Wireless Data Technologies

Transmission Impairments

When transmitting radio signals between two points, there are various factors that affect how far the signal can travel before it becomes too weak to be detected. Knowledge of the mathematics behind this will enable calculations to be made to determine coverage of a certain antenna's design. This lecture will examine some of those factors to help in the design of a wireless system.

Transmitter Patterns
Fresnel zone
System Operating Margin
Transmitter Patterns
Isotropic Antennae
Antenna Gain - Directionality
Gain Figures dBd or dBi?
Example 1
Freespace Loss
Antenna Gain
Effective Isotropic Radiated Power
Receiver Sensitivity
Example 2
2.4 GHz Concerns

Fresnel Zone
The Fresnel (pronounced Frennel) zone is a 3-dimensional area that exists around the LOS (line of sight) of a transmitted radio signal. Its shape is similar to a rugby ball (or American football), i.e. it is narrower near the transmitter, reaches a maximum halfway between the transmitter and receiver and diminishes once more near the receiver.

Any objects that lie within the Fresnel zone, e.g. buildings, trees, ground, water, will degrade the transmitted signal. The following table shows the losses experienced by signals that lie within mobile telephone frequencies. Notice that the maximum diameter of the Fresnel zone varies with distance between the antennae and also diminishes as the frequency rises. In any practical system, a minimum of 60% clear Fresnel 1st Zone is acceptable, but the losses will be high, therefore the transmitter power will need to be raised or the receiver sensitivity must be increased or alternatively the path between the TX and RX antennae must be decreased.

An alternative is to raise the antennae even higher and clear the Fresnel zone further.

900 MHz
2.4 GHz
Distance between antennae
Fresnel zone diameter
Freespace loss (dB)
Fresnel zone diameter
Freespace loss (dB)
1000 ft (300 m)
16 ft (7 m)
11 ft (5.4 m)
1 Mile (1.6 km)
32 ft (12 m)
21 ft (8.4 m)
5 miles (8 km)
68 ft (23 m)
43 ft (15.2 m)
10 miles (16 km)
95 ft (31 m)
59 ft (20 m)
20 miles (32 km)
138 ft (42 m)
87 ft (27 m)
40 miles (64 km)
192 ft (59 m)
118 ft (36 m)

In order for successful transmission to take place, there must be no objects within the Fresnel zone, including the ground. Therefore the antenna height must be such that the Fresnel zone does not touch the ground. Examination of the chart above shows that as the transmitted distance increases, the height of the antennae must increase too, to keep the Fresnel zone clear of the ground or other obstructions.
Courtesy of
Incorrect installation, the trees obstruct the line of sight. The received signal will be severely attenuated.

Courtesy of
Incorrect Installation, the first Fresnel zone is partially obscured. The received signal will suffer attenuation.

Courtesy of
Correct installation. The first Fresnel zone clears the trees.
*Images courtesy of http://www.radiolan.hu

It is important to notice that there are many Fresnel zones, each of which is an integer e.g. 1st Fresnel zone, 2nd Fresnel zone, 3rd ....etc. etc

In this lecture, we are primarily concerned with the 1st Fresnel zone and therefore N in the equation below will be set to 1.

(For those of you who understand music, the Fresnel zones are harmonics of the fundamental)

If you want to calculate radius of the Fresnel zone, use the following equation:

The Nth Fresnel zone radius (FN) is a function of the wavelength (l ) and the distance along the path from each endpoint (D1 and D2):

For an instructive exercise, calculate the 1st Fresnel zone radius and hence the diameter for 5.8 GHz for the distances in the table above. Note that the maximum Fresnel zone diameter is 1/2 way between transmitter and receiver i.e. when D1 = D2.

You can also use a free Java calculator to work out these values. There are various online resources to help in calculating the size of the Fresnel zone - see http://www.afar.net/fresnel-zone-calculator/

A screenshot of a Fresnel calculator is shown below. You may care to create something similar in Java (or other suitable language) using the formula above. Note that the calculator shown below takes into account the curvature of the Earth.

System Operating Margin
For a wireless link to operate, the available system operating margin (SOM) must be larger than the Freespace loss and any other losses in the system.

The system operating margin is: Transmitted power
+ Antenna gain - Receiver sensitivity

The units here will be dBm for power and sensitivity and dBi for antenna gain.

Note: Transmitted power + Antenna Gain = EIRP

Transmitter Patterns
When a radio signal is transmitted, there is a certain pattern produced. In the real world, the simplest of transmitters is called a dipole. This is a simple design, the most common being the 1/2 wave dipole. As its name suggests it is 1/2 a wavelength long (the real world dictates that it is around 0.96 to 0.98 times 1/2 wavelength, owing to the ratio between the diameter of the antenna compared to its length). 

