Radio Propagation
4.1 Propagation Mechanisms
4.1.1 Free-Space Propagation
4
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and the equation for receive powerPrwith a directive transmit antenna is given by Pr=ArPtGt• 1
4𝜋R2 (4.4)
The product of transmit power and gain in the considered direction is also known as Effective Isotropic Radiated Power (EIRP).
EIRP=PtGt (4.5)
The effective antenna area is proportional to the power that can be extracted from the antenna radiators with a given energy density. For example, for a parabolic antenna, the effective antenna area is roughly the geometrical area of the surface. However, antennas with a very small (in terms of wavelength) geometrical area – for example dipole anten- nas – can also have a considerable effective area. Isotropic antenna can be represented by a short dipole with a gainG=1, so the effective aperture for isotropic antennaAiis given by
Ai= 𝜆2∕4𝜋 (4.6)
Substitution of these formulas leads to the ‘Friis law’ or equation for a relation between received and transmitted power in a free space:
Pr=GrPtGt• 𝜆2
(4𝜋)2R2 (4.7)
The free-space equation is valid in a ‘far-field’ region, for example, at the distanceR from transmitter not less than a Fraunhofer distance (also called Rayleigh distance):
df = 2D2a∕𝜆 (4.8)
whereDais the largest dimension of the antenna. The far field requires thatR≫Daand R≫ 𝜆.
It is important to note that the free-space propagation mechanism has to be inde- pendent of wavelength or frequency. This is due to the fact that the radiated energy is not lost, but rather redistributed over a sphere surface of area 4𝜋R2, as observed from equations (4.1) and (4.2). On the other hand, Friis’ law seems to indicate that the ‘atten- uation’ in free space increases with frequency. This seeming contradiction is caused by the definition of antenna gain via effective aperture (4.3) and the following presumption that antenna gainGis independent of frequency.
In the case of transmit and receive isotropic antennas, the free-space equation takes the form
Pr=