microwave radio propagation

We will now start the course by defining the characteristics of the radio wave.

The first characteristic is the frequency.

Frequency

By frequency we mean how often the two poles in an electric circuit or the electrical field

in a radio wave change polarity.

In every day life we meet this for example when connecting a device to a mains power

outlet.

The sinusoid curve in the slide is describing one complete oscillation. Half of the time it is

positive and half of the time negative. Frequency is measured in the unit Hertz and is the

number of times per second which the one oscillation curve is repeated.

If a complete oscillation happens one time per second this is defined as one Hertz.

In ordinary mains power the curve shape is repeated 50, in some countries 60, times per

second. We say that the mains frequency is 50 Hertz or 60 Hertz.

In radio communication much higher frequencies are used, actually up to several tens of

thousand million hertz.

To describe higher frequencies in a practical way the terms kilohertz, megahertz and

gigahertz are used. Kilohertz for thousands of hertz, megahertz for millions of hertz and

gigahertz for thousands of million hertz.

In writing the shown abbreviations are used.

The definition of the term microwave is not strict and has changed over time. Today it is

commonly used for the frequency range from 1 gigahertz and up to 100 gigahertz. The

movement of electromagnetic waves in this range in the earth’s atmosphere is the subject

of this course.

Applications

The frequency bar shows the frequency range which is of most interest for radio communication.

Because of increasing bandwidth demand and thanks to technology achievements the trend in radio

communication is and has always been to deploy higher and higher frequency bands.

Generally speaking low frequencies have an ability to follow the earth curvature and to overcome

obstacles. Higher frequencies behave the opposite, in fact more like light, and require a free path with

visibility from transmitter to receiver. The further we go in each direction the more this behavior is

accentuated.

Some examples of frequency usage for the range from 100 kilohertz to 100 gigahertz are presented in the

slide.

Various applications for marine, air and land mobile radio are located within a wide range from below a

Megahertz and up a few Gigahertz.

At around 100 Megahertz we have the well known FM broadcast radio band and slightly higher the band

for digital broadcast as for example digital TV.

Another well known application for radio communication is digital cellular mobile devices, mobile phones,

which resides approximately between 800 Megahertz and 2 Gigahertz.

This course is about Microwave Radio Links which are located between 4 and 80 Gigahertz. As seen in

the slide, this range is shared with satellite communication.

It might be interesting to note that Microwave ovens have a dedicated frequency at approximately 2.5

Gigahertz. Basically a microwave oven is a strong radio transmitter imprisoned within a box.

To summarize this slide in a somewhat simplified way:

Low frequencies give long range and can overcome obstacles but give low traffic rate.

High frequencies can be used only for short ranges; they need a free path but can provide high traffic rate.

Frequency Bands

The radio link frequency range of most interest and which will be studied here is

from approximately 4 gigahertz and up to 80 gigahertz.

Propagation properties will differ quite much over this large range. The choice to

use frequencies from the lower or higher part of the range is mainly based on the

application.

By international regulations the range is subdivided into individual frequency

bands. Each band is covering a certain frequency interval and is further

subdivided into a number of individual channels.

As example the 23 gigahertz band covers the range from 21.2 gigahertz up to

23.6 gigahertz.

To exactly show how the range is subdivided into channels is not the objective of

this course but as an example the frequency 22.26 gigahertz is used. This is the

channel center frequency, f zero.

Channel Bandwidth

The transmitter sends a digital stream of information over the channel by

introducing small changes to the radio wave.

This process at the transmitter is called modulation. It can change the radio wave

in phase and in amplitude.

The receiver at the opposite station de-modulates the signal. This means that it

reads the changes in the signal and translates them back into digital data.

When the transmitter modulates the radio wave, signal frequencies surrounding

the centre frequency will be produced.

The faster the carrier state is changed the higher the information rate gets but at

the same time frequencies further away from the centre frequency are produced.

This is defined as the channel bandwidth.

There are international regulations that define in certain steps how wide the

channel bandwidth is allowed to be. Most common bandwidth range is from 3.5

megahertz up to 56 megahertz, but this can differ between countries.

Wavelength and Polarization

The antenna converts the electrical signal from the transmitter into an electro magnetic field with

changing polarity.

The field is propagated from the antenna as a wave front travelling with approximately the speed

of light. In what direction or directions is decided by the antenna design.

While looking at this slide it is easy to define the parameter “wave length”. This is another way to

express frequency which is sometimes used and helps for example to understand reflection

phenomena. The wave length is a measurement in meters for how long distance the wave front

will travel during one oscillation. The Greek letter lambda, as shown in the slide, is commonly

used to represent the wave length.

