# Objective 3.4 — Line of Sight and Wireless Channels
| LO# | Description |
|----------|----------|
| 3.4 | I can calculate the maximum line-of-sight (LOS) distance between two terrestrial objects. |
By the end of this reading you should be able to:
1. Name the **four wireless propagation methods** and the bands each works in (context only — not assessed).
2. Match a mission to the right **propagation mode** (context only — not assessed).
3. Compute the **maximum LOS distance** for one or two elevated antennas.
4. Explain why LOS is the mode modern military communications rely on.
## Communications Introduction
Today, communication affects our lives in so many different ways. Given
the ubiquity of smart phones and other connected devices, we can
communicate with anyone at any given time. In the civilian world, we can
request an Uber, buy tickets to a Denver Broncos game, or have
near-instantaneous communication with someone across the country. In
military operations, communication is even more important, as it
provides critical information across the battlefield in near-real time.
Delivering information using electromagnetic signals from one location
to another requires some form of pathway or medium. These pathways can
be broadly categorized as either wired (such as a transmission line) or
wireless. We call these pathways *communication media*. Some people
refer to them as communications channels, so you may hear these two
terms used synonymously. In this lesson, we will discuss
four types of wireless radio frequency (RF) propagation methods and compute the distance at which terrestrial objects can communicate with RF using Line of Sight.
## Wireless Communications
*Wireless* communications use the electromagnetic spectrum to transmit
and receive information without the use of wires, waveguides, or other
conductors. Typically, a wireless signal is transmitted from an antenna,
then it travels through free space until it is acquired by the receiving
antenna. This is exactly what happens every time you use your cell
phone. Even though radio frequencies and antennas are commonly
associated with wireless communications, laser beams can also be used to
communicate. A great example of this is the Lunar Laser Communications
Demonstration (LLCD) developed by MIT Lincoln Laboratory. The LLCD used
lasers to successfully transmit at a data rate of 622 Mbps from lunar
orbit to Earth!
The primary advantages of using wireless communications are flexibility
and cost. Wireless communications can be used virtually anywhere, as
long as the transmitter and receiver have the required equipment. There
is no need to install or repair wires over long distances, so they are
relatively cheap to use and maintain.
The primary disadvantages of wireless communications are that they have
limited bandwidth and are not as reliable as the other communications
media. The radio frequency
spectrum in the United States is full, meaning there is no more
bandwidth available at radio frequencies for wireless communications.
Additionally, wireless communications are not as reliable as the other
communications media. For example, satellite TV, which uses wireless
communications, can lose service during severe storms whereas cable TV,
a transmission line, does not. Despite these disadvantages, wireless
communications are widely used in today's world, and for that reason,
various wireless communications will be the focus of the rest of this
block.
>Imagine this scenario: you are stranded behind enemy lines, a few
kilometers from the smoking remains of your airplane. From intelligence
briefs received before the mission, you know you're in a safe area, with
only a very slight chance of capture. Still, you find a reasonably
sheltered spot and pull out your survival radio, hoping to contact a
rescue helicopter.
>
>In order to communicate with the helicopter, you will need to
communicate wirelessly. In your situation, though, how does it work? To
be successful, you will need to understand how wireless communications
work and what factors affect your communication system's performance.
### Radio Frequency (RF) Spectrum
The lower end of the electromagnetic spectrum, called the RF spectrum,
is subdivided into eight bands spanning from 3 kHz to 300 GHz. Each band
has a name, as shown in Figure 1. Civilian applications, such as
commercial AM and FM radio, television, cellular telephony, civilian
aviation navigation, and air traffic control frequencies are found in
this portion of the electromagnetic spectrum. These bands are also used
in many military applications: global positioning system (GPS); radar;
munitions guidance and fusing systems; strategic and tactical
communications systems; and intelligence, surveillance, and
reconnaissance (ISR) systems.
Figure 1: The RF spectrum.
