Radio Propagation

Radio propagation can be one of the most difficult subjects to understand if you don't work with the concepts every day. One of the reasons for this is that all electromagnetic energy behaves is best described by the wonderfully strange theories of Quantum Mechanics. Since most of us are exposed to, and can sense light, on a daily basis it is easy to believe we understand how it works. The effects of Quantum Mechanics though are proportional to wavelength. Typically the human eye can sense light in wavelengths of 390 nanometres to 750 nanometres. A nanometre is 1/1,000,000,000 of a metre. The radio signal from an emergency transmitter has a wavelength of 2.47 metres. This means that the quantum effects on the emergency transmitter radio signal will be 500,000 times larger than for light. In most every day experience the strangest behaviour of visible light is too small for us to detect, but later we will show you how to do some home experiments that will allow you to see some of this behaviour. The quantum effects on the emergency transmitter signal, on the other hand, are easily large enough not only to be detected with the right equipment, but to have a significant impact on our efforts to locate the emergency transmitter. This means that you can't normally extrapolate your other experiences or common sense to the field of radio propagation.

Radiation Patterns

A good place to start is with the concept of the radiation pattern. This is simply a description of how electromagnetic energy is distributed in different directions from the point where it is produced. Our lamps all have radiation patterns. A room light will have a nearly omnidirectional pattern so that it lights up the room as evenly as possible. A desk lamp will have a pattern that directs the light down onto the work surface. A flash light has a pattern that allows us to direct the light to the area we want to look at. Radio systems will similarly have different pattens as well depending on the purpose. An emergency transmitter will usually be designed to have a nearly omnidirectional radiation pattern so it may be detected from all directions.

Radiation patterns can be described mathematically, but most often they are shown as a two or three dimensional graph. The distance of the line or surface from the origin of the graph is determined by the relative amount of energy sent in a particular direction.

Isotropic Radiation Pattern

Radio engineers have defined a special radiation pattern called Isotropic radiator for convenience. An Isotropic radiator sends the same amount of energy in all directions and is often called an ideal radiator. This makes the mathematics easy. The graph to the right is an Isotropic radiator sitting on a surface so the bottom half of the spherical pattern can not bee seen. 

Toroidal Radiation Pattern

An Isotropic pattern would be ideal for an emergency transmitter, but it can not be achieved in practice. Most emergency transmitters use what is commonly called a whip antenna, but is more formally know as a monopole. A monopole radiates in an a doughnut shape or toroidal pattern. To the right is a three dimensional plot of an idealized monopole radiation pattern. You can see that the antenna does not send any energy directly up, the direction of the free end of the whip.
Here we have a graph of the profile of an actual monopole antenna. This is also an example of a two dimensional radiation pattern. It looks roughly like the ends of a doughnut that has been cut in half. This antenna will radiate in three dimensions, but sometimes a two dimensional graph can more accurately capture the most interesting or important features of the pattern. The full three dimensions can usually be inferred by mentally 'rotating' the two dimensional image.

Radiation Patterns for Reception

Antennas don't care if you use them for transmission or reception, they retain their pattern. What is the radiation pattern, the amount of energy sent in each direction during transmission, becomes the reception pattern, the amount of energy received from each direction, during reception. The shape remains the same. 

One thing radiation patterns will not tell us is how far the energy will be sent, or more precisely: what the strength of the signal will be at a particular distance. There are still some more items we have to take into account.

Inverse Square Law

When energy radiates outward from a source in three dimensional space, even though the total energy remains the same, it is spread out over the surface of an ever expanding sphere as it moves away from the source. So the energy at any point is will be proportional the the inverse of the square of the distance. As you can see from the graph on the right (click it to make it bigger), the power level drops away very rapidly initially, but the rate of decline decreases very rapidly as well leading to a relatively flat curve for most of the graph. The level is so low that it is very difficult to see any detail, and the line is quickly obscured by the X axis. That is why these kinds of graphs will often use a logarithmic Y axis like the next image which is in all other respects identical to the first.

Logarithmic graphs will often show details that are hidden by linear graphs. Because of this logarithmic graphs will make a return appearance from time to time.