The relationship between wave length and frequency is as shown dependant on the propagation

speed, the speed of light.

Here are some examples of approximately how long the wavelength is in the microwave band.

The short wavelength is the reason why the gigahertz part of the frequency spectrum is called

“microwave”.

As we have said, the radiation from the antenna is an electro magnetic radiation. This means it

consists of an electric field and a magnetic field perpendicular to each other. The electric field is

the one of interest. If this is vertical the radio wave is called vertically polarized,

if it is horizontal the radio wave is consequently called horizontally polarized.

The polarization is set by the antenna. Using different polarizations is one way to minimize

disturbance, so called interference, between neighboring paths sharing the same frequency.

Another use is to double the traffic rate over a certain bandwidth by letting two parallel paths

share the same frequency and to separate them by polarization.

Power

The next radio wave property to look at is the power of the signal.

At the transmitter’s antenna interface the power is measured in Watt, or more commonly for microwave

radio links in the logarithmic correspondence dBm with the reference value 0dBm equal to 1 milliwatt. An

example of a typical microwave radio link transmitter output power is 0.2 Watt, corresponding to 23 dBm.

Compared to other kinds of wireless technology operating over similar distances this is a very low output

power. For comparison a GSM mobile phone handset has a max transmit power of 2 Watts.

The low demand for transmitter power in microwave links is achieved thanks to the type of antenna

which is used. Because a microwave link is communicating with only one opposite station and the two

stations are not moving, the signal can be directed in a narrow beam. This substantially reduces the

demand for output power compared to that of applications which are communicating in many directions.

When the radio wave leaves the transmitter antenna the electrical field in the wave front has a high

concentration of power per square meter. The signal has high amplitude.

On its way to the receiver antenna the amount of power per square meter gradually decreases and when

the receiver antenna catches it there is just a small part of the power left. The signal has low amplitude.

The received signal strength is measured in Watt, or more commonly dBm. The minimum received signal

strength level the receiver needs to detect the information carried by the signal correctly is called the

receiver’s threshold level. The value of the threshold level depends on different factors, for example the

bandwidth of the signal. The value given in the slide can be regarded as a quite typical example. As seen

there is a huge difference between the transmitter output power of 0.2 Watt, 23dBm, and the receiver

threshold level of zero point ten zeros 1 Watt, -70dBm.

By this the radio wave is defined; now let us study how it travels in the

atmosphere

The Atmosphere

On the earth we are surrounded by the atmosphere, a prerequisite for life, but

with impact on microwave propagation.

The atmosphere is most dense at sea level and then gradually gets thinner with

altitude up to the vacuum of space.

This changing air density is impacting the propagation speed so that radio waves

at low altitudes are travelling slower compared to those travelling at high

altitudes. The relative difference is small but has an impact.

Radio Refractivity

Atmospheric density is described as radio refractivity which depends on pressure,

humidity and temperature.

The radio refractivity is normally highest at sea level and then gradually

decreases with altitude until it finally reaches the value 0 in vacuum.

Waves travelling in these typical atmospheric conditions will be bent down

towards the surface of the earth. This is because the lower part of the wave front

is travelling slower than the upper part. The bending effect is exaggerated in the

slide but even in reality the antennas may be slightly tilted upwards.

How fast the radio refractivity changes by altitude differs around the world and

local short term variations are common. In general the conditions in inland

temperate climate are quite stable while the variations can be large in tropical and

costal climates. A standard atmosphere model with a certain bending effect has

been defined and in absence of local data this can in many cases serve as a

good enough estimation.

How much the wave front is bent is described by the equivalent earth radius

factor, commonly called the k factor. For the standard atmosphere this factor is

1.33. Later we will show how it is used.

k Factor Values

The slide shows a microwave link at the top of the world and will be used to show wave front

bending at some different values for the k factor.

The k factor for the standard atmosphere is 1.33. This means the wave front is bent downwards

and somewhat follows the earth curvature. This bending effect can help the radio wave to reach

beyond the horizon and to overcome obstacles.

The higher the k factor value gets the faster the radio refractivity changes by altitude and the more

the wave front is bent downwards. When the k factor reaches infinity the bending is the same as

the earth curvature itself. The radio wave will then experience the world as flat. When this

happens it can result in interference between microwave radio links far away from each other.