### RF Propagation methods
*Context only: the propagation modes are not assessed. Objective 3.4 is the line-of-sight range.*
There are four different kinds of wireless RF propagation methods. They
are:
1. Direct or line-of-sight (LOS)
2. Surface wave
3. Sky wave
4. Forward scatter
Each of these pathways involves a propagation path. Since it is possible
for a signal to be transmitted over several paths simultaneously, this
may cause interference. However, some of the pathways only work for
certain bands within the RF spectrum.
1. **Line-of-sight (LOS) Propagation:** All electromagnetic energy (to
include all the RF bands) will propagate by LOS. If you, the
transmitter, are in view of the receiver, then line-of-sight is
established, thus the name. In practice, this means that if nothing
can obstruct the waves traveling directly between the transmitter
and receiver, then line-of-sight propagation can occur. As shown in
Figure 2, LOS communications on the earth are limited by the
curvature of the earth and the heights of transmitting and receiving
antennas. Of course, transmitter power is also a limiting factor.
The signal transmitted from point *T* reaches the receiving antennas
*R1* and *R2*. However, *R3* is not in the LOS path of the
signal and cannot receive any of the radio's energy. For
communication and telemetry between earth and space vehicles, LOS
propagation is used. At short distance, secure military
communications commonly occur through LOS microwave links. Some
telephone company "trunks" and cell phone towers also use LOS.
Figure 2: Line-of-sight (LOS) propagation between several repeater
stations.
2. **Surface Wave Propagation:** In surface wave propagation, the radio
wave travels from the transmitting antenna to the receiving antenna
along the surface of the earth. This wave essentially diffracts
around the surface of the earth, so you can reach distances greater
than LOS. In this waveguiding process, minute eddy currents are
induced in the ground directly beneath the surface wave. Although
the ground is a fairly good conductor, it does have some resistance
and the energy required for these currents to flow is absorbed from
the wave. This in turn limits how far the wave can effectively
travel.
As frequency increases, losses due to the conductivity of the ground
also increase and greatly attenuate the surface wave. This means
surface waves cannot travel as far at higher frequencies. Surface
waves are very effective for signal propagation in the VLF and LF
bands. However, near the MF band, this effectiveness decreases
rapidly. Surface waves are not generally useful above about 3 MHz.
Commercial AM broadcasting stations typically use surface waves to
transmit their signals - this is one of the main reasons AM radio
signals can travel much further than FM radio signals.
Figure 3: Surface wave propagation.
3. **Sky Wave Propagation:** Radio energy reflected or refracted from
the ionosphere back to Earth is known as a sky wave. To understand
how the ionosphere affects radio waves of different frequencies,
think of the ionosphere as a huge mesh sieve surrounding the earth.
Whether or not a wave passes through this sieve depends partially
upon the relative dimensions of the wavelength and of the mesh
openings. Therefore, radio energy with a long wavelength (low
frequency) is more likely to be reflected back to Earth than that
with a short wavelength (high frequency), which will pass through
the mesh. In addition to frequency, the angle of incidence, *β* in
Figure 4 below, plays a role in determining whether the radio energy
will be reflected back to Earth.
Figure 4: Sky wave propagation.
In general, the larger the angle, *β*, the greater the probability the
wave will be reflected. However, if *β* is too large, the layers of
the ionosphere will act like a waveguide and the wave will effectively
remain in the ionosphere and not be returned to Earth. As with the
other wireless RF propagation methods, there is often a tradeoff
between this angle of incidence and frequency. That is, for a given
angle, there is some maximum frequency that can be used for sky wave
propagation. Likewise, for a given frequency (within certain limits),
there is some maximum angle that will produce a sky wave.
Maximum usable frequencies usually lie in the HF band; waves whose
frequencies are above this are refracted slightly by the ionosphere
but propagate through it. A peculiarity of the ionosphere is that its
lower layers readily absorb energy in the MF band. Thus, sky waves in
this band are possible only at night when the lower ionospheric layers
are less dense. Narrowband long haul communications are often
conducted in the HF band via sky wave.
