Wave Propagation

Propagation models What are they for? Regulatory vs. scientific issues. Modes of propagation. The models.

ITU Recommendations on Radiowave Propagation

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 and ducting, forward scattering • Diffraction over knife edge & rounded edge • Atmospheric attenuation • Variability & Statistics

Free space propagation • EIRP (watts) to pfd (w/m^2) = P/(4.pi.D^2) –

equivalent to (dBW –11 -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)

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.

Ground wave propagation • Most relevant for low frequencies (<30 MHz) • Depends on ground constants (conductivity, permittivity) • Various ITU recommendations: ITU-R P.368 etc. Program GRWAVE available from ITU web pages

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

Tropospheric • Variations of radio refractive index • “Normal” change with height causes greater than line-of-sight range. Often taken into account by assuming increased radius for the earth – e.g. (4/3) • Temperature inversions can cause ducting, with relatively 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.

Obstacles • Terrain features, and buildings, usually attenuate signals. (NB in some circumstances knife edge diffraction can enhance propagation beyond the horizon) • The OKUMURA-HATA model calculates attenuation taking account of the percentage of buildings in the path, as well as natural terrain features.

Is an Obstruction Obstructing?

Fresnel ellipsoids and Fresnel zones In 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: λ AM + MB = AB + n 2 where n is a whole number characterizing the ellipsoid and n =1 corresponds to the first Fresnel ellipsoid, etc., and λis 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.

(1)

The radius of an ellipsoid at a point between the transmitter and the receiver is given by the following formula: 1/ 2

n λd1 d 2  Rn =   d1 + d 2 

(2)

or, in practical units: 1/ 2

 n d1 d 2  Rn = 550   (d1 + d 2 ) f  where f is 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.

(3)

An approximation to the 0.6 Fresnel clearance path length The 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:

D f ⋅ Dh D06 = D f +Dh

km

(30)

where: Df :

frequency-dependent term

Dh :

km =0.0000389 f h1 h 2 asymptotic term defined by horizon distances

f  : h1, h2 :

km = 4.1( h1 + h 2 ) (Radio frequency (MHz) antenna heights above smooth earth (m).

(30a)

Horizon)

(30b)

Knife Edge diffraction FIGURE 6 Geometrical elements (For definitions of θ, α1 , α2 , d, d1 , d 2 and R, see § 4.1 and 4.3)

θ>0 d1

d2

h>0

α1

α2

a)

α1 d1

α2

h<0 θ<0

b)

d2

FIGURE 7 Knife-edge diffraction loss

–2 0 2 4 6

J(ν) (dB)

8 10 12 14 16 18 20 22 24 –3

–2

–1

0 ν

1

2

3 0526-07

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 10 2

5

H2O

2

10

5

Specific attenuation (dB/km)

2

1

5

2

10– 1 5

2

Total Dry air

Dry air

10 – 2 5

2

H 2O

10 – 3 1

2

5

10

2

Frequency, f (GHz) Pressure: 1 013 hPa Temperature: 15° C Water vapour: 7.5 g/m3

5

10 2

2

3.5

0676-05

Propagation models • The ITU recommendations give many “approved” methods and models • Two popular methods are are the Okumura-Hata and the Longley Rice

FIGURE 18 2 000 MHz, land path, 10% time 120 110 100 90 80 Maximum (free space) 70

µ V/m)) for 1 kW e.r.p. Field strength (dB(

60 50

h1 = 1 200 m

40 30 20 h1 = 10 m 10 0 –10 –20 Transmitting/base

–30

antenna heights, h1 1 200 m

–40

600 m 300 m

–50

150 m 75 m

–60

37.5 m 20 m

–70

10 m

–80 1

10

100

1 000

Distance (km) 50% of locations h2: representative clutter height

1546-18

Okumura-Hata method E = 69.82 −6.16 log f +13.82 log H1 + a(H2) −(44.9 −6.55 log( H1)(log d)b where: E : f : H1 :

field strength (dB(µV/m)) for 1 kW e.r.p. frequency (MHz) 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 log f −0.7) H2 −(1.56 log f −0.8) b = 1 for d ≤20 km b = 1 +(0.14 +0.000187 f +0.00107 H1′ ) (log [0.05d])0.8 for d > 20 km where: H1′ = H1 / 1 +0,000007 H12  

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. …]

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 ...

Problems with models • All models have limitations: e.g. Longley Rice doesn’t 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 different answers. • 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?

Where does this leave us? • In spite of the difficulties, propagation models have come a long way. • We can’t 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.