If the radio refractivity change is even larger than in previous example the k factor will become

negative and the radio wave will bend more than the earth curvature and hit the earth at some

point. This phenomenon is named ducting and it will most probably result in lost communication

over the radio link. It is unusual but can occur occasionally in parts of the world during unfavorable

climate conditions.

k factor equals 1 means that there is no change in radio refractivity by altitude. The wave front will

not be bent and will continue in a straight line to the horizon and there vanish out into the space.

k factor less than 1, but larger than 0, means the wave front is bent upwards. In this case the radio

refractivity increases by altitude, the opposite to what it does in the standard atmosphere. This can

happen in certain combinations of temperature and moisture in the atmosphere. Microwave

planners often take this phenomenon into consideration when designing a path. If this has been

done the communication is likely to continue.

Free Line of Sight

Radio signals at frequencies in the microwave band do not have the ability to

travel around obstacles in the path.

The very short wave length makes this impossible.

Antennas must therefore be placed so that there is a free line of sight for the

radio signal between them. In most cases, but not necessarily in all, this means

there is also an optical free line of sight between the antennas.

If microwaves are bad in overcoming obstacles they are instead good at

bouncing. This gives the possibility to use passive radio mirrors to direct the

signal around an obstacle to reach a location which would have been impossible

to reach via a direct free line of sight path. But this is beyond the scope of this

course.

Use of the k Factor

The world is round so to obtain a free line of sight the first thing to overcome is

the earth curvature, the earth bulge, which here is expressed as delta h.

Please remember that this is just the earth curvature itself, hills, mountains,

valleys, buildings and so on are added to this.

Previously we saw that the radio wave in a standard atmosphere is bent

downwards. If the antennas are slightly up tilted this can actually help to

overcome obstacles by reducing the needed antenna mounting height. This is

where the k factor comes into use.

The earth radius is multiplied by the k factor. In the case of the standard

atmosphere where the k factor is 1.33 it will make the earth larger. By making the

earth larger the earth bulge over a given distance will decrease compared to that

of the true earth size, as shown in the slide.

For free line of sight planning the wave propagation is considered to be a straight

line. The down-bending of the waves is modeled by multiplying the earth radius

with the k factor.

Earth Bulge

The earth bulge can be calculated in meters by the presented formula.

Included variables are distances in kilometers from the two end points to the point

of interest, d1 and d2, and the k factor.

This diagram will present the approximate earth bulge in meters at mid path for

path lengths of up to 100 kilometers. Please note that both vertical earth bulge

scale and horizontal distance scale are logarithmic. The distance scale

represents the total distance between the two end points.

The red line represents the true earth bulge and the blue line the earth bulge for

the standard atmosphere. At standard atmosphere and up to approximately a

distance of 9 kilometers the earth bulge is less than a meter; a 10 meter earth

bulge is passed at approximately 25 kilometers, and 100 meter at a path length of

approximately 80 kilometers. So for a path length of 80 kilometers, which is quite

long but not in any way unrealistic, the antennas have to be mounted at least 100

meters above ground to have a free radio line of sight between each other. Since

the k factor 1.33 is applied there will not be an optical line of sight at this height.

To get that we would need to climb approximately another 30 meters up to the

red line.

Obstacles

The height of any obstacles in path has to be added to the earth bulge.

The First Fresnel Zone

To transport the radio signal from transmitter to receiver without additional loss it is

necessary to keep a certain zone around the direct line sight free from obstacles.

This ellipsoid shaped zone is called the first Fresnel zone. The basic rule for free line of

sight operation is to keep the zone 100% free from obstacles.

The definition of the 1:st Fresnel zone says that a wave which is reflected once at any

place at the edge of the zone has travelled half a wavelength longer path compared to

the direct signal. Depending on the frequency it has in practice travelled an extra

distance of between a few millimeters and up to a few centimeters.

The radius of the zone can at any point be calculated in meters by the presented

formula. Included variables are the total path length, d, the distances from the two end

points to the point of interest, d1 and d2, and the frequency. So the radius is dependant

on the frequency and the distance. The lower the frequency is and the longer the path

length is the larger is the radius.

The table gives examples of approximate radius of the first Fresnel zone at mid path for

some plausible combinations of frequency and total path length. These figures shall be

added to the earth bulge height and the height of possible obstacles to get the needed

antenna height for free radio line of sight operation. For microwave radio links operating

in low frequency bands over long path lengths where both the earth bulge and the first

Fresnel zone radius are quite large the rule of keeping the first Fresnel zone 100% free

from obstacles sometimes needs to be violated for practical reasons.

Obstacle Loss

So if there is an obstacle intruding into the first Fresnel zone – what loss of signal

strength will it cause?

This depends on the shape of the obstacle and how far into the zone it intrudes.

