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Propagation models

What are they for?Regulatory vs. scientific issues.

Modes of propagation.

The models.

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ITU Recommendations on Radiowave Propagation

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Modes of propagation &

propagation loss Free space

Ground wave. Diffraction around a smooth earth.

Ground reflections. Effect of terrain. Ionospheric, including sporadic E

Tropospheric: refraction, super-refraction andducting, forward scattering

Diffraction over knife edge & rounded edge Atmospheric attenuation

Variability & Statistics

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Free space propagation

EIRP (watts) to pfd (w/m^2) = P/(4.pi.D^2)

equivalent to (dBW11 -20.log(D))

EIRP (watts) to E (V/m) = sqrt(30.P)/D

EIRP (kW) to E (V/m) = 173*sqrt(P)/Dkm

Also: pfd (W/m^2)=E^2/Z0=E^2/(120.pi)

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Free space loss

Note that EIRP(W) to pfd(W/m^2) is

frequency independent

EIRP(W) to Prx(W) in isotropic antenna is:

Prx={Peirp/(4.pi.D^2)}*{lambda^2/(4.pi)}

I.e. isotropic to isotropic antenna free-space

loss increases as frequency squared.

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Ground wave propagation

Most relevant for low frequencies (

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Ionospheric propagation

Most relevant up to about 30 MHz

Many modes of propagation: a complicated

topic.

Sporadic E can be important up to about 70

MHz. (ITU-R P.534)

Highly variable

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Tropospheric

Variations of radio refractive index

Normal change with height causes greater than

line-of-sight range. Often taken into account byassuming increased radius for the earthe.g. (4/3)

Temperature inversions can cause ducting, withrelatively low attenuation over large distances

beyond the horizon Small scale irregularities are responsible for

forward scatter propagation.

Rain scatter can sometimes be a dominant mode.

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Obstacles

Terrain features, and buildings, usually

attenuate signals. (NB in some

circumstances knife edge diffraction canenhance propagation beyond the horizon)

The OKUMURA-HATA model calculates

attenuation taking account of the percentageof buildings in the path, as well as natural

terrain features.

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Is an Obstruction Obstructing?

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Fresnel ellipsoids and Fresnel zonesIn studying radiowave propagation between two points A and B, the

intervening space can be subdivided by a family of ellipsoids, known

as Fresnel ellipsoids, all having their focal points at A and B such that

any point M on one ellipsoid satisfies the relation:

2ABMBAM n (1)

where n is a whole number characterizing the ellipsoid and n 1 correspondsto the first Fresnel ellipsoid, etc., and is the wavelength.As a practical rule, propagation is assumed to occur in line-of-sight, i.e. with

negligible diffraction phenomena if there is no obstacle within the first Fresnel ellipsoid.

The radius of an ellipsoid at a point between the transmitter and the receiver isgiven by the following formula:

2/1

21

21

dd

ddnRn (2)

or, in practical units:

2/1

21

21

)(550

fddddnRn (3)

wherefis the frequency (MHz) and d1 and d2 are the distances (km) between transmitter

and receiver at the point where the ellipsoid radius (m) is calculated.

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An approximation to the 0.6 Fresnel clearance path lengthThe path length which just achieves a clearance of 0.6 of the first Fresnel zone

over a smooth curved earth, for a given frequency and antenna heights h1 and h2,

is given approximately by:

D06 hf

hf

DD

DD

km (30)

where:

Df: frequency-dependent term

210000389.0 hhf km (30a)

Dh: asymptotic term defined by horizon distances

)(1.4 21 hh km (30b)

f: frequency (MHz)h1, h2: antenna heights above smooth earth (m).

(Radio Horizon)

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h > 0

2

d2

a)

1

d1

1

d1h< 0

2

b)

d2

FIGURE 6

Geometrical elements

1 2 1 2(For definitions ofd, d , d andR,see 4.1 and 4.3)

h > 0

2

d2

a)

1

d1

1

d1h< 0

2

b)

d2

FIGURE 6

Geometrical elements

1 2 1 2(For definitions ofd, d , d andR,see 4.1 and 4.3)

Knife Edge diffraction

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2

0

2

4

6

8

10

12

14

16

18

20

J()

(dB)

FI GURE 7

K ni f e-edgediffraction loss

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Atmospheric attenuation

Starts becoming relevant above about 5 GHz

Depends primarily, but not exclusively on water

vapour content of the atmosphere Varies according to location, altitude, path

elevation angle etc.