Sky wave propagation has a significant limitation. At the point where
a sky wave returns to Earth, you can detect a very strong signal.
However, between this point and the transmitter, there is essentially
no energy from the sky wave at all. The distance between the
transmitting antenna to the spot where the reflected wave strikes the
earth is called the *skip distance*. At all locations less than the
skip distance from the transmitting antenna, none of the sky wave
signal is received. Therefore, the only way to communicate at points
less than the skip distance is through LOS or surface wave
communications.
In the HF band, where surface wave propagation is somewhat less than
200 miles, there is often a considerable distance in which essentially
no radiated energy from either the surface wave or the sky wave is
present and no communication is possible. This region is called the
*quiet zone*. Figure 5 below illustrates the concepts of skip distance
and quiet zone.
Figure 5: Skip Distance and Quiet Zone.
4. **Forward Scatter Propagation:** When a radiated signal strikes the
discontinuous "blobs" of air in the troposphere, it is scattered in
various directions. Some of this scattering is in the forward
direction, and the resulting radio signal, although relatively weak,
can be received at a point that is beyond the horizon from the
transmitter. Most of the Air Force's non-satellite wideband long
haul communications use forward scatter (with carriers in the 300 to
400 MHz range).
Although the scatter is dependent upon atmospheric conditions, it is
possible to achieve reliable communications using high-power
transmitters and sensitive receivers. Tropospheric forward scatter is
effective in the VHF, UHF, and SHF bands. These tropo links use large
rectangular "billboard" antennas and typically transmit about 100 kW
of power. Before satellite communication became prevalent, much
in-theater military communication was accomplished using this type of
propagation.
Figure 6: Forward scatter propagation.
### Range and Bandwidth Considerations
At higher carrier frequencies, more bandwidth is available for use. As a
rough estimate, the available bandwidth for a signal is about 1% of the
carrier frequency.
AM radio stations, operating around 1 MHz, only have 10 kHz of bandwidth
available. Fiber optics, however, use beams of light with carrier
frequencies on the order of 100 THz (100 trillion cycles per second).
These light beams have available bandwidths up to 1 THz. In other words,
we can transmit approximately 100 Million times more information over a
light beam than we can over a radio signal.
Unfortunately, the transmission range of signals also depends on the
frequency. AM radio stations can easily transmit signals hundreds of
miles, and as said earlier, these signals can even follow the curvature
of the earth to reach beyond line of sight (surface waves). Light beams,
on the other hand, are quickly attenuated by atmospheric effects. In
order to overcome this limitation while still reaping the benefits of
the huge bandwidth available in beams of light, optical fibers are
generally used. We'll discuss how frequency affects a signal's range in
more depth in future lessons.
:::{admonition} Key Concept
:class: key-concept
Context only — not assessed. Which propagation mode you get is decided by **frequency**, not by preference. Low frequencies buy range and obstacle penetration but very little bandwidth; high frequencies buy bandwidth and antenna gain but demand line of sight.
:::
### RF Summary
Let's quickly summarize which types of wireless communication pathways
are used by different radio frequency bands. This information is
identified below in Figure 7. The ITU (International Telecommunication Union)
designation of frequency bands (e.g., VHF, UHF) and the frequency ranges
for some of the more common uses of radio waves are indicated. Since the
transmitted signal in a communication system usually has a relatively
narrow bandwidth, the propagation characteristics are determined almost
exclusively by the carrier frequency. This figure also summarizes which
radio frequencies are best suited to the four primary pathways that
radio frequency waves propagate through the air and space: direct or
line-of-sight (LOS), surface wave, sky wave, and forward scatter.
Figure 7: The RF spectrum and the associated wireless RF propagation
methods.
