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ELG4179: Wireless Communication Fundamentals © S.Loyka

Lecture 3 30-Oct-20 1(19)

Semi-Empirical Models Simple theoretical models (i.e., free-space, ideal ground, etc.) do

not fit well into real-life scenarios (bad accuracy, disregard of

many factors). Practical models are based on combination of

measurement and theory (i.e., semi-empirical).

Semi-empirical models: try to make sense of massive

measurements based on a few theoretical principles.

Important effects (difficult for theoretical modeling):

• Rough terrain

• Buildings, LOS blockage due to Earth curvature

• Refection

• Moving user (vehicle)

A simple, but popular, generalization of the two-ray model:

0 0

0 0

[dB] [dB] 10 lg

v

P P

d dL L L L v

d d

= ↔ = +

(3.1)

0d is the reference distance, 0L is the path loss at 0d , v is the

path loss exponent (can assume different values at different

scenarios). 0d is selected in such a way that there is an LOS Tx-

Rx path (e.g. 0d =1 m).

0 0, ,d L v are obtained from measurements or from theory.



Equivalently, the received power rP is:

00 0

0

[dBm] [dBm] 10 lgv

r r r r

d dP P P P v

d d

= ↔ = +

(3.1a)

where 0rP is the Rx power at reference distance 0d .

Example: 2v = for free space; 4v = for ideal ground (2-ray

model). In practice, 2 8v≤ ≤ .

Q.: find 0L , 0rP for free-space and two-ray models.



Okumura-Hata Model

Correction factors are introduced to account for:

• Terrain profile (urban/suburban, rural, hilly etc.) • Antenna heights • Building profiles (height, type, concentration) • Street shape/orientation • Lakes

Okumura-Hata model is a very popular one.

• Generalization of Okumura measurements (1968) by Hata

(analytical presentation of graphs) (1980).

• Predicts average (median) path loss (attenuation).

• Terrain profile is taken into account

P.M. Shankar, Introduction to Wireless Systems, Wiley, 2002.



Average (median) path loss in urban areas:

( ) 69.55 26.16lg( )

(44.9 6.55lg ) lg( )

13.85lg ( )

p

b

b mu

L dB f

h d

h a h

= + +

−

− −

(3.2)

where: f is the carrier frequency (MHz);

d is the distance (km);

bh is the BS antenna height (m) (effective);

muh is the MU antenna height (m) (above ground);

)(muha is the correction factor;

The correction factor ( )mu

a h is

2

2

3.2(lg(11.75 )) 4.97, large city, 300

( ) 8.29(lg(1.54 )) 1.1, large city, 300

(1.1 lg( ) 0.7) (1.56lg 0.8), small and medium

mu

mu mu

mu

h f MHz

a h h f MHz

f h f

− ≥

= − < ⋅ − − −

(3.3)

Limits of validity:

150 1500( )

30 200( )

1 20( )

1 10( )

b

mu

f MHz

h m

d km

h m

≤ ≤

≤ ≤

≤ ≤

≤ ≤

(3.4)



Suburban areas: 2

2 lg 5.428

sub P

fL L

= − −

(3.5)

where PL is the path loss in small to medium cities.

Rural areas

2( ) 4.78(lg ) 18.33lg 40.94rur P

L dB L f f= − + − (3.6)



Question: Compare to the free-space and two-ray models, what

is the path loss exponent?

1 10160

140

120

100

80

large city (f=1GHz)

small and medium city (f=1GHz)

suburban area (f=1GHz)

rural area (f=1GHz)

Free space gain (f=1GHz)

Two rays model gain

Averge Path Gain vs. Distance

km

dB

.

2 , 30mu bsh m h m= =



An Extension

Cost-231 extension of the Hata model:

( ) 46.3 33.93lg 13.82lg ( )

(44.9 6.55lg )lg

P b mu

b

L dB f h a h

h d c

= + − − +

− +

(3.7)

where c is a correction factor :

0 , medium city and suburban areas

3 , metropolitan areas

dBc

dB

=

Limits: the same as for the Hata model, except for

MHzf 20001500 ≤≤ .

Major limitation of the 2 models above: kmd 1≥

The model does not take into account building’s profile, street

type/orientation etc.

Many other models are available.



COST-Walfisch-Ikegami Model Includes 3 components: free-space loss, roof-to–street diffraction

loss (scattering) and multiscreen loss.

The average path loss for non-LOS (NLOS):

[dB]P fs rts msL L L L= + + (3.8)

where:

[dB] 32.4 20lg 20lg (free space loss)fsL d f= + + = −

rtsL is the roof-to-street diffraction loss

ms

L is the multiscreen loss (rows of buildings)

T.S. Rappaport, Wireless Communications, Prentice Hall, 2002



LOS path loss (in a street canyon):

[dB] 42.6 26 lg 20lg (d 0.02km)PL d f= + + ≥ (3.11)

where d is in km, and f is in MHz.

Limits:

800 2000

4 50

1 3

0.02 5

b

mu

f MHz

h m

h m

d km

≤ ≤

≤ ≤

≤ ≤

≤ ≤

Accuracy: mean error is about 3dB with standard deviation of 4-

8dB.

Applications: 3G, macrocells and microcells.


Lecture 3 30-Oct-20 10(19)

Recent Activities: LTE (4G) Pathloss Models

Z. Shen et al, Dynamic Uplink-Downlink Configuration and Interference Management in TD-LTE, IEEE Communications Magazine, Nov. 2012, pp. 51-59.