Therefore this leads to the important conclusion that a particular antenna must be designed to be a certain length to operate at a given frequency/wavalength.

In its simplest form, a 1/2 wave dipole transmitter can be two pieces of straight wire, as shown below.

The required signal is input to the feeder and the horizontal arms of the dipole are the transmitting elements. Often the feeder will be coaxial cable as this does not act as a transmitter due to the shielding. When the antenna is connected to a signal, the pattern of radio wave power produced by the dipole is similar to that of a doughnut (toroid) as shown below.

mmmmm, doughnuts
This means that no power is transmitted in the line of the dipole itself. All power is radiated perpendicular to the dipole itself. This type of transmitter radiates power equally in a 360o arc around the dipole. This type of antenna is used as a reference for all other antennae and is given a gain of 0dB. Antennae that are compared against a dipole antenna are given gain figures expressed in dBd. A particular antenna (not a dipole) may perhaps appear in a manufacturer's specification as having a gain of 5.5 dBd. This means that its gain is 5.5 dB greater than a dipole.

However, since construction methods and materials for this type of antenna will vary, so the actual performance of one dipole will differ from another. This makes exact performance figures difficult to achieve. A more uniform approach to compare antenna gain is to refer to a theoretical antenna known as an isotropic antenna.

Isotropic Antenna
This is an imaginary type of antenna which has a theoretical pattern which is a perfect sphere around the transmitter. Bear in mind that such an aerial does not exist, but is very often used for comparison purposes when looking at the gain of a real-world aerial.

Sometimes antennae gain figures in specification sheets are referenced to the isotropic antenna and in this case the figure is given as dBi, the gain referenced to the gain of our imaginary isotropic antenna. If we now compare a dipole to an isotropic antenna, the dipole will have a gain of (approx) 2.15 dB. We would now be able to say that the gain of a dipole antenna is 2.15 dBi.

This can make the gain from an antenna's data sheet seem a lot greater than if it is referenced to a dipole antenna, giving a 2.15dB gain!

Gain Figures dBd or dBi?
Some manufacturers express antenna gain in dBd, some in dBi, some just state dB.

This can be confusing since 2.15dBi = 0 dBd

Be sure that the manufacturer's figure is either dBd or dBi. If the seller can't tell you, don't trust them!!

Antenna Gain - Directionality
If we have a particular antenna characteristic that we want to exploit, e.g. the sectored transmitters used in mobile telephony, we want the power to be radiated in a narrow beam rather than in a 360o arc. By shaping the antenna to meet these characteristics, the power is radiated as we want it and does not transmit (very much) in the other directions. To view beam patterns simulated by software, see http://www.borg.com/~warrend/guru.html (no longer available).

The typical horizontal beam widths of commercially available antennae are 30o, 65o
90 and 120o. Specifications for some of these are available at http://www.antennaall.com/ (no longer available).

If we want to transmit in a 360o arc, we might choose the 30o flat panel base station antenna. We will need 360
o/ 30 = 12 of these to achieve 360o coverage.

A pdf document giving specifications of the antennae used at 2.4 GHz can be found at http://www.stelladoradus.com/pdfs/2.4Base/12008%20Patch%202.4GHz%20(17-10-05).pdf

Other documents from the same manufacturer can be found at http://www.stelladoradus.com/2.4.ghz.base.station.antennas.php

This manufacturer offers products in the 1.8 and 5.8 GHz bands too.

Another directional antenna is the Yagi-Uda array.

The dBm is a useful measurement for power in radio systems. One dBm 
indicates dB referenced to 1.0 milliwatt. 1 milliwatt is 0 dBm. This allows exact power measurements to be made rather than the relative power measurements offered by the ordinary dB.

Sometimes you may see dBW, this is power referenced to 1 watt. Since this is 1000 times greater than 1 milliwatt, we can calculate the difference between dBm and dBW

dB = 10 log10 (Pout/Pin)

10 log10 (1000/1)

= 10 x 3


Therefore to convert between dbW and dBm, add 30 to the dBW figure.

Example (note correction to figures 21/11/07)
A certain set of hardware that operates at 900 MHz has the following characteristics:
According to the equation above, the system operating margin is 21.8 - (-105) + 4.3 = 131.1 dBm

Note that receiver sensitivity (RX) is an indication of the lowest power that a receiver can decode a packet without errors.

Now we need to refer to the table above to check what the freespace dB loss figures are to see how far we could transmit. Remember to look at the 900 MHz column!

So long as our system operating margin (131 dBm) exceeds the freespace loss, we can transmit that distance. It is easy to see that we could potentially transmit 40 miles as the freespace loss is 128 dB (leaving 3dB over). The limiting function here would be that the towers would need to be high enough to prevent the 1st Fresnel zone from touching the ground, so our towers would need to be high enough to prevent anything getting within the 1st Fresnel zone. At 40 miles, the curvature of the Earth would need to be factored in here too.  In a real-life situation, there are other factors that will reduce our transmission power, so a healthy margin of 10 to 20dB should be allowed for.