- **VLF and LF (Very Low Frequencies and Low Frequencies):** At these
lower frequencies, surface waves are attenuated very little and may
be used for signal propagation of a thousand miles or more. This
maximum distance gradually decreases with increasing frequency and
is about 400 miles at 300 kHz. The sky wave does exhibit slight
fluctuations with changes in the ionosphere, but it is still fairly
reliable. Sky waves can be used for communication over distances
from about 500 to 8000 miles in the LF band. In the VLF range, the
combination of the surface and sky wave mechanisms make worldwide
signal propagation possible with radiated power levels of about 1
MW.
- **MF (Medium Frequencies):** In this band, the maximum distance for
surface wave propagation varies from about 400 miles at 300 kHz to
about 200 miles at 3MHz. Ionospheric absorption of electromagnetic
energy in this band (maximum absorption occurs at 1.4 MHz) makes sky
wave propagation impossible during the day. At night, sky waves
furnish reception at distances from about 100 to 3000 miles.
- **HF (High Frequencies):** The attenuation of surface waves above
about 3 MHz is so great that the surface wave is effectively of no
use for communication in this band. Sky waves are used extensively,
and their behavior is mostly governed by ionospheric conditions.
Although sky wave propagation is not always reliable, it is possible
over distances of 12,000 miles and more. For distances such as this,
frequencies from 5 to 20 MHz have proven most effective. Many
military aircraft have HF radios onboard used for long-range
communication. Also, amateur radio (ham radio) operates primarily in
this part of the spectrum. Amateur radio is primarily used by
hobbyists who are interested in RF communications.
- **VHF (Very High Frequencies):** Although sky waves may occur at
lower VHF frequencies, their reliability is so poor in the VHF band
that they are virtually useless for communication. The predominant
form of propagation in this band is line-of-sight. The effectiveness
of forward scatter becomes increasingly important as frequencies
reach 50 MHz and above.
- **UHF and SHF (Ultra High Frequency and Super High Frequency):**
Line-of-sight propagation is widely used at these frequencies since
excellent low-noise reception is possible. Ranges of a few hundred
miles can be realized up to about 10 GHz. Most forward scatter
applications use frequencies well below this. Many space assets use
this frequency band for communications.
- **EHF (Extremely High Frequency):** Line-of-sight is the only
propagation method used with EHF. Radio waves at these frequencies
attenuate quickly in many uses, such as radar and wireless
communications, so range is limited for these frequencies.
Additionally, the atmosphere absorbs energy from waves, further
attenuating them while in the atmosphere. However, EHF is still
used. Each satellite in the Advanced Extremely High Frequency (AEHF)
satellite constellation uses EHF for uplink communications.
Additionally, 5G cellular networks will use frequencies in the lower
portion of the EHF band. Specifically, Verizon has stated that they
use 28 GHz (SHF) and 39 GHz (EHF) for their 5G network.
## Line-of-sight Communications
Returning to our original question, "What kind of wireless RF
propagation method would you use between you and a rescue helicopter?"
Realistically, you'll most likely find yourself trying to establish a
LOS link. A survival radio does not have the power required to use the
more specialized forms of wireless communications (surface waves, sky
waves, and forward scatter). In LOS, the key to establishing
communications is actually being able to "see" the helicopter and having
enough transmission power.
Obviously, there are a number of variables associated with determining
the LOS between you and the helicopter. Are you on a hill or in a
valley? How high is the hill? Is the terrain flat or bumpy? How high is
the helicopter?
If we assume the terrain is relatively flat, we can use a simple
equation to give us a good idea of how far the helicopter (or anything
else) can see. Consider an antenna sitting at height, *h*, above sea
level. The maximum range, *r*, between transmit and receive antennas is
calculated as the distance from the transmit antenna to the point that
is tangential to the surface of the earth as shown in Figure 8.
Figure 8: Line-of-sight communication range.