The Friis Transmission Equation

But even the Inverse square law does not tell the whole story. Many other things affect the power that our receiver can pick up as we move away from the transmitter. We must consider the output power of the transmitter, the transmit antenna radiation pattern, the receive antenna reception pattern, and absorption in the propagation media. Radio engineers pile all these parameters into the Friis Transmission Equation. There are simple forms, which we will use here, and more complex forms that allow for non-isotropic radiation and reception pattern and other real world possibilities. All of these values are normally expressed in decibels. 

For transmitter output we will use the normal rated power on 121.5 MHz of a TSO C91A ELT which is 100 milliwatts or, expressed in decibels 20 dBm. The result of the Friss equation will also be in dBm. This results in the graph to the right showing expected signal strength out to 1000 nm. A normal receiver is quite capable of detecting a signal at -120 dBm. You will notice the shape is not much different from the logarithmic inverse square plot above. Unfortunately the Friis equation, even the complex one, does not take into account everything that can happen to a signal on its trip from transmitter to receiver, but we will leave that aside for the moment. 

You may have started to wonder, if an ELT could be detected up to, and perhaps even further away than 1000 nm, how in the world can any light aircraft, or indeed any aircraft hope to fly from one side to the other? As we will see in the next section that won't be a problem. But just in case you are sceptical that an ELT could be detected at such large ranges remember that COSPAS/SARSAT listened for 121.5 MHz signals up until February 2009. Up until then it was quite routine for the satellites to pick up these transmissions from well over 800 km (their orbital altitude) away. Some times they would even detect and fix ELTs that had no antenna, were packed in a box and riding in a courier truck to be delivered to a repair facility. 

So why is the range an aircraft can detect the transmitter from so limited in comparison? Line of Sight.

Line of Sight

Line of sight simply refers to a straight line between an observer and the observed object that does not pass through any obstructions that block the view. When observing by eye we can not see any part of the Earth's surface past the furthest point where our line of sight intersects the surface. All such point surrounding us form a circle we call the true horizon. If obstructions like trees, buildings or hills block our line of sight closer than the true horizon this forms a visible horizon. As you can see from the diagram on the right the distance to the true horizon, and almost always to the visible horizon is determined by the elevation of our eyes. This is why the view is so much better from the top of a tall mountain or building. 

Radio Horizon

Not all radio waves are constrained by line of sight, but Signals in Very High Frequency (VHF) radio band 30 MHz - 300 MHz, and higher are only received when there is a line of sight path between the transmitter and receiver. What is, or is not, an obstruction to radio signals depends on the material the obstruction is made of, and the frequency. For example some radio frequencies penetrate buildings quite well, others do not. Considering obstacles to the radio signal gives us a horizon analogous to the visible horizon for sight that is called the radio horizon. The situation we are interested in the the transmitter is on the surface, the receiver is in an aircraft. In this case any aircraft that is above a line drawn between the transmitter and the radio horizon will be able to receive the signal if it is strong enough. As we saw above, the signal from an emergency transmitter should be strong enough to be received at a large distance. We can see that aircraft A and C will be able to detect the transmitter, but aircraft B won't. Aircraft B could either climb, or fly towards the transmitter until it crossed above the line of sight path.

It is the reduction in detection distance due to radio horizon that makes aural searches practical. It is the movement of the aircraft from below to above, or above to below the line of sight path, taking it into or out of an area where the transmitter may be heard that will provide the information needed to locate the transmitter.

Some claim that the radiation pattern determines how far the aircraft can receive the signal, others that transmitter power sets the distance. Clearly neither of those claims can be true unless the transmitter power is reduced a large amount. As we saw above, even removing the antenna is not always enough to reduce reception range below 800 km. The earth has no problem getting in the way and reducing reception range down to a few dozen miles if the altitude of the search aircraft is low enough.

Avoiding Obstacles - Fresnel Zones

When we started this section we mentioned that some strange things can happen to radio waves, this is where the strangeness starts. All light particles, photons, travel from origin to destination by all possible paths. If you think this is strange, try reading this explanation as to why. One of the results of this property it that you can't block a radio transmission by just blocking the visual line of sight, you must block the 'radio' line of sight which is much larger because it is proportional to the wavelength. 

I won't put the maths for calculating how large an obstacle must be, but it is not that complicated. A Fresnel Zone, named for physicist Augustin-Jean Fresnel, is one of a theoretically infinite number of concentric ellipsoids which define volumes in the radiated signal. The first Fresnel zone surrounds the line of sight path. As obstacles intrude into this zone the radio signal at the receiver will begin to degrade. For a communications link, engineers will strive for less than 20% obstruction, though a usable link can usually be established with up to 40% obstruction. Since we are not interested in establishing a usable link, only in detecting the signal, we can accept even more than 40% obstruction. 

