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Electrical & Computer Engineering Wireless Communications Channel Modeling – Large Scale Hamid Bahrami
Electrical & Computer Engineering
Wireless Communications
Channel Modeling – Large Scale
Hamid Bahrami
EM Spectrum
Radio Wave
l Radio wave: a form of electromagnetic radiation, created whenever a charged object accelerates with a frequency
l How are EM waves produced?
Charged particle à E-field and moving charged particle à B-feild
Review: Radio Wave Propagation
l Electric field and magnetic fields are orthogonal l The direction of propagation of the EM wave is
orthogonal to both the electric and magnetic fields l EM wave is propagating in the z direction l E field in orientated along the x axis l B field in orientated along the y axis
Radio Wave Propagation
l Statement of the problem l Path loss, reflection, diffraction, and scattering l Lack of direct line-of sight path between the Tx and Rx l Multipath fading
l Large-scale fading: transmission over large T-R separation distance (hundreds or thousands meters)
l Small-scale fading: transmission over short travel distance (a few wavelengths) or short time duration (seconds)
Free Space Propagation Model
l To predict received signal strength when the Tx and Rx have a line-of-sight (LOS) path l Satellite communication systems l Microwave LOS radio links l Friis free space equation
( ) LdGGPdP rtt
r 22
2
4)(
πλ
=
Transmitted power
Received power
Transmitter antenna gain
Receiver antenna gain
System loss factor L=1: no loss
Wavelength in meters
Distance between the Tx and Rx
Earth StationTransceiver
Satellite
c
cfc
ωπ
λ2
==
Example: page 109, 4.2 l If 50W is applied to a unity gain antenna with a 900M Hz carrier
frequency, find the received power in dBm at a free space distance of 100 m from the antenna. Assume unity gain for the receiver antenna.
( )( )
mWPr3
22
268
105.3)1()100(410900/100.3)1)(1)(50()100( −×=××
=π
( ) LdGGPdP rtt
r 22
2
4)(
πλ
=
( ) dBmmW 5.24105.3log10105.3 33 −=×⇒× −−
Free Space Propagation Model
l Path loss l Signal attenuation l The difference between the effective transmitted power and the
received power l May or may not include the effect of the antenna gains l Measured in dB
22
2
)4(log10log10)(
dGG
PPdBPL rt
r
t
πλ
−==
22
2
)4(log10log10)(
dPPdBPLr
t
πλ
−==
( ) LdGGPdP rtt
r 22
2
4)(
πλ
=
Free Space Propagation Model
l Review: near-field l The close-in region of an antenna where the angular
field distribution is dependent upon the distance from the antenna
l The region close to a source
l Review: far-field l The close-in region of an antenna where the angular
field distribution is independent upon the distance from the antenna
Free Space Propagation Model
l Far-field (Fraunhofer region) l The region beyond the far-field distance df
λ
22Dd f =
λ>>>> ff dDd
The largest physical linear dimension of the antenna
frr ddddddPdP ≥≥⎟⎠
⎞⎜⎝
⎛= 0
20
0 )()(
fr
r ddddddPdBmdP ≥≥⎟⎠
⎞⎜⎝
⎛+= 000 log20
001.0)(log10)(
Reference point:
Example: page 109, Ex. 4.1
l Find the far-field distance for an antenna with max. dimension of 1m and operating frequency of 900 MHz
mfc 33.0
10900100.3
6
8
=×
×==λ
mDd f 633.022 2
===λ
λ>>>> ff dDd
Answer: Largest dimension of antenna, D=1m Operating frequency, The far-field distance
λ
22Dd f =
Example: page 109, 4.2 l If 50W is applied to a unity gain antenna with a 900M Hz carrier
frequency, find the received power in dBm at a free space distance of 100 m from the antenna. What is Pr(10km)? Assume unity gain for the receiver antenna.
