View source for Line-of-sight propagation

{{Short description|Characteristic of electromagnetic radiation}}
{{Other uses|Line-of-sight (disambiguation)}}
[[File:VHF propagation.png|thumb|Line of sight (LoS) propagation from an antenna]]
'''Line-of-sight propagation''' is a characteristic of [[electromagnetic radiation]] or acoustic [[wave propagation]] which means waves can only travel in a direct visual path from the source to the receiver without obstacles.<ref>{{Cite web |title=Line-of-sight propagation |url=https://technav.ieee.org/textui/ |access-date=2023-05-10 |website=IEEE Technology Navigator |language=en}}</ref> Electromagnetic [[transmission (telecommunications)|transmission]] includes light emissions traveling in a [[straight line]]. The rays or waves may be [[diffraction|diffracted]], [[atmospheric refraction|refracted]], reflected, or absorbed by the atmosphere and obstructions with material and generally cannot travel over the [[horizon]] or behind obstacles.

In contrast to line-of-sight propagation, at [[low frequency]] (below approximately 3&nbsp;[[Hertz|MHz]]) due to [[diffraction]], [[radio wave]]s can travel as [[ground wave]]s, which follow the contour of the Earth. This enables [[AM radio]] stations to transmit beyond the horizon. Additionally, frequencies in the [[shortwave]] bands between approximately 1 and 30&nbsp;MHz, can be refracted back to Earth by the [[ionosphere]], called [[skywave]] or "skip" propagation, thus giving radio transmissions in this range a potentially global reach.

However, at frequencies above 30&nbsp;MHz ([[VHF]] and higher) and in lower levels of the atmosphere, neither of these effects are significant. Thus, any obstruction between the transmitting antenna ([[transmitter]]) and the receiving antenna ([[receiver (radio)|receiver]]) will block the signal, just like the [[light]] that the eye may sense. Therefore, since the ability to visually see a transmitting antenna (disregarding the limitations of the eye's resolution) roughly corresponds to the ability to receive a radio signal from it, the propagation characteristic at these frequencies is called "line-of-sight". The farthest possible point of propagation is referred to as the "radio horizon".

In practice, the propagation characteristics of these radio waves vary substantially depending on the exact frequency and the strength of the transmitted signal (a function of both the transmitter and the antenna characteristics). Broadcast [[frequency modulation|FM]] radio, at comparatively low frequencies of around 100&nbsp;MHz, are less affected by the presence of buildings and forests.

== Impairments to line-of-sight propagation ==
[[File:Fresnel zone disrupted.png|thumb|right| Objects within the [[Fresnel zone]] can disturb line of sight propagation even if they do not block the geometric line between antennas.]]
Low-powered [[microwave]] transmitters can be foiled by tree branches, or even heavy rain or snow. The presence of objects not in the direct line-of-sight can cause diffraction effects that disrupt radio transmissions. For the best propagation, a volume known as the first [[Fresnel zone]] should be free of obstructions.

Reflected radiation from the [[ground plane|surface of the surrounding ground or salt water]] can also either cancel out or enhance the direct signal. This effect can be reduced by raising either or both antennas further from the ground: The reduction in loss achieved is known as ''height gain''.

See also [[Non-line-of-sight propagation]] for more on impairments in propagation.

It is important to take into account the curvature of the Earth for calculation of line-of-sight paths from maps, when a direct visual fix cannot be made. Designs for microwave formerly used {{frac|4|3}}&nbsp;Earth radius to compute clearances along the path.

== Mobile telephones ==
Although the frequencies used by [[mobile phone]]s (cell phones) are in the line-of-sight range, they still function in cities. This is made possible by a combination of the following effects:
* {{frac|1|''r''<sup>&nbsp;4</sup>}} propagation over the rooftop landscape{{clarify|date=June 2016}}
* diffraction into the "street canyon" below
* [[multipath fading|multipath]] reflection along the street
* diffraction through windows, and attenuated passage through walls, into the building
* reflection, diffraction, and attenuated passage through internal walls, floors and ceilings within the building