According to the table, a little under 5 miles would be the SAFE distance that our link should run. This gives a 18 dB margin and our receiver should be able to pick up transmissions in all circumstances.

Note that there will also be losses associated with the coaxial cabling between the transmitter amplifier and the antenna and also at the receiving end between the antenna and the receiver amplifier. These losses will be in the order of 1dB each end, rising as the length of the coaxial cable increases.

Freespace Loss
This is the loss of power as a signal travels from transmitter to receiver. It can be calculated using the following formula

FSL (dB) = 36.6 + 20 log D + 20 log f

Note that D is the distance between TX and RX in MILES
f is the frequency in MHz

WARNING: If you do not use these units, you will get the wrong result.

Antenna Gain
Various antenna designs appear to give high gains when compared to a dipole. This is not power for nothing. What we are doing is taking the power that is transmitted and shaping the transmitted beam so that it is no longer a doughnut (toroidal). By making the beam more directional, we are concentrating the power that was originally radiated in 360o into a tighter beam. The beam edges are defined by the 3dB point where the power drops to 1/2 of that at the centre. It may be easier to think of the antenna as a lens that has the ability to focus radio waves.

Common antennae types  and their corresponding gains are shown in the table below.
Type Typical Gain Range (dBd) Typical Gain Range dBi
Dipole 0 2.15
Omni 0 2.15
Gain Omni 3 to 12 5.15 to 14.15
Mobile Whips -0.6 to +5.5 1.55 to 7.65
Corner Reflector 4 to 10 5.15 to 12.15
Log Periodic 3 to 8 5.15 to 10.15
Horn 5 to 12 7.15 to 14.15
Helix 5 to 15 7.15 to 17.15
Microstrip-Patch 3 to 15 5.15 to 17.15
Yagi 3 to 20 5.15 to 22.15
Panel 5 to 20 7.15 to 22.15
Parabolic Dish 10 to 30 12.15 to 32.15

Effective Isotropic Radiated Power
The EIRP is the power radiated by the antenna in the centre of the beam lobe. It is calculated by adding the transmitter amplifier power to the antenna gain and taking into account any loss associated with the cable between amplifier and antenna.

Receiver Sensitivity
Typical receiver sensitivity for a mobile handset can range between -80 dBm and -160 dBm.

Example 2
A  mobile base station amplifier transmits at 300 mW. There are a total of 1.5 dB losses between the amplifier and the antenna. The antenna gain is 12 dBi. The mobile handset has a receiver sensitivity of -105 dBm. The system runs at 2.4 GHz. Can this system transmit under all conditions at a distance of 10 miles?

Convert 300 mW to dBm

10 log10 (300/1) =  24.8 dBm

EIRP = 24.8 -1.5 +12 = 35.3 dBm

The system operating margin (SOM) is: Transmitted power - Receiver sensitivity

SOM = 35.3 - (-105) = 140.3 dBm

We need to allow for around 20dB for losses in the transmission of the radio signal

SOM = 140.3 - 20 = 120.3 dBm

Now refer to the table above.

Freespace loss at 10 miles is 124 dB. we cannot guarantee error free operation at this distance. There is a chance that the signals will be received at this distance under good conditions, but no guarantee that this will operate 365/24/7.

Manipulation of the freespace equation will allow a guaranteed distance to be calculated.

2.4 GHz Concerns
At 2.4 GHz, the frequency is able to make water molecules vibrate and therefore absorb signal energy. The microwave oven operates at 2.4 GHz and heats our food by making the water molecules vibrate and absorb the energy of the microwaves.

Now that we know this, it is easy to understand why our mobile phone, Bluetooth and 802.11b/g (all in the 2.4 GHz band) signals travel quite easily through a brick wall, which is dry, but will be heavily attenuated by a tree (containing water), rain or fog. Because humans are largely made of water, it is also easy to see why there are concerns over human safety when using wireless devices.

The Fresnel zone is a 3-D region around a radio signal. If any obstructions fall within the 1st Fresnel zone, the signal will undergo significant attenuation. The simplest antenna is the dipole, but a theoretical isotropic antenna is often used as a reference for all other antennae. The dipole antenna has a 2.15 dB gain over the isotropic antenna. Gains are measured in dBi for the isotropic antenna. The gain of an antenna is a measure of the directionality of that particular antenna and shows how directional the antenna is. Freespace loss is a function of frequency and distance between transmitter and receiver.

http://www.maxstream.net (no longer available).






Useful Links

http://www.aurimpex.com/dtra900.html (no longer available).



MMClements 2007

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