Radio Wave Propagation

Radio waves propagation shows different behaviors depending on the physical properties and the shape of the propagation medium. The following sequel gives a brief introduction.

Radio waves can reach to the receiver antenna through a direct path with a loss due to distance. If there is a close obstruction to the path, then a diffracted wave is received from the obstruction with an additional attenuation. A hill or building is an obstruction if it lies within the Fresnel zone around line of sight. If receiver antenna is within the shadowed region of the obstruction, then the direct path component can not be a part of the received signal. It is only due to diffracted signals from the obstruction.

Diffraction is not limited to the upper surface of the obstructions. Radio waves can be diffracted around the vertical edge of obstructions as well. The reflected radio waves from ground and large surfaces with small roughness (if compared to wavelength) can constitute the second strong component of the received signal. If roughness of these surfaces is high, then scattering can be observed. That is, radio signals are scattered to large range of different directions with small field strength. These, diffraction from vertical edges, reflections and scattering cause indirect paths.

If the characteristics of medium change in time, then received signal's phase and amplitude changes in time. For example, if a receiver is a mobile and moving through a street, the propagation characteristics of the signal changes in time, and so does the received signal.

From the signal domains, the effects of all these phenomena can be classified into two groups: fading in frequency domain and fading in time domain. By the duality of frequency and time, the former is considered a modulation in frequency domain, and so causes the energy distribution over time. The latter is considered as modulation in time domain, and therefore causes the energy distribution over frequency. Multipath corresponds to different received signal components reaching to the receiver antenna in different paths and so with different time delays. Hence, the power of the received signal is distributed in time. This causes fading in frequency domain. Some part of the signal band can be suppressed. Therefore, this phenomenon is also called distortion in frequency domain. That is, the frequency spectrum of the received signal is distorted.

The characteristics of the multipath can change in a distance of one fourth of the wavelength. The wavelength of the radio waves in UHF band is in the range of 0.1m to 1m. If a mobile is moving at 60km/h and frequency is 800MHz, than it takes only 6.75ms to move one forth of the wavelength. Therefore, multipath fading is also called as fast fading.

On the other hand, if the propagation medium properties change in time, the amplitude and phase of the some components of received signal change in time. This corresponds to modulation with the time varying characteristics of the medium. Therefore, this phenomenon can be explained as distortion in time.
The main contribution to the received signal in a shadowed region comes from the diffraction of radio waves over nearby obstructions. The amplitude of the received signals within the shadowed region of an obstruction changes with the height of the obstruction. This is called as shadow fading.

In addition, a mobile moving through a street is subject to different shadow fading due to the buildings with different heights. If the average of blocks is 50m, and speed of a vehicle is 50km/h,  then the change of shadow fading takes about 3.6s. Therefore, shadow fading for a mobile is sometimes called as slow fading.

As a side note, in general sense, the distinguishing multipath and shadow fading as fast and slow fading causes conflicts.

The effects of fading in time and frequency are dependent on the signal bandwidth and modulation. For example, assume a digital communication system with symbol duration T. Let D be the time delay between the first and second strong multipath components. If D is too smaller than T, then fading in frequency will occur out of its bandwidth and the sum of the multipath components are closely processed as a unique single component. In other word, no significant distortion in frequency occurs.

A city can be divided into some zones such as low density building area, city center or forest. The morphology (form and structure)  of these zones differs considerably from each other. The average building height, the density of trees, the width of streets, the distribution of buildings are some morphological properties. These properties strongly affect the propagation of radio waves. In other words, the propagation of radio waves also shows strong differences from one area to another if their morphological properties are different.

Roughness affects the field strength of reflected radio waves from ground. If roughness is large, then the reflected signal strength becomes lower. On the other hand, if roughness is small, then reflection becomes stronger. A general definition of roughness for a zone is the standard deviation of the distribution of elevations in that zone. An alternative definition is based on the distribution statistics: Let 10% and 90% of the heights in a zone be less than or equal to X and Y, respectively. Then, the roughness of the area is defined to be the difference Y - X.

There are two other factors that impact the propagation: Average building height and clearance distance in a zone.

It is a reasonable approximation to suppose that the radio waves propagates like a plane wave in the far region of the transmitter antenna. Figure 1 shows an example case. The building height is h. If the receiver antenna is at Point A and it is sufficiently above the building, then the field strength at that point can be directly calculated as in free space. Point B is at the height of h. Radio waves up to height h are blocked by the building. Hence, the field strength at B will be lower than the field strength at A. The field strength at C depends to the diffraction, and it is a function of the distance from top r, and the clearance from the building d.

Figure 1

 An example case on diffraction loss is give in Figure 2 and Figure 3 below at 900 MHz. Four curves shown in Figure 3 correspons to four clearance distances. Figure 4 shows a typical example case with double and single  diffraction situations. We can replace buildings with dense trees, and we expect the similar behavior.

Figure 2

Figure 3

Figure 4

Another phenomenon in propagation is back-scattering. It occurs when the radio waves hit a surface against the propagation direction. A typical case can be observed in valleys as shown in Figure 5 below. The diffracted signals on the left top can reach to the side sufficiently strong due to enough clearance, and the scattered waves from right side, can increase the signal level on the left side more than a few dB.

Figure 5

The contributions to the received signal in high density long building zones are more complicated. Figure 6 shows an example case. The received signal is a result of the diffracted signals from the top and side of the left building. The reflections and scattering from the right building also have a contribution in the received signal.

Figure 6

Indoor propagation is impacted due to penetration loss, and narrow clearances. If the frequency is high, the absorption loss increases, tables and other small objects can constitute high roughness relative to the wavelength.

References

1. Bertoni H.L., Radio Propagation for Modern Wireless Systems,  Prentice Hall, New Jersey, 2000.
2. J. H. Whitteker, “The CRC VHF/UHF Propagation Prediction Program”, Beyond Line of Sight Conference, Texas, 1994.
3. Dolukhanov M., Propagation of Radio waves, Mir Publishers, Moscow 1971.