The combination of all these effects makes the mobile phone propagation environment highly complex, with [[multipath fading|multipath]] effects and extensive [[Rayleigh fading]]. For mobile phone services, these problems are tackled using:
* rooftop or hilltop positioning of base stations
* many [[base station]]s (usually called "cell sites"). A phone can typically see at least three, and usually as many as six at any given time.
* "sectorized" antennas at the base stations. Instead of one antenna with [[omnidirectional antenna|omnidirectional]] coverage, the station may use as few as 3 (rural areas with few customers) or as many as 32&nbsp;separate antennas, each covering a portion of the circular coverage. This allows the base station to use a directional antenna that is pointing at the user, which improves the [[signal-to-noise ratio]]. If the user moves (perhaps by walking or driving) from one antenna sector to another, the base station automatically selects the proper antenna.
* rapid [[handoff]] between base stations (roaming)
* the radio link used by the phones is a digital link with extensive [[Error detection and correction|error correction and detection]] in the digital protocol
* sufficient operation of mobile phone in tunnels when supported by split cable antennas
* local repeaters inside complex vehicles or buildings

A [[Faraday cage]] is composed of a conductor that completely surrounds an area on all sides, top, and bottom. Electromagnetic radiation is blocked where the wavelength is longer than any gaps. For example, mobile telephone signals are blocked in windowless metal enclosures that approximate a Faraday cage, such as elevator cabins, and parts of trains, cars, and ships. The same problem can affect signals in buildings with extensive steel reinforcement.

[[File:Repeater-schema.svg|thumb|right|Two stations not in line-of-sight may be able to communicate through an intermediate [[radio repeater]] station.]]

== Radio horizon ==
{{see also|Radar horizon}}

The ''radio horizon'' is the [[locus (mathematics)|locus]] of points at which direct rays from an [[antenna (electronics)|antenna]] are tangential to the surface of the Earth. If the Earth were a perfect sphere without an atmosphere, the [[radio]] horizon would be a circle.

The radio horizon of the transmitting and receiving antennas can be added together to increase the effective communication range. <!-- Antenna heights above {{convert|1,000,000|ft|mi km|0|abbr=off}} will cover the entire hemisphere and not increase the radio horizon.{{Citation needed|reason=This not only contradicts the formulae presented elsewhere, it seems axiomatically wrong - no matter how high an antenna/observer is, it is impossible to (fully) 'see' an entire hemisphere, so unless I'm missing something, this is nonsense. |date=April 2016}}{{Citation needed|reason=If I rearrange the equation, the satellite would have to be over 3179km above the Earth's surface. |date February 2017}} -->

[[Radio propagation|Radio wave propagation]] is affected by atmospheric conditions, [[ionospheric absorption]], and the presence of obstructions, for example mountains or trees. 
Simple formulas that include the effect of the atmosphere give the range as:
:<math>\mathrm{horizon}_\mathrm{mi} \approx 1.23 \cdot \sqrt{\mathrm{height}_\mathrm{feet}}</math><!--As per geometric distance shown below-->

:<math>\mathrm{horizon}_\mathrm{km} \approx 3.57 \cdot \sqrt{\mathrm{height}_\mathrm{metres}}</math>
The simple formulas give a best-case approximation of the maximum propagation distance, but are not sufficient to estimate the quality of service at any location.

=== Earth bulge ===
In [[telecommunications]], '''Earth bulge''' refers to the effect of [[earth's curvature]] on radio propagation. It is a consequence of a circular segment of earth profile that blocks off long-distance communications. Since the vacuum line of sight passes at varying heights over the Earth, the propagating radio wave encounters slightly different propagation conditions over the path.{{citation needed|date=October 2022}}

=== Vacuum distance to horizon ===
{{main|Horizon distance}}
[[File:RadioHorizont_h_d.jpg|thumb|318x318px|''R'' is the radius of the Earth, ''h'' is the height of the transmitter (exaggerated), ''d'' is the line of sight distance]]
Assuming a perfect sphere with no terrain irregularity, the distance to the horizon from a high altitude [[Transmitter station|transmitter]] (i.e., line of sight) can readily be calculated.

Let ''R'' be the radius of the Earth and ''h'' be the altitude of a telecommunication station. The line of sight distance ''d'' of this station is given by the [[Pythagorean theorem]];

: <math>d^2=(R+h)^{2}-R^2= 2\cdot R \cdot h +h^2</math>

The altitude of the station ''h'' is much smaller than the radius of the Earth ''R.'' Therefore, <math>h^2</math> can be neglected compared with <math> 2\cdot R \cdot h</math>. 