Lecture 3 30-Oct-20 11(19)

Recent Activities: 5G & related models

1. T. S. Rappaport et al., “Overview of millimeter wave

communications for fifth-generation (5G) wireless networks —

with a focus on propagation models,” IEEE Trans. Antennas

Propag., vol. 65, no. 12, pp. 6213–6230, Dec. 2017.

2. S. Sun et al., “Investigation of prediction accuracy, sensitivity,

and parameter stability of large-scale propagation path loss

models for 5G wireless communications,” IEEE Trans. Veh.

Techl., vol. 65, no. 5, pp. 2843–2860, May 2016.

3. S. Sun, T.S. Rappaport, et al, Propagation Models and

Performance Evaluation for 5G Millimeter-Wave Bands, IEEE

Trans. Veh. Tech., vol. 67, no. 9, pp. 8422-8439, Sep. 2018.

4. K. Briggs, A. Shojaeifard, Coverage Regions Under Multi-

Slope Pathloss Propagation, IEEE Trans. Veh. Tech., vol. 69, no.

10, pp. 11786-11789, Oct. 2020.

5. Study on Channel Model for Frequencies from 0.5 to 100

GHz (Release 16), TR 38.901, 3GPP, Sophia Antipolis, France,

2019.


Lecture 3 30-Oct-20 12(19)

Recent Activities: 5G & related models

General form of [dB]PL for UMa/UMi/RMa (see [1]-[3][5]):

0

0

[dB] [dB] 10 lgP

dL L v

d

= +

, 0

0

4[dB] 20 lg

dL

π =

λ

Usually, 0 1d = m (LOS). Equivalently,

[dB] 32 10 lg 20 lgP cL v d f= + +

cf in GHz, 0 1d d≥ = m;

10v [dB] = extra loss per decade of d

LOS (street canyon): 2...2.1v =

NLOS: 3...4v =

Also: multi-break-point model [5]. You can use its simplified

form:

2 minmax{ , , , }ray FS t rL L L L G G−

= , 2

min 10L ≈

Note: do not forget to check the LOS distance!

( )4 [km]LOS t rd d h h< ≈ +


Lecture 3 30-Oct-20 13(19)

Fresnel Zones and Diffraction Diffraction: penetration of EM waves into non-LOS area (“ray

bending”).

Any obstruction of LOS path will result in diffraction. While the

diffracted field is much weaker than LOS, it can still be

important.

Fresnel zones: define the space essential for EM wave

propagation.

n-th Fresnel zone: region of space where the path length is

[ ]( 1) / 2, / 2n n− λ λ larger than LOS path length. The zone

boundaries are the circles; the path length through each circle is

/ 2nλ .



Lecture 3 30-Oct-20 14(19)

Fresnel zone radius:

21

21

dd

ddnrn

+

=

λ (3.12)

where nrdd >>

21, .

Diffraction and Fresnel zones can be explained using Huygen’s

principle (secondary sources).

Contribution of each successive zone is less than the previous

one. Blockage of some zones results in diffraction.

Area essential for EM wave propagation

There is no disturbance to the wave propagation along a certain

path provided that 1st Fresnel zone is cleared.

Rule of thumb for LOS microwave link design: ~50% of 1st zone

must be kept clear.


Lecture 3 30-Oct-20 15(19)

Knife-Edge Diffraction

Fresnel-Kirchoff diffraction parameter

1 2

1

1 2

2( )2 /

d dv h h r

d d

+= =

λ (3.13)



Lecture 3 30-Oct-20 16(19)

The field is given by Fresnel integral

2

0

1( ) exp( / 2)

2v

E jF v j t dt

E

∞

+= = − π∫ (3.14)

where 0

E is the LOS field (no obstruction).

The field has oscillating behavior w.r.t. h. This is a simple model

(approximation). Yet, it is good enough to model many obstacles

(buildings, mountains, etc.). Generalizations are possible:

multiple knife-edge models.

Another representation: introduce Fresnel integrals,

2 2

0 0

( ) cos , S( ) sin2 2

x x

C x t dt x t dtπ π

= =

∫ ∫ (3.15)

Then,

[ ]1 1

( ) ( ) ( )2 2

jF C jS

+ν = − ν − ν (3.16)

Note that 12

( ) ( )C S∞ = ∞ = .

The total path loss is

0p dL L L= (3.17)

where 2

0 (4 / )L R= π λ is the free-space path loss,

2

( )dL F−

= ν is the diffraction loss.


Lecture 3 30-Oct-20 17(19)

An Approximation1

If 1 2,d d h>> >> λ :

2

2 1 2

2 20 1 2

1( )

4d

E d dF

L E d dh

λ= ν = ≈

+π

Note: if the edge is not sharp but rounded, expect 10-20 dB

more loss.

1 see Kraus, Fleish, Electromagnetics with Applications, 5th Edition, McGraw Hill, 1999. (p.235-236).


Lecture 3 30-Oct-20 18(19)

20− 10− 0 10 2050−

40−

30−

20−

10−

0

10

Diffraction Loss

height

gai

n, dB

1 2 50d d m= =


[ ]m

1 GHzf =

10 GHzf =

2( )dL F

−

= ν

approx.←


Lecture 3 30-Oct-20 19(19)

Summary

• Average (median) path loss. Semi-empirical models.

• Okumura-Hata model. Extension to PCS environments.

• COST-Walfisch-Ikegami Model.

• Fresnel zones and diffraction. Knife-edge diffraction.

Reading:

o Rappaport, Ch. 4.

References:

o S. Salous, Radio Propagation Measurement and Channel

Modelling, Wiley, 2013. (available online)

o J.S. Seybold, Introduction to RF propagation, Wiley, 2005.

o Other books (see the reference list).

Note: Do not forget to do end-of-chapter problems. Remember

the learning efficiency pyramid!

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