How Fresnel Zones Help

So, even though there may be obstructions between the transmitter and the true horizon, in order for them to reduce the radio horizon distance they must obstruct more that 40% of the first Fresnel zone defined by the locations of the transmitter, receiver and the obstacle. The further the receiver, the search aircraft, is from the transmitter, the larger the size of the Fresnel zone for at any given obstacle. This means that for an aircraft further away from the transmitter, as aircraft C is further away than aircraft A in the diagram above, the larger an obstacle needs to be to block the signal. An aircraft operating at a greater distance from the transmitter will be more likely to observe a radio horizon that is closer to the true horizon than an aircraft operating a a closer distance. The graph to the right shows the cross sectional area of the first Fresnel zone versus the range of the aircraft from the transmitter for obstacles at 1 km, 2 km and 3 km from the transmitter.

It is commonly recommended that search aircraft fly as low as it is safe to in order to reduce the distance at which the transmitter can be detected. This is done to reduce the amount of flying need to locate the the transmitter. Flying low is problematic for many reasons: communications with search base; visibility of developing weather, hills and towers; and it may make the radio horizon less regular and a fix more difficult to compute. Later we will describe a technique that reduces the flight time without the necessity of descending. 

Fading

In radio communications fading is a change in received signal strength resulting from the propagation of the signal in the environment. Fading may vary in time, location or frequency. Often it is convenient to model fading as a random process which results in the predicted probability of the amount of change in signal strength. Fading may be due to multipath propagation, referred to as multipath fading, or due to shadowing from obstacles, sometimes referred to as shadow fading. In airborne electronic search shadow fading will normally occur when the aircraft is near its radio horizon from the transmitter. In practice there is no way for a search crew to know for sure if fading is the result of multipath or shadowing.

Multipath Fading

Multipath is the phenomenon of a radio signal (or any electromagnetic signal, including light) arriving at the receiver by two or more paths. Multipath is caused by atmospheric ducting, ionospheric refraction and reflections. Reflections may arise from anything large enough, smooth enough and with the right electrical and magnetic properties. For visible light this usually requires a very smooth and shiny surface like glass, polished metal or polished paint. This process is also proportional to the wavelength. So for our radio signals the reflective area must be larger, but what looks smooth to radio may not seem smooth to us. Radio signals will reflect off of bodies of water, large paved surfaces (airport aprons and runways), fields, mountains, and even open metal mesh fences. 

When the signals arrive in phase they will combine in a way that increases the strength of the received signal. When they arrive out of phase they combine in a way that reduces the signal strength, possibly even to the point of preventing reception of the signal entirely. This is called constructive and destructive interference.

Constructive and Destructive Interference

Wave Interaction

Thanks to Richard Glenn and Konstantin Lukin and the Earth Science Education Resource Center we can use the Java applet included here to experiment with wave interaction and see constructive and destructive interference.

The diagram below shows what happens when a signal arrives at the aircraft over two paths, either in phase or out of phase. When they arrive in phase the aircraft receives an unexpectedly strong signal, when out of phase the aircraft receives no signal.



As the aircraft moves around the search area the multipath propagation can change from constructive to destructive and back. This leads the aircraft to encounter a signal strength field that has many areas of relatively strong, but slightly different signal strength, and many areas of relatively weak, but also slightly different signal strength. The signal strength field begins to look more like a topographic map of a hilly area rather than the theoretical ideal where there is only one peak in signal strength co-located with the transmitter. This is depicted in the graph on the right.

This is the output of a propagation analysis and prediction program that is simulating the presence of multipath fading. In
this graph one may clearly see that an aircraft seeking maximum radio signal, and not familiar with the properties of multipath fading, and because they can not see the signal strength field, may end up at the location 10 nm North, and 10 nm East of the transmitter. 

The simulation was also programmed with the radio horizon for the altitude the simulated search aircraft was flying at. This forms the circular line outside of which no signal is detected at all. One can also clearly see that areas of equal signal strength, areas of the same colour, do not form a circle with the transmitter at the centre.

We now have the information we need to start discussing the procedures for flying Aural Null searches.
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