Propagation of Radio Waves

248 Radio Engineering for Wireless Communication and Sensor Applications

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.

Radio waves can propagate from one point to another in many ways. The most important mechanisms of propagation used in radio systems are, in order of decreasing frequency, the following:

1.Propagation along a line-of-sight (LOS) path. This resembles the propagation in free space. Because of refraction, the radio horizon is farther away than the geometrical horizon. In UHF, SHF, and EHF bands most radio systems require an LOS path. From the millimeter-wave band to infrared, the radio link hops are short because of attenuation due to precipitation and gas molecules. In VHF and UHF bands multipath propagation is common: The LOS path may be complemented or interfered by diffraction and reflection from buildings and ground as well as by propagation through vegetation and building walls.

2.Scattering from inhomogeneities of the atmosphere. The applicable frequency range is from 300 MHz to 10 GHz.

3.Propagation via the ionosphere. A radio wave may reflect from the ionosphere at frequencies below 30 MHz. A wave may also reflect multiple times between the ionosphere and ground, and thus propagate round the globe.

4.Ground-wave propagation. The attenuation of the ground wave increases rapidly versus frequency; this phenomenon is important at frequencies below 10 MHz.

Figure 10.1 illustrates different propagation mechanisms. In a given radio link, the waves may propagate through several different mechanisms. In long hops, a ground wave is dominating up to 150 kHz, and the ionospheric wave in the frequency range of 1.5 MHz to 30 MHz, depending on the state of the ionosphere. At frequencies from 150 kHz to 1,500 kHz both mechanisms are equally important. As it does in VHF and UHF bands, the wave propagates through several paths, but now the reason is diffraction and reflection from buildings and ground. Due to the interference of waves

Figure 10.1 Propagation mechanisms of radio waves (numbers refer to different mechanisms described in text).

propagating via different routes, the power level of the received signal may alternate considerably over time and location (fast fading).

Propagation beyond the radio horizon is also possible due to tropospheric reflections at frequencies from 30 MHz to 1,000 MHz, and due to ducting at frequencies above 1 GHz. These propagation mechanisms are, however, so unreliable, that one cannot build a continuous radio path based on them. On the contrary, they cause interference to other radio links in the same frequency band.

In general, the available power received cannot be accurately predicted. The signal power level may alternate several tens of decibels in a given radio path. In order to reach a high reliability in a radio system, one must know the statistical distribution of the link attenuation and design the antenna sizes and power of transmission accordingly.

10.2 Tropospheric Attenuation

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

250 Radio Engineering for Wireless Communication and Sensor Applications

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.

Figure 10.3 presents attenuation due to rain and fog. Attenuation of rain is mainly due to scattering: The electric field of the radio wave polarizes

Figure 10.2 Attenuation in clear atmosphere versus frequency. Curve A: at sea level (T = 20°C, water vapor density 7.5 g/m3 ). Curve B: at altitude of 4 km (T = 0°C, water vapor density 1 g/m3 ).

Figure 10.3 Attenuation due to rain and fog.

the water molecules of the raindrop, and then the raindrop acts like a small electric dipole radiating over a large solid angle. A heavy rain makes long radio hops impossible at frequencies above 10 GHz. In a moderate rain (5 mm/hr) attenuation is 0.08 dB/km at 10 GHz and 3 dB/km at 100 GHz. In a pouring rain (150 mm/hr) these values are about tenfold, but on the other hand the time percentage of such strong rains is small. In a heavy rain the drops are large and their shape is ellipsoidal. Then a horizontally polarized wave attenuates more than a vertically polarized wave. This phenomenon, depending on the wind speed, also causes depolarization of the wave, if the electric field is not along either axis of the raindrop. Depolarization results in unwanted coupling between orthogonally polarized channels and an extra loss in reception because the receiving antenna can accept only that polarization for which it is designed. The attenuation constant due to fog and clouds is nearly directly proportional to the amount of water.

Both real and imaginary parts of the dielectric constant of ice are clearly smaller than those of water. Therefore, attenuation due to dry snow is low. Wet snow causes more attenuation, and its attenuation is directly proportional to the amount of water.

Turbulence in the troposphere may cause also scintillation, that is, random changes in amplitude and phase of the wave as it propagates via different routes due to turbulence (refractive index may vary strongly over short distances). Atmospheric propagation phenomena were the subject of

252 Radio Engineering for Wireless Communication and Sensor Applications

many studies at Helsinki University of Technology in the 1990s; some examples of the results are presented in [1–4].

10.3 Bending (Refraction) of Radio Waves in Troposphere

The refraction index n = √er 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.

Because n is always close to unity, we often use the so-called refractivity N, which is the difference of the refraction index value from unity in parts per million:

where T is the absolute temperature, p is the barometric pressure (unit mb = hPa), e is the partial pressure of water vapor (mb), and R is the relative humidity. The error of (10.2) is less than 0.5%, if f < 30 GHz, p = 200–1,100 mb, T = 240–310K, and e < 30 mb. If there is no resonance frequency of oxygen or water vapor molecules in the vicinity, this equation is useful up to 1,000 GHz.

According to an ITU-R specification, the average refractivity of the atmosphere versus altitude follows equation

where NA = 315 and bA = 0.136 km−1. These values are calculated using the standard-atmosphere model: p = 1,013 mb, its change −12 mb/100m

254 Radio Engineering for Wireless Communication and Sensor Applications

as n ≈ 1, and for terrestrial radio paths in general f ≈ 0°, that is, cos f ≈ 1. In an average atmosphere at sea level, the curvature (= −1/bending radius, i.e., the rate of change of direction with distance) of the ray is

that is, the ray bends downward.

Also the Earth’s surface bends downward, and its curvature is −1/R , where the Earth’s radius is R = 6,370 km. Therefore the curvature of the ray in reference to the Earth’s surface is

When analyzing radio paths in the troposphere, we can imagine that the ray is straight, if we use an effective Earth radius KR (see Figure 10.5). In the average atmosphere KR = 8,760 km or K = 1.375. Often we use a value of K = 4/3.

Temporarily the distribution of the refraction index versus altitude may differ considerably from that of the average atmosphere. If dn /dh = −157 × 10−6 km−1, the ray bends as fast as the Earth’s surface (K = ∞). If dn /dh < −157 × 10−6 km−1, the ray bends toward the Earth’s surface (K < 0). The wave may propagate long distances with successive reflections, as illustrated in Figure 10.6. Propagation with this mechanism is called ducting. Ducting may happen in the so-called inversion layer, where temperature increases rapidly as altitude increases. Such an inversion layer may range in height from a few meters to about 100m and may appear near the ground or at a high altitude.

Figure 10.5 Propagation in the troposphere: (a) refraction; (b) a model of straight propagation above the surface of an extended globe.