260 Radio Engineering for Wireless Communication and Sensor Applications

Example 10.2

The transmitting antenna is located at a height of 300m. The frequency is 225 MHz, and the polarization is horizontal. What is the best height for a receiving antenna at a distance of 12 km, if the terrain between the antennas is a flat field?

Solution

Reflection from the surface causes a phase shift of 180°. Therefore the electric fields of the direct and reflected wave add up in phase when the path difference r 1 + r 2 − r 0 ≈ 2h1 h2 /d is equal to l/2. The optimum height of the receiving antenna mast is h2 = l d /(4h1 ) = 13.3m. Other solutions are (2n + 1) × 13.3m.

In the preceding discussion we have assumed that the wave propagates as a ray. However, as we discussed in Section 10.4, the ray requires the volume of the first Fresnel ellipsoid as free space. The surface area, where the reflection may happen, is therefore large. If the distance between the antennas is long, bending of the Earth’s surface must also be taken into account in determining the location of reflection.

The surface may be considered smooth, if the rms value of the surface roughness, Dh, fulfils the following condition:

If the surface is rough, a considerable part of power will scatter; that is, it will radiate into a large solid angle.

10.6Multipath Propagation in Cellular Mobile Radio Systems

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 [6, 7].

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.

When there is a dominant LOS wave in a multipath environment, the amplitude of the signal envelope has a Rician probability distribution. If there is no LOS wave, as in Figure 10.12, the envelope has a Rayleigh probability distribution. There are reflected, diffracted, and scattered waves as well as waves propagating through vegetation and buildings. The Rayleigh distribution is obtained by summing up a large number of independent field components, and its probability distribution is

Figure 10.12 Multipath propagation in an urban environment and the signal envelope in a fading radio channel.

262 Radio Engineering for Wireless Communication and Sensor Applications

where the envelope r (t ) of the complex signal E (t ) is given as r (t ) =

√[Re E (t )]2 + [Im E (t )]2 , and s2 is the mean power, and r 2(t )/2 is the short-term signal power.

The effect of small-scale fading may be mitigated by using in receiving or transmitting multiple antennas, time redundancy, several polarizations, or several frequencies (space, time, polarization, and frequency diversity). The diversity increases the probability that at least one of the received signals will be strong enough to be detected. Spread spectrum or multicarrier systems can mitigate the small-scale fading due to their large bandwidth, that is, their frequency diversity. A rake receiver can mitigate it using time diversity by detecting replicas of the transmitted signal with different time delays [7]. A smart antenna system such as multiple-in-multiple-out (MIMO) can mitigate it through space and polarization diversity [8]. Moreover, a MIMO system can increase the spectral efficiency by utilizing different independently fading propagation paths as parallel data channels.

In rural areas the base station antennas are located in high antenna masts so that most of the path is in free space or along the treetops. The final meters or tens of meters of the path to the mobile terminal may cause a lot of attenuation; in a forest the average excess attenuation through vegetation at 2 GHz is about 0.4 dB/m; however, the attenuation of a tree with or without foliage is very different. In urban areas the base station antennas may be located at the roofs or walls of the buildings, while the mobile terminals move along the street canyons or are inside the buildings.

Both deterministic and stochastic propagation models are used in design, optimization, and performance evaluation of cellular mobile radio systems. Deterministic models are based on electromagnetic simulations (utilizing ray tracing together with geometrical optics and uniform theory of diffraction, finite difference time domain method, and so forth) making use of information of the specific physical environment or on measurements. Stochastic models describe the propagation phenomena on average; they are based on defining the fading distributions (log-normal, Rayleigh, Rician). The model parameters are based on measurements or on a deterministic model in a given type of environment [9, 10].

The deterministic propagation models can be divided into simplified semiempirical path loss models and computational site-specific models. An example of the empirical models is the Okumura-Hata model [11]. In the Okumura-Hata model the physical environment can be selected among a large city, a medium to small city, a suburban area, or a rural area, and the model takes into account the antenna heights and frequency. The Walfisch-

Bertoni model [12] allows slightly more detailed characterization of the environment; for example, the average building height and the width and orientation of the streets can be taken into account. It counts the propagation loss as a function of distance (free-space loss), multiscreen diffraction due to rows of houses, and finally the roof-to-street diffraction. Inside the buildings, site-specific computational models are often used, but simplified models such as the Motley-Keenan model [13], which calculates the path loss from the free-space path loss according to the distance added by attenuation of each wall along the path, are also in use.

10.7 Propagation Aided by Scattering: Scatter Link

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 er 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 .

If the density of small scattering particles is r (particles per cubic meter), the scattering cross-section density is sd = rs. In a symmetric radio path utilizing scattering as shown in Figure 10.14, the power received is