Radio Wave Propagation

SOURCE: ICAO Handbook on radio frequency spectrum requirements for Civil Aviation

**1 - Introduction**

The ITU has developed a number of propagation models some of which are applicable to the aeronautical systems. The common propagation models used in aeronautical spectrum studies are described below.

**2 - Free – Space Propagation Model**

The free space propagation model assumes an ideal propagation path where the transmitter and receiver antennas are considered isotropic antennas located in a perfectly dielectric, homogeneous, isotropic and unlimited environment with no obstructions. The free space attenuation or propagation loss can be calculated with formula:

Lbf=20 log (4πd/λ) … (1)

where:

Lbf : free-space basic transmission loss (dB)

d : distance

λ : wavelength

Note that d and λ are expressed in the same unit.

The same formula can be re-written using the frequency instead of the wavelength:

Lbf=32.4+20 log f + 20 log d … (2)

where:

f : frequency (MHz)

d : distance (km).

or

Lbf=37.8+20 log f+ 20 log d … (3)

where:

f : frequency (MHz)

d : distance (NM)

It should be noted that the propagation of radio waves, typical of VHF, UHF & Microwave frequencies, is subject to a number of additional conditions, compared to the free space propagation. **Refraction** and **ducting** as described below can extend the range over which this propagation model is applicable:

**Refraction** – Gradual changes in the refractive index of the [standard] atmosphere with altitude causes the bending of radio waves slightly towards (or in some cases away from) the Earth. The effect is that radio waves can propagate beyond the physical horizon to and can be received up to a distance which is commonly referred to as the radio horizon as shown in Figure 1. Along this path no other (significant) losses than the free space propagation loss between the transmitter and the receiver has to be considered. Variations in the refractive index of the atmosphere however cause the radio horizon to vary as well.The bending effect of refraction is corrected in radio propagation by calculation the distance to the radio horizonusing a 4/3 Earth radius. The 4/3 Earth radius approximation has been derived based on a standard atmosphere at sea level and is therefore not universally applicable. However, it is very widely used and provides a good approximation to describe the effect of radio path propagation globally.

Figure 1 - Radio Horizon versus physical horizon

**Ducting** – The change in refractive index is normally gradual, but under certain atmospheric conditions a layer, of warm air may be trapped above cooler air, often over the surface of water. The result is that the refractive index will decrease far more rapidly with height than is usual. The rapid reduction in refractive index (and therefore dielectric constant) may cause complete bending down, as illustrated in the Figure 2. The unusual atmospheric condition traps the radio waves in a duct. Extreme bending of the radio waves between the top of the atmospheric duct and reflection of the radio waves from the surface of the Earth may propagate the radio waves over extreme long distances (e.g. more than 500 NM). Other phenomena such as sand storm may also cause ducting of radio waves.

Figure 2 - Propagation through ducting

In aeronautical frequency assignment planning neither variations in the refractive index of the atmosphere (which causes variations in the distance to the radio horizon and effectively modify the 4/3 factor)) nor the effect of ducting is taken into account.In cases where these phenomena cause serious problems, consideration can be given to accommodate different criteria.

In the aeronautical standard propagation model free space propagation conditions are assumed when the transmitter and the receiver are within the distance to the radio horizon (line of (radio) sight).

The distance to the radio horizon (4/3 Earth radius) can be calculated using following equation.

Drh=1.23 (√Htx) … (4)

where

Drh: the distance of the station to the radio horizon (NM)

Htx: the height of the transmitter above the Earth’s surface (feet)

Note: The same formula can be used to calculate the radio horizon of the receiver by substituting the height of the transmitter with the height of the receiver.

Applying this formula to both the transmitter and the receiver (e.g. between an airborne transmitter and an airborne receiver) formula below can be used for the calculation of the distance to the radio horizon between the transmitter and receiver.

Drh=1.23 (√Htx + √Hrx) … (5)

where

Drh: the radio horizon separation distance between the transmitter and receiver (NM)

Htx: the height of the transmitter above the Earth’s surface (feet)

Hrx: the height of the receiver above the Earth’s surface (feet)

**2 - Aeronautical propagation curves**

Recommendation ITU-R P.528 “Propagation curves for aeronautical mobile and radio navigation services using the VHF, UHF and SHF bands” contains a method for predicting the transmission loss in the frequency range 125 MHz - 5,100 MHz for aeronautical and satellite services. The method uses an interpolation method on basic transmission loss data from sets of curves. These sets of curves are valid for ground-air, ground-satellite, air air, air-satellite, and satellite-satellite links. The only data needed for this method are the distance between antennas, the heights of the antennas above mean sea level, the frequency, and the time percentage. The curves for 1200 MHz are given below.

This Recommendation also gives the calculations for the expected protection ratio or wanted-to-unwanted signal ratio exceeded at the receiver for at least 95% of the time, R (0.95). This calculation requires the following additional data for both the wanted and unwanted signals: the transmitted power, the gain of transmitting antenna, and the gain of receiving antenna.

These propagation curves are based on empirical data of actual propagation losses for 5%, 50% and 95% time availability. Within the radio horizon these curves are consistent with free-space path loss and allows for an offset to account for the various time availability percentages. These curves were derived from the IF-77 model. The curves are also valid when the propagation path extends beyond the radio horizon and were used to determine the attenuation of radio signals beyond the radio horizon.

Aeronautical frequency assignment planning is based on the curves for 50% of the time. These give a good approximation of the free space propagation (until the radio horizon, beyond which the path losses apply.

For propagation over the horizon and based on Recommendation ITU-R P.528 curves for 125 MHz, 1200 MHz and 5100MHz the following path losses expressed in dB per nautical mile (a) were established:

in the band 108 – 137 MHz a is 0.5 dB/NM

in the band 960 – 1215 MHz a is 1.6 dB/NM

in the band 5030 – 5091 MHz a is 2.7 dB/NM

If the actual distance d between the transmitter and the receiver is less than the distance to the radio horizon, the free space transmission loss can be calculated with formula (3).

If the actual distance d between the transmitter and the receiver is greater than the distance to the radio horizon, (i.e. the receiver is beyond direct radio line of sight of the transmitter), the total transmission loss is the sum of the free space transmission loss for the distance to the radio horizon and the transmission loss for propagation beyond the radio horizon (e.g. 0.5 dB/NM for VHF frequencies as shown above. The total transmission loss can be calculated with following formula.

Lbf = 37.8 + 20 log(Drh ) + 20 log(f) + a.(d - Drh ) … (6)

A Windows version of the IF 77 model is contained in the ICAO frequency assignment planning program FREQUENCY FINDER and can be used for assessing more precise signal parameters. Normally, for radio paths up to the radio horizon, aeronautical frequency assignment planning is based on free space propagation loss. For the path beyond the radio horizon, as in above formula, the transmission loss is calculated, depending on the frequency range, as shown above in paragraph 1. Applying the IF-77 model may result in a more accurate prediction of the actual radio wave propagation characteristics.

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