fr
r ddddddPdBmdP ≥≥⎟⎠
⎞⎜⎝
⎛+= 000 log20
001.0)(log10)(
dBmdBmdPr 5.6410000100log205.24)( −=⎟
⎠
⎞⎜⎝
⎛+−=
frr ddddddPdP ≥≥⎟⎠
⎞⎜⎝
⎛= 0
20
0 )()(Reference point:
Review: Radio Wave Propagation
l Statement of the problem l Reflection, diffraction, and scattering l Lack of direct line-of sight path between the Tx and Rx l Multipath fading
l Large-scale fading: transmission over large T-R separation distance (hundreds or thousands meters)
Take a look of this case first…
Reflection
l When a radio wave propagating in one medium impinges upon another medium have different electrical properties
l The wave is partially reflected l The reflection coefficient
l The material properties l The wave polarization l The angle of incidence l The wave frequency
Ground Reflection Model
l Two-Ray model
ht hr
d
θ θ
ELOS
Ei Eg
|ETOT|=|ELOS|+|Eg|
10(ht+hr)
The path distance between the LOS and the ground reflected path
Taking notes in class
( ) ( )
rtrt
rtrt
hhddhh
dhhdhhdd
+>>≈Δ
+−−++=ʹ−ʹ́=Δ
when ,2
2222
d1
d
ht
ht
hr
ht+hr
d2
ht-hr
t r t r t rd h h ; d h h ;d h h>> + >> − >>
h hd
and h hd
t t t r+<<
−<<1 1
( )2 2 2 2 21 2 22
r tt t r r r t r t
h hd d d h h h h h h h hd d
Δ ≅ − + − + − + + ≅
n
nn
n
xnnnx ∑
∞
= −−
=+0
24!)21()!2()1(1Taylor Series
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛ −+−⎟
⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛ ++=⎟
⎠
⎞⎜⎝
⎛ −+−⎟
⎠
⎞⎜⎝
⎛ ++⇒
⎟⎠
⎞⎜⎝
⎛ +−−
+=⎟⎠
⎞⎜⎝
⎛ ++
222
22
211
21111
)4)(1()2)(1(11
dhhd
dhhd
dhhd
dhhd
dhh
dhh
rtrtrtrt
rtrt
Ground Reflection Model
l The received E-field
dhh
ddEE rt
TOT λπ22 00≈
l The received power at a distance d
( )rtrt
rtrttr
hhGGddBPLdhhGGPP
log20log20log10log10log40)(
4
22
+++−=
=
rt hhd +>>
Ground Reflection Model
l Advantage l Consider both the direct path and a ground reflected
propagation path between the Tx and Rx l Disadvantage
l Oversimplified: does not include factors like terrain profile and surroundings
l Whether the two-ray model could be applied? l Case 1: ht=35 m, hr=3m, d=250 m l Case 1: ht=30 m, hr=1.5m, d=450 m
Review: Radio Wave Propagation
l Statement of the problem l Reflection, diffraction, and scattering l Lack of direct line-of sight path between the Tx and Rx l Multipath fading
l Large-scale fading: transmission over large T-R separation distance (hundreds or thousands meters)
Diffraction
l Signals propagate around the curved surface to the earth, beyond the horizon and to propagate behind obstructions
l Caused by the propagation of secondary wavelets into a shadowed region
Diffracted power
Obstruction(e.g. mountain)
Tx RxShadowed fading
Fresnel Zone Geometry
dbda
htho
hr
hβ γ
α
RxTx
( )( )
22 2
2 2 2a b
a b a b
d d hh hdd d d d
+Δ ≅ + =
( ) 22 22a b
a b
d d hdd d
π πθ
λ λ+Δ
Δ = ≅ ×
Excess path length
Fresnel-Kirchoff diffraction parameter
( )ba
ba
ddddhv
λ+
=2
Phase difference: • Height of the obstruction • Position of the obstruction • Position of Tx and Rx
Fresnel Zone Geometry
dbda
ht ho hr
h'βγ
α
RxTx
h
dbda
ho-hr
β
γ
α
θ aθ b
ht-hr
Tx Rx
Fresnel Zone Geometry
l Diffraction Loss l An function of the path difference around an
obstruction l An obstruction causes a blockage of energy from some
of the Fresnel zones, thus allowing only some of transmitted energy to reach the receiver
l Design LOS microwave links: 55% of the first Fresnel zone is clear
l Prediction of the diffraction loss is not easy in a real life due to complex and irregular terrain
Knife-edge Diffraction Model
l The simplest diffraction model l When shadowing is caused by a single object l In practice, graphical or numerical solutions are relied
upon to compute diffraction gain
( )1020dG ( dB ) log F v=
( )
( )( )
( )( )
12
0 9512
2
0 225
0 120 0 62 1 020 0 1
20 0 4 0 1184 0 38 0 1 1 2 4
20 2 4
. v
d
.v
vlog . v , vlog e , vG dBlog . . ( . . ) , v .
log , v .
−
≤ −⎧⎪ − − ≤ ≤⎪⎪ ≤ ≤=⎨⎪ − − − ≤ ≤⎪⎪ >⎩
Multiple Knife-edge Diffraction
l More than one obstructive object l The total diffraction loss due to all of the obstacles must
be computed l Replace all obstacles by a single equivalent one
dbda
htho
hr
hβ γ
α
RxTx
Scattering
l When a radio wave impinges on a rough surface, the reflected energy is spread out (diffused) in all directions due to scattering
l Resulting in the stronger received signal
Example 4.8, pp. 133 l Given the following geometry, determine (a) the loss due
to knife-edge diffraction, and (b) the height of the obstacle required to induce 6 dB diffraction loss. f=900 MHz.
