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 32EE6763 Cellular Mobile Communications
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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
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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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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 33EE6763 Cellular Mobile Communications
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path-loss exponent
n
d
ddPL
∝
0
)(
+=
00 log10)(][
d
dndPLdBPL
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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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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 34EE6763 Cellular Mobile Communications
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– For free space n=2
• d0 – close-in reference distance
• The value of n depends on the specific propagation environment
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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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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 35EE6763 Cellular Mobile Communications
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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
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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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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 36EE6763 Cellular Mobile Communications
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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)()()(
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
Log-normal Shadowing 2
• Xσ - zero mean Gaussian distributed random σ
)(dPLPP tr −=
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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 37EE6763 Cellular Mobile Communications
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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
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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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EE, MAJUEE, MAJUEE, MAJUEE, MAJURadio Transmission 38EE6763 Cellular Mobile Communications
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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
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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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