# Wireless Networking Fundamentals

02

## Radio signal propagation fundamentals

account course progress

### Fresnel Zone

Most of the energy of the electromagnetic wave is concentrated in the ellipsoid of rotation, the axis of which is the straight line connecting the receiving and transmitting antennas. This area is called the first Fresnel zone and is shown in Figure 1. There are several Fresnel zones forming in section concentric circles of different diameters. In following text only the first Fresnel zone will be considered, since most of the signal energy is concentrated in it. Usually, overlapping of the Fresnel zone by external objects by 20-40% is not a significant obstacle to wave propagation, however, it is necessary to aim to minimize overlapping.

Figure 1 Fresnel zone

To calculate first Fresnel zone the value of it's radius must be used if it is known it is possible to determine the presence of obstacles in the Fresnel zone:

Figure 2 The calculation of Fresnel zone radius

The value of the Fresnel zone radius at an arbitrary point is calculated by the formula:

There are three cases of a Fresnel zone overlapping:

• Line of sight (LOS) - the overlap of the Fresnel zone does not exceed 40%, is shown in Figure 1;
• Near line of sight (nLOS) - the overlap of the Fresnel zone is 40-60%, is shown in Figure 2;
• Non line of sight (NLOS) - the overlap of the Fresnel zone exceed 60%, is shown in Figure 3.

Figure 3 Fresnel zone in case of non line of sight

Under nLOS conditions part of the signal due to physical obstructions will not reach the receiver, as a result the signal level will be lower than with LOS. Thus, nLOS sets restrictions on the maximum distance of the wireless link in comparison with the propagation of the signal under LOS conditions. Besides that, as it will be shown in following lessons (see Analog and digital signals. Modulation), the signal level indirectly affects using of manipulation scheme and the data rate. The establishing of the link in condition of NLOS is possible due to such characteristics of wave propagation as reflection, scattering and diffraction, which highly reduce the level of signal on the receiving side. Thus, when designing and implementing projects using wireless communication channels it is necessary to aim to the LOS conditions.

### Characteristics of electromagnetic wave propagation

In the wireless link establishment it is necessary to take into account a number of effects that will appear depending on specific factors. For example, the location used: the propagation of a radio signal in conditions of dense urban development and forest will differ. Weather conditions also have an influence on propagation of the signal.

#### Attenuation in free-space

The process of propagation of an electromagnetic wave in free space leads to the effect of link energy reduction, due to the propagated radio signal amplitude decreasing. To make a precise calculation of the attenuation a lot of parameters must be taken into account for example, the attenuation coefficient, which depends on the propagation medium and weather conditions, however to make rough estimation we can use the following expression:

This formula shows the relationship between the attenuation and the frequency of the signal, thus the higher the frequency of the electromagnetic wave the faster it fades out while propagating in free-space. It means with all else being equal the operation of the communication system at low frequencies will allow to reach a larger distance than at high frequencies, or better energy values, at equal distances. But as it is shown in section

Antennas using of low frequencies will require using of antennas with large dimensions.

Practical results indicate that the frequency and number of losses in free-space have a logarithmic dependence with deviations for some frequency ranges. For example, a radio signal with a 60 GHz frequency attenuates faster than signals of adjacent frequencies.

In one of the following lessons the example of link budget calculation will be reviewed (see Link budget).

#### Diffraction

Signal propagation in non line of sight conditions allows to establish the connection due to the diffraction effect, in other words due to signal is getting round an obstacle. The diffraction effect is demonstrated in Figure 4:

Figure 4 The diffraction effect in radio wave propagation

The Fresnel zone between the receiver and the transmitter is blocked by the structure, however the radio signal from the transmitter gets round the corner of the building and reaches the receiver. Note, the signal strength will be scattered in the medium because of diffraction, it will lead to decreasing of distance in compare with LOS condition.

#### Absorption

In case the signal does not reflect when meet an obstacle, does not go around or through it, then such a signal is considered as absorbed. Different materials absorb the radio signal differently: brick and concrete walls absorb the signal well enough, while the drywall not so good. Absorption is a result of a significant attenuation of the signal. Thus, the amplitude of the current at the receiver's antenna depends on which part of the transmitted power was absorbed.

#### Reflection

If the radio signal mets a barrier, which in size exceeds the wavelength, the effect of the wave reflection is appear. This effect can be used in the organization of communication in non line of sight conditions.

Figure 5 Reflection effect in the wave propagation

#### Scattering

The specific case of reflection is scattering it works in the opposite way to absorption: if the obstacle on the propagation path is less than the wavelength, then the electromagnetic wave is reflected from this object in all directions. An example of such effect is the propagation of a signal in rainy weather or through a coniferous forest.

Figure 6 Scattering effect in the wave propagation

#### Multipath effect

In dense urban development, the reflection effect during the propagation may appear many times, it leads to receiving several copies of the signal that have come along different paths, as it is shown in Figure 7. This effect is called multipath.

Figure 7 Multipath effect in the wave propagation

Note, the reflected signal can differ from the original by its parameters: amplitude, frequency, phase and polarization. In addition, each copy of the signal received has had a different path and spent a different time, that negatively affects the signal delay. In the Figure 8 red and green lines show copies of the signal on the receiving side phase shifted due to different propagation times, the blue shows the resulting signal. In first case - Figure 8(a), the phase shift of the signals is 0-120 degrees so the resulting amplitude signal exceeds each of the received copies, in the second case shift is 121-179 degrees, Figure 8(b), amplitude of the resulting signal below the received copies, in the third case, Figure 8(c), the received copies are in antiphase and the resulting signal is zero.

Figure 8 Oscillograms of resulting signal after multipath propagation, a - the phase shift is 0-120 degrees, b - the phase shift is 121-179 degrees, c - the phase shift is 180 degrees

Figure 8 demonstrates the resulting signal in case then multipath consists of two version of signal. More often in dense development greater amount of signal copies reach the receiver it leads to deformation of the resulting signal, as it is demonstrated in Figure 9:

Figure 9 Oscillograms of resulting signal after multipath propagation: a - signals at the output of the receiver, b - resulting signal

#### Refraction

When building wireless links over long distances, keep in mind the curvature of the Earth's surface, which can be neglected at short distances. The solution of this problem is to increase the height of the antenna suspension, as it is shown in Figure 10:

Figure 10 NLOS due to the curvature of the Earth's surface

Such problems can be solved by using the effect of refraction, the wave is reflected from the dense layers of the atmosphere, it allows to establish wireless conection over long distances in non line of sight conditions. The disadvantage of refraction is limitation of using - the effects appears only in systems using the short-wave part of the spectrum - from 25 to 30 MHz.

The refraction effect consists in changing of the direction of a wave propagation on the border of two media or in one inhomogeneous medium in which a wave propagation speed differs. The troposphere is a layered structure, each layer of which has its own permittivity index ε, which affects the propagation speed of a radio signal, therefore the troposphere is a medium there refraction appears. The nature of the refraction effect depends on the time of day, season and weather conditions.

Figure 11 Refraction effect in the wave propagation