Thus:

: <math>d \approx \sqrt{ 2\cdot R \cdot h}</math>

If the height ''h'' is given in metres, and distance ''d'' in kilometres,<ref>Mean radius of the Earth is ≈ 6.37×10<sup>6</sup> metres = 6370 km. See [[Earth radius]]</ref>
: <math>d \approx 3.57 \cdot \sqrt{h}</math>

If the height ''h'' is given in feet, and the distance ''d'' in statute miles,

: <math>d \approx 1.23 \cdot \sqrt{h}</math>

[[File:RadioHorizont h H.jpg|thumb|318x318px|''R'' is the radius of the Earth, ''h'' is the height of the ground station, ''H'' is the height of the air station ''d'' is the line of sight distance]]
In the case, when there are two stations involve, e.g. a transmit station on ground with a station height ''h'' and a receive station in the air with a station height ''H'', the line of sight distance can be calculated as follows:
 <math>d \thickapprox \sqrt{2 R} \, \left( \sqrt{h} + \sqrt{H}\right) </math>

=== Atmospheric refraction ===
{{main|Atmospheric refraction}}
The usual effect of the declining pressure of the atmosphere with height ([[vertical pressure variation]]) is to bend ([[refraction|refract]]) radio waves down towards the surface of the Earth. This results in an '''effective Earth radius''',<ref name="ITU 2021">{{cite web | title=P.834 : Effects of tropospheric refraction on radiowave propagation | website=ITU | date=2021-03-05 | url=https://www.itu.int/rec/R-REC-P.834/en | access-date=2021-11-17}}</ref> increased by a factor around {{frac|4|3}}.<ref>Christopher Haslett. (2008). ''Essentials of radio wave propagation'', pp&nbsp;119&ndash;120. Cambridge University Press. {{ISBN|052187565X}}.</ref> This ''k''-factor can change from its average value depending on weather.

====Refracted distance to horizon====
The previous vacuum distance analysis does not consider the effect of atmosphere on the propagation path of RF signals. In fact, RF signals do not propagate in straight lines: Because of the refractive effects of atmospheric layers, the propagation paths are somewhat curved. Thus, the maximum service range of the station is not equal to the line of sight vacuum distance. Usually, a factor ''k'' is used in the equation above, modified to be

: <math>d \approx \sqrt{2 \cdot k \cdot R \cdot h}</math>

''k''&nbsp;>&nbsp;1 means geometrically reduced bulge and a longer service range. On the other hand, ''k''&nbsp;<&nbsp;1 means a shorter service range.

Under normal weather conditions, ''k'' is usually chosen<ref>Busi, R. (1967). ''High Altitude VHF and UHF Broadcasting Stations''. Technical Monograph 3108-1967. Brussels: European Broadcasting Union.</ref> to be {{frac|4|3}}. That means that the maximum service range increases by&nbsp;15%.

: <math>d \approx 4.12 \cdot \sqrt{h} </math>
for ''h'' in metres and ''d'' in kilometres; or

: <math>d \approx 1.41 \cdot\sqrt{h} </math>
for ''h'' in feet and ''d'' in miles.

But in stormy weather, ''k'' may decrease to cause [[rain fade|fading]] in transmission. (In extreme cases ''k'' can be less than&nbsp;1.) That is equivalent to a hypothetical decrease in Earth radius and an increase of Earth bulge.<ref>This analysis is for high altitude to sea level reception. In microwave radio link chains, both stations are at high altitudes.</ref>

For example, in normal weather conditions, the service range of a station at an altitude of 1500 m with respect to receivers at sea level can be found as,

: <math>d \approx 4.12 \cdot \sqrt{1500} = 160 \mbox { km.}</math>

== See also ==
* [[Anomalous propagation]]
* [[Dipole field strength in free space]]
* [[Knife-edge effect]]
* [[Multilateration]]
* [[Non-line-of-sight propagation]]
* [[Over-the-horizon radar]]
* [[Radial (radio)]]
* [[Rician fading]], stochastic model of line-of-sight propagation
* [[Slant range]]
{{Portal|Radio}}

== References ==
{{reflist}}
* {{FS1037C MS188}}

== External links ==
* http://web.telia.com/~u85920178/data/pathlos.htm#bulges
* [https://web.archive.org/web/20100921070856/http://techsonar.com/license_4.html Approximating 2-Ray Model by using Binomial series by Matthew Bazajian]

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