Since $R_{e}$ and *r* make two sides of a right triangle, with
($R_{e}$ + *h*) as the hypotenuse, we can use the Pythagorean theorem
($a^{2} + b^{2} = c^{2}$) to find:
$$R_{e}^{2} + r^{2} = \left( R_{e} + h \right)^{2}$$
$${(R_{e} + h)}^{2} = R_{e}^{2} + 2R_{e}h + h^{2}$$
$$R_{e}^{2} + r^{2} = R_{e}^{2} + 2R_{e}h + h^{2}$$
$$r^{2} = R_{e}^{2} + 2R_{e}h + h^{2} - R_{e}^{2}$$
$$r^{2} = 2R_{e}h + h^{2}$$
$$r = \sqrt{2R_{e}h + h^{2}}$$
For terrestrial and even some airborne applications (i.e., non-space),
we can assume that $R_{e}$ is much greater than the antenna height
($R_{e} \gg h)$, so the $h^{2}$ can safely be ignored. This results in a
maximum LOS range equation of:
$$r_{\max} = \ \sqrt{2R_{e}h}$$
Furthermore, the radius of the Earth is adjusted to account for
atmospheric effects (decreasing atmospheric pressure helps bend radio
waves downward thus increasing range). The resultant radius is increased
from 3960 miles to 5280 miles, using the common 4/3 radius model.
Coincidentally, there are 5280 feet in a mile. As a result, we can
employ a "mixed units" equation, entering the antenna height (*h*) in
feet to find the range in miles. This makes our LOS equation:
$$r = \ \sqrt{2h}$$
In this equation, *h* is the height (***in feet***) of the observer, and
*r* is the distance (***in miles***) the observer can see before the
horizon gets in the way. Notice this is an "improper" equation, which is
to say the units don't match - if we take the square root of feet, we
should not end up with miles. As engineers, we're willing to overlook
this discrepancy and use this improper equation because it is useful,
and its derivation produces a mathematically logical result.
:::{admonition} Key Concept
:class: key-concept
$r = \sqrt{2h}$ with $h$ in **feet** and $r$ in **statute miles**. The units do not balance — it is an 'improper' equation that works because the 4/3 Earth-radius model happens to make the numbers coincide. Engineers use it anyway because it is right and fast. The equation sheet writes it for two elevated ends, $R_{LOS,mi} = \sqrt{2h_{ft,1}} + \sqrt{2h_{ft,2}}$, where the subscripts are the units; one end on the surface is that row with a height of zero. The conversions around it are also on the sheet: 1 ft = 0.305 m and 1 mi = 1.61 km.
:::
### Example Problem 1
A helicopter is searching for a downed airman
from 2000 feet AGL (above ground level). Assuming relatively flat
terrain, how close will it have to get to the airman before it can
establish line-of-sight?
**Understand**: Military survival radios require line-of-sight to
communicate, so we need to calculate the maximum LOS distance.
**Identify Key Information**:
- **Knowns:** We know the height of the CSAR helicopter.
- **Unknowns:** The maximum line of sight distance.
- **Assumptions:** We assume the terrain is flat (mountains cause
significant problems).
**Plan:** We will use the LOS equation to solve for the maximum LOS
distance.
**Solve:** We know the helicopter is 2000 feet above the earth. Plugging
this into the LOS equation gives:
$$r = \ \sqrt{2h} = \ \sqrt{2*2000} = \ \sqrt{4000} = 63.25\ miles.$$
Recall, we put feet into the equation and the answer will be given in
miles.
**Answer**: At 2000 feet AGL, the helicopter can see for approximately
63.25 miles. Therefore, it needs to be within 63.25 miles to see an
airman on the ground. With the equation sheet's conversion, that is
$63.25\ \text{mi} \times 1.61\ \text{km/mi} = 101.8$ km.
### Example Problem 2
The helicopter in the previous example is still
flying at 2000 feet AGL. If the airman climbed to the top of a 50-foot
tall hill, how far away could the helicopter establish line-of-sight?