To estimate the loss some different models are used. For obstacles with a

thickness which is very short compared to the total path length, for example a

single house in a long path, the so called knife edge model can be used. A knifeedge

obstacle will cause an extra loss of approximately 6dB if it reaches up the

direct line of sight. This is a large loss. To compensate for this we would have to

double the antenna size at one end of the hop.

For an obstacle covering the major part of the path, for example the earth bulge

itself the loss will be higher. If such a smooth earth obstruction reaches up to the

direct line of sight it will cause an extra loss of approximately 15dB.

Basic Free Space Loss

The distance related loss which a microwave link on the earth is influenced by

consists of two components; basic free space loss and atmospheric gas

absorption loss.

In the commonly used microwave frequency bands the basic free space loss is

the clearly dominating part.

Basic free space loss is closely related to the radiation pattern of the antenna. It

is basically about over how large area the power is spread. Close to the antenna

the power is spread over a small area and the power per square meter is high. At

a larger distance the power is spread of a larger area and the power per square

meter is consequently less. In addition to this, there is a frequency dependant

part that gives that the power per square meter is further decreased by distance

the higher the frequency gets.

Basic free space loss is not influenced by the atmosphere. It is the same for radio

links in the vacuum of space.

Frequency Dependency

Basic free space loss is calculated according to the formula presented in the slide.

Apart from a constant it only holds the two variables distance and frequency. The

formula will give the basic free space loss for the case that so called isotropic antennas

are used.

Isotropic antenna is an antenna model which is radiating equally in all directions, as a

sphere. Such antennas can actually not be designed, a close correspondence would be

the sun, but not even this is a perfect isotropic antenna. In the formula the power

emitted from the antenna is supposed to be spread over the area of the sphere. When

calculating the actual radio path performance a variable must therefore be included that

describes how much the deployed antennas are focusing the radiation compared to an

isotropic antenna. This parameter is known as antenna gain.

The diagram has basic free space loss on the vertical axis and distance on the

horizontal logarithmic axis.

At 4 gigahertz the isotropic loss is approximately 104 dB at 1 kilometer and increases to

approximately 145 dB at 100 km.

For every time the frequency is doubled the loss will increase by 6dB. In practice this

means that low frequencies are used over long distance while high frequencies are

used over short distance. Depending on local conditions a 4 Gigahertz radio link hop

can reach well over 100 km while a 70/80 Gigahertz hop normally reaches up to just a

very few kilometers.

Loss from Atmospheric Gases

When operating at the surface of the earth gases in the atmosphere must be taken into

consideration.

From a microwave point of view the atmosphere consists of two gases, oxygen and water

vapor.

The logarithmic diagram gives atmospheric loss in dB per kilometer related to the frequency.

This graph is a combination of loss from oxygen and water vapor. Some peaks are of special

interest, the peak at around 20 gigahertz caused by water vapor and the peak from oxygen at

around 50 to 60 gigahertz. The amount of oxygen is constant around the world so frequency

bands around 50 to 60 gigahertz are typically assigned for use at very short distances, often

for free use in unlicensed band because of the very short range.

This diagram gives the maximum water content of the air related to temperature. The higher

the air temperature gets the more water it can hold.

The slide example is for a water vapor content of 7.5 grams of water per cubic meter of air

corresponding to an air humidity of 100% at approximately 12 degrees centigrade. This

amount of water in the air will cause an approximate loss of 0.2dB per kilometer at around 20

Gigahertz.

As the temperature rises the air can hold more water and at a temperature of 35 degrees

centigrade the maximum water content is around 40 gram per cubic meter which will cause a

loss of approximately 1dB per kilometer.

In practical planning situations the maximum water content of the air is estimated based on

statistics related to latitude.

Summary

The course was started by describing the radio signal. It has a certain center

frequency around which the frequency is allowed to vary to create the bandwidth

which is necessary to carry the information.

The radio signal travels with approximately the speed of light. The wave length is

a measurement of how far the signal will travel during one full oscillation.

Depending on the antenna properties the radio signal can be vertically or

horizontally polarized.

The properties of the atmosphere, the radio refractivity and its changes, will

cause the radio signal to bend, commonly slightly downwards. This bending effect

is described by the equivalent earth radius factor, the k factor.

Microwave operation requires free line of sight between transmitter and receiver

antenna. To reach this the curvature of the earth must be taken into account and

a certain zone around the direct line of sight must be free This ellipsoid shaped

zone is called the first Fresnel zone.

The distance related loss to the radio signal depends on two factors. First basic

free space loss which relates to the frequency and to the fact that the radiated

power is spread over a larger and larger area the further away from the

transmitter antenna it gets. The higher the frequency is the higher the loss is.

Secondly the frequency dependant absorption from the atmospheric gases

oxygen and water vapor.