Propagation of Radio Waves

The troposphere is the lowest part of the atmosphere, where all weather phenomena occur. It extends on the poles to about 9 km and on the equator to about 17 km. The troposphere is inhomogeneous and constantly changing. Temperature, pressure, humidity, and precipitation affect the propagation of radio waves. In the troposphere the radio waves attenuate, scatter, refract, and reflect; the amplitude and phase of the received signal may fluctuate randomly due to multipath propagation; the polarization of the wave may change; noise originating from the atmosphere is added to the signal. The ionosphere extends from about 60 km to 1,000 km. It contains plasma, which is gas ionized by the solar ultraviolet and particle radiation.

The free electrons of the ionosphere form a mirror, which reflects the radio waves at frequencies below about 10 MHz. The upper frequency limit of reflection depends on time of day and season, and on solar activity. Also terrain and man-made objects diffract, scatter, and reflect radio waves. At low frequencies the attenuation of the ground waves (waves propagating close to the Earth’s surface) depends on the electrical properties of the ground.

At frequencies above a few gigahertz, the attenuation due to atmospheric absorption and scattering must be taken into account. This attenuation can be divided into two parts: attenuation due to clear air and attenuation due to precipitation (raindrops, hail, and snow flakes) and fog. Attenuation of the clear air is mainly due to resonance states of oxygen (O2 ) and water vapor (H2O) molecules. An energy quantum corresponding to the resonance frequency may change the rotational energy state of a gas molecule. When the molecule absorbs an energy quantum, the molecule is excited to a higher energy state. When it returns back to equilibrium—that is, drops back to the ground state—it radiates the energy difference, but not necessarily at the same frequency because returning to equilibrium may happen in smaller energy steps. Under pressure the molecular emission lines have a wide spectrum. Therefore the energy quantum is lost from the propagating wave, and for the same reason the atmosphere is always noisy at all frequencies

The lowest resonance frequencies of oxygen are 60 GHz and 119 GHz, and those of water vapor are 22, 183, and 325 GHz. The amount of oxygen is always nearly constant, but that of water vapor is highly variable versus time and location. The attenuation constant due to water vapor is directly proportional to the absolute amount of water vapor, which is a function of temperature and humidity. Figure 10.2 presents the clear air attenuation versus frequency. Between the resonance frequencies there are so-called spectral windows centered at frequencies 35, 95, 140, and 220 GHz. At resonance frequencies the attenuation may be tens of decibels per kilometer. These frequencies are, however, suitable for intersatellite links, for short terrestrial links, and for WLANs.

The refraction index n = √e r of the troposphere fluctuates over time and location. In normal conditions the refraction index decreases monotonically versus altitude, because the air density decreases. Because a phenomenon of this kind is a weak function of altitude, it causes slow bending of the ray. Fast changes in the refraction index cause scattering and reflections. Turbulence, where temperature or humidity differs strongly from those of the surroundings, gives rise to scattering. Reflections are caused by horizontal boundaries in the atmosphere due to weather phenomena.

In an LOS path the receiving antenna is above the radio horizon of the transmitting station. Links between two satellites and between an earth station and a satellite are LOS paths, and a path between two terrestrial stations may be such. In the two latter cases the tropospheric effects discussed previously must be taken into account. According to the ray theory, it is enough that just a ray can propagate unhindered from the transmitting antenna to the receiving antenna. In reality a radio wave requires much more space in order to propagate without extra loss.

Figure 10.8 shows the extra attenuation due to a knife-edge obstacle in the first Fresnel ellipsoid. According to the ray theory, an obstacle hindering the ray causes an infinite attenuation, and an obstacle just below the ray does not have any effect on the attenuation. However, the result shown in Figure 10.8 is reality and is better explained by Huygens’ principle: Every point of the wavefront above the obstacle is a source point of a new spherical wave. This explains diffraction (or bending) of the wave due to an obstacle.

 Diffraction also helps the wave to propagate behind the obstacle to a space, which is not seen from the original point of transmission. When the knifeedge obstacle is just on the LOS path (h = 0), it causes an extra attenuation of 6 dB. When the obstacle reaches just to the lower boundary of the first Fresnel ellipsoid, the wave arriving at the receiving point may be even stronger than that in a fully obstacle-free case. If there is a hill in the propagation path that cannot be considered a knife-edge, extra attenuation is even higher than in case of a knife-edge obstacle.

Taking K = 4/3 we get from (10.13) that the radio horizon of the antennas is in the middle point of the path between the antennas, when hH = 36.8m. By introducing l = 0.03m and r 1 = r 2 = 25 km into (10.12) we get the radius of the first Fresnel ellipsoid in the middle point as hF = 19.4m. The antenna heights must be then at least h = hH + hF = 56.2m. In addition, if there are woods in the path, the height of the trees must be taken into account.