**Understand**: We have to use the LOS equation twice because the airman
has raised himself above the surface, as shown below.
**Identify Key Information**:
- **Knowns:** We know the height of both the helicopter and the
stranded airman.
- **Unknowns:** The maximum LOS distance.
- **Assumptions:** The terrain is flat and no mountains are in the
way.
**Plan:** Recall, we are trying to determine the *maximum* distance the
helicopter can see the airman. As the picture above hopefully shows,
this occurs when the airman climbs high enough to just barely be in the
helicopter's line-of-sight. At this point, the helicopter will see the
airman on the horizon, not even knowing the airman is standing on a hill
(since the hill is below the helicopter's horizon). From the point of
view of the airman, the helicopter will also appear right at the
horizon. Calculating this maximum LOS distance is very straightforward.
We first figure out how far the horizon is from the helicopter, and
then, we figure out how far the horizon is from the airman. If we add
these two distances, we get the maximum distance they can see each
other.
**Solve**: We already calculated the distance from the helicopter to the
horizon in the previous problem. It is 63.25 miles. Since the airman is
on a 50-foot hill, the distance for him to the horizon is:
$$r = \ \sqrt{2h} = \ \sqrt{2*50} = \ \sqrt{100} = 10\ miles$$
Adding these distances together gives us our answer:
$$r_{total} = 63.25\ miles + 10\ miles\ = 73.25\ miles$$
This is the equation sheet's line-of-sight row,
$R_{LOS,mi} = \sqrt{2h_{ft,1}} + \sqrt{2h_{ft,2}}$, with
$h_{ft,1} = 2000$ and $h_{ft,2} = 50$.
**Answer:** The airman and the helicopter now have a maximum LOS
distance of 73.25 miles, which is 10 miles farther than before. In
kilometers that is $73.25 \times 1.61 = 117.9$ km.
::::{admonition} Type-along
:class: type-along
An E-3 AWACS orbits at **30,000 feet** and needs a Link 16 connection to a fighter at **25,000 feet**.
1. What is the maximum separation for line of sight, in miles and in kilometers?
2. A ground station's antenna is 30.5 m above the ground. How far can the AWACS be from it?
3. To *double* the AWACS-to-ground range, what altitude would the ground antenna need?
:::{admonition} Solution
:class: dropdown
**1.** $R_{LOS,mi} = \sqrt{2(30000)} + \sqrt{2(25000)} = 244.95 + 223.61 = 468.6$ miles, which is $468.6 \times 1.61 = 754.4$ km.
**2.** Heights go in as feet: $30.5\ \text{m} \div 0.305\ \text{m/ft} = 100$ ft. Then $R_{LOS,mi} = 244.95 + \sqrt{2(100)} = 244.95 + 14.14 = 259.1$ miles.
**3.** You would need $2 \times 259.1 = 518.2$ miles in total. The AWACS contributes 244.95, so the ground station must contribute 273.2 miles — requiring $h = 273.23^2/2 \approx 37{,}330$ feet. Absurd: that is higher than the AWACS.
Range grows only as $\sqrt{h}$, so you cannot build a tower out of the problem. That is exactly why the airborne platform does the work, and why satellites exist.
:::
::::
## Wrap-Up
There are four wireless modes — **surface wave**, **sky wave**, **forward scatter**, and **line of sight** — and frequency decides which you get (context only — not assessed). LOS works in every band and is what modern military communications rely on; its geometric limit is the curvature of the Earth, $r = \sqrt{2h}$ with $h$ in feet and $r$ in statute miles, with the ranges of two elevated ends adding — the equation sheet's $R_{LOS,mi} = \sqrt{2h_{ft,1}} + \sqrt{2h_{ft,2}}$. Multiply by 1.61 for kilometers.
Objective 3.5 adds the other half of the question: having line of sight is necessary, but you also need enough power.