50m 25m
100m
10km 2km
Practical Path Loss Model
l Path loss is the loss in signal strength as a function of distance l Terrain dependent l Site dependent l Frequency dependent l May or may not depend on line of sight (LOS)
l Commonly used to estimate link budgets, cell sizes and shapes, capacity, handoff criteria, etc.
l Models are approximations of losses derived from measurements
Practical Path Loss Model
l Log-distance path loss model l The average received signal power decreases
logarithmically with distance
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
⎟⎟⎠
⎞⎜⎜⎝
⎛∝
0100
0
log10)()(
)(
ddndPLdBPL
dddPL
n
n: the path loss exponent d0: the close-in reference distance d: the T-R separation distance
Practical Path Loss Model – cont.
l Log-distance path loss model l Path loss exponents for different environments
Free space 2 Urban area cellular radio 2.7 to 3.5 Shadowed urban cellular radio 3 to 5 In building LOS 1.6 to 1.8 Obstructed buildings 4 to 6 Obstructed factories 2 to 3
Practical Path Loss Model
l Log-normal shadowing l Considering the different surrounding environmental
clutter with the same T-R separation l The path loss PL(d) at a particular location is random
and distributed log-normally (dB)
(dB)deviation standardwith (dB) RV ddistributeGaussian mean -zero a :
log10)()(0
100
σσ
σ
X
XddndPLdBPL +⎟⎟⎠
⎞⎜⎜⎝
⎛+=
Review: Gaussian Distribution
l Q function or error function (erf)
)(1)(2
121
2exp
21)(
2
zQzQ
xerfdxxzQz
−−=
⎥⎦
⎤⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−= ∫
∞
π
[ ]
[ ] ⎟⎟⎠
⎞⎜⎜⎝
⎛ −=>
⎟⎟⎠
⎞⎜⎜⎝
⎛ −=>
σγ
γ
σγ
γ
)Pr()Pr(Pr
)Pr()Pr(Pr
dQd
dQd
Problem 4.21 l During the first month of work, you get an assignment to perform a
measurement campaign to estimate the channel path loss exponent for a new wireless product.
l You performed field measurements and collected the following data: l reference path loss: PL (d0) l Path loss measurements: PL (d1), PL (d2), …
l Using the path loss exponent model, find an expression for the optimum value of the path loss exponent n, which minimizes the mean square error between measurements and the model.
l Hint: the optimum value of n should minimize the mean square error (MSE) between your predicted path loss and measured path loss.
Take notes
Outdoor Propagation Models
l Longley-Rice model [ITS Irregular Terrain Model] l Point-to-point communication systems l Frequency range: 40 MHz ~ 100 GHz l Techniques
l The two-ray ground reflection model l The Fresnel-Kirchoff knife-edge model l Forward scatter theory over long distances
l Shortcomings l Does not provide corrections due to environment factors l Does not consider multipath
Outdoor Propagation Models
l Durkin’s model l Considering the nature of propagation over irregular
terrain and losses caused by obstacles in a radio path l Typically used for the design of modern wireless
systems l Durkin path loss simulator
l Non-LOS l LOS, but with inadequate first Fresnel-zone clearance
l Shortcomings l Does not consider man-made structures l Does not consider multipath
Outdoor Propagation Models
l Okumura model l One of the most widely used models in urban areas l Frequency range: 150 MHz ~ 1920 MHz l Distance: 1km ~ 100 km l Station antenna heights: 30m ~ 1000m l Wholly based on measured data and does not provide
any analytical explanation l Shortcomings
l Slow response to rapid changes in terrain
Outdoor Propagation Models
l Hata model l An empirical formulation of the graphical path loss data l Frequency range: 150 MHz ~ 1500 MHz
l Well suited for large cell mobile systems, but ot personal communication systems (PCS)
l Cost-231 l PCS extension to Hata model
dhhahfdBurbanL teretec log)log55.69.44()(log82.13log16.2655.69))((50 −+−−+=
30m ~ 200m 1m ~ 10m
Indoor Propagation Models
l Differ from the traditional mobile radio channels l The distance covered are much smaller l The variability of the environment is much greater l Relatively new research field
l Partition losses (same floor) l Hard partition: partitions are formed as part of the
building structure l Soft partition: partitions may be moved and do not
span to the ceiling
Indoor Propagation Models
l Partition losses between floors l The external dimensions l Materials of the buildings l The type of construction used to create the floors l The external surroundings l The number of windows
Indoor Propagation Models
l Log-distance path loss
l Ericsson multiple breakpoint model l Measurements in a multiple floor office building l Four breakpoints l Both upper and lower bound on the path loss are
considered
σXddndPLdBPL ++=0
0 log10)()(
Indoor Propagation Models
l Attenuation factor model l Accurately deploy indoor and campus networks l Reduce the standard deviation between measured and
predicted path loss to around 4 dB
∑++++= PAFFAFddndPLdBPL0
0 log10)()(
FAF: a floor attenuation factor for a specified number of building floors PAF: the partition attenuation factor for a specific obstruction encountered by a ray drawn between the TX and Rx in 3-D