At low frequencies, fulfillment of the requirement of leaving the first Fresnel ellipsoid empty is difficult. Often we must compromise. For example, at 100 MHz in the 50-km hop of the example, the maximum radius of the first Fresnel ellipsoid is 194m. A radio-link hop design is aided by using a profile diagram of the terrain, which takes into account the bending of the radio ray in standard conditions. In the diagram, the height scale is much larger than the horizontal scale, and the terrain along the hop is drawn so that perpendicular directions against the Earth’s surface are parallel. The middle point of the hop is placed in the middle of the diagram. After drawing the terrain, the antenna heights are selected so that the first Fresnel ellipsoid is fully in free space, if possible. Figure 10.9 presents a profile diagram between Korppoo and Turku in the Finnish archipelago.

In an LOS path, the receiving antenna often receives, besides a direct wave, waves that are reflected from the ground or from obstacles such as buildings. This is called multipath propagation.

Let us consider a simple situation, where there is a flat, smooth ground surface between the transmitting and receiving antenna masts, which are located so that their distance is d, and the distance between the transmitting and receiving points is r 0 , as presented in Figure 10.10. In practice this situation may be quite typical in VHF and UHF radio broadcasting, where an antenna mast with a height h1 is at the broadcasting station. Let us further assume that the transmitting antenna radiates isotropically. The electric field strength due to the direct wave at the distance r 0 from the transmitter is E0 .

The actual radiation pattern corresponds to that of the array formed by the transmitting antenna and its mirror image. The electric field strength E varies as a function of distance between values 0 and 2E0 , as shown in Figure 10.11(a). Note that E0 decreases as 1/d. The nulls of the field strength (maxima for vertical polarization in case of an ideal conducting surface) are at heights h2 ≈ nld/(2h1 ), where n = 0, 1, 2, . . . , as shown in Figure 10.11(b). The receiving antenna height must be selected correctly. In order to reduce the effects of reflections, it is possible to use a transmitting antenna that has radiation nulls at directions of the reflection points. Also, a forest at the theoretical reflection points helps because it effectively eliminates reflections.

Figure 10.11 presents the field strength as a function of distance when a strong reflected wave interferes with an LOS wave. As the receiver moves away from the transmitter, the signal fades wherever the two waves are in opposite phase. In mobile radio systems, the situation is generally much more complex due to the multipath propagation .

We can categorize fading phenomena in many ways. Prominent obstacles between the transmitter and receiver cause large-scale fading. Because of this, the path loss increases rapidly over distance and is log-normally distributed about the mean value. Small-scale fading refers to signal amplitude and phase variations due to small changes (order of a wavelength) in position. Interference of several waves—multipath propagation—causes this type of fading. Because of the multipath propagation the signal spreads in time (dispersion) and the channel is time-variant due to the motion of the mobile unit. Both phenomena degrade the performance of the system. Depending on the effect of dispersion, we categorize fading either as frequency-selective or flat. If the radio channel is frequency-selective over the signal bandwidth, intersymbol interference (ISI) will degrade the performance. In the case of flat fading all signal components fade equally. According to the rapidity of changes in the time-variant channel, we categorize fading as fast or slow.

 Inhomogeneities of the atmosphere cause scattering. Scattering means that part of the coherent plane wave is transformed into incoherent form and will radiate into a large solid angle. Normally, scattering will weaken the radio link by attenuating the signal. However, the scattered field may also be useful: A scatter link takes advantage of scattering.

Let us first consider scattering by a single object or particle. The scattering cross section s of an object to a given direction describes the effective area of the object when it is illuminated by a plane wave. The power intercepted by this area, when scattered equally in all directions, produces the same power density as the object. The scattering cross section also depends on the direction of the incident wave and its polarization. Figure 10.13 shows how the scattering cross section of a conducting (metal) sphere behaves as a function of frequency, when the direction of incidence and the direction of observation are the same. The scattering cross section of a small (in comparison to a wavelength), metallic sphere (or of an object of another shape) is proportional to f 4 (Rayleigh scattering). The scattering cross section s of a large (in comparison to a wavelength) sphere is equal to its geometric cross section sg . This is called the optical region. Between these regions there is a resonance region (Mie scattering).

 Because the relative permittivity e r of water is large, the curve in Figure 10.13 also describes the scattering of a raindrop. The total scattering cross section ss multiplied by the power density of the incident wave gives the total power scattered by the object into the solid angle of 4p. The total scattering cross section ss of a large object is 2sg .