Can add to system noise as well as attenuating

desired signal

Precipatation has a significant effect

Specific attenuation due to atmospheric gases

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0676-0

H O2

H O2

102

10

10 1

10 2

1

10 3

2

5

5

2

5

2

5

2

5

2

Specificattenuation(dB/km)

3.52 52 2

102101

Dry airDry airTotal

Frequency,f(GHz)

Pressure: 1 013 hPaTemperature: 15 CWater vapour: 7.5 g/m3

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Propagation models

The ITU recommendations give many

approved methods and models

Two popular methods are are the

Okumura-Hata

and the

Longley Rice

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1546-18

1 200 m

600 m

300 m

150 m

75 m

20 m

10 m

120

110

100

90

80

70

60

50

40

30

20

10

0

10

20

30

40

50

60

70

80

10 100 1 000

h1 = 1 200 m

h1 = 10 m

1

Distance (km)

Fieldstrength

(dB(V/m))for1kWe.r.p.

50% of locations

h2: representative clutter height

FIGURE 18

2 000 MHz, land path, 10% time

Maximum (free space)

Transmitting/base

antenna heights, h1

37.5 m

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Okumura-Hata methodE 69.82 6.16 logf 13.82 logH1 + a(H2) (44.9 6.55 log(H1)(log d)b

where:

E: field strength (dB(V/m)) for 1 kW e.r.p.f: frequency (MHz)

H1: base station effective antenna height above ground (m) in the range 30 to 200 m

H2: mobile station antenna height above ground (m) in the range 1 to 10 m

d: distance (km)a(H2) = (1.1 logf 0.7)H2 (1.56 logf 0.8)

b = 1 for d 20 km

b = 1 (0.14 0.000187f 0.00107 1 ) (log [0.05d])0.8

for d > 20 kmwhere:

1H H1/210,0000071 H

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Longley-Rice model

TRANSMISSION LOSS PREDICTIONS FOR

TROPOSPHERIC COMMUNICATION

CIRCUITS

Longley Rice has been adopted as a standard by the FCC

Many software implementations are available

commercially

Includes most of the relevant propagation modes [multiple

knife & rounded edge diffraction, atmospheric attenuation,

tropospheric propagation modes (forward scatter etc.),

precipitation, diffraction over irregular terrain,

polarization, specific terrain data, atmospheric

stratification, different climatic regions, etc. etc. ]

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NRAO: TAP model(SoftWright implementation with the Terrain Analysis

Package

Notes on The Prediction of Tropospheric Radio Transmission Loss Over Irregular Terrain

(the Longley-Rice Model) propagation in the Terrain Analysis Package (TAP).

The Longley-Rice model predicts long-term median transmission loss over irregular

terrain relative to free-space transmission loss. The model was designed for frequencies

between 20 MHz and 40 GHz and for path lengths between 1 km and 2000 km.

...

This implementation is based on Version 1.2.2 of the model, dated September 1984. Note

also that the version 1.2.2 implemented by SoftWright does not utilize several other

corrections to the model proposed since the method was first published (see A. G. Longley,

"Radio propagation in urban areas," OT Rep. 78-144, Apr. 1978; and A. G. Longley,"Local variability of transmission loss- land mobile and broadcast systems," OT Rep., May

1976).

Technical Foundation

...

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Problems with models

All models have limitations: e.g. Longley Rice doesnt

include ionosphere, so limited applicability at lower

frequencies. Some skill is needed in choosing the right

model for the right circumstances.

Accuracy is limited. Different models can give differentanswers.

May need a statistical interpretation

Need good input data (e.g. terrain models)

Any model needs fairly universal acceptance, to avoid

legal arguments. Acceptance may be more important than

accuracy.

What is the height of a radio telescope?

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Where does this leave us?

In spite of the difficulties, propagation models

have come a long way.

We cant live without them. The best guide we have to whether a given

terrestrial transmission will cause interference to a

radio telescope.

The best guide we have as to whether a given size

of coordination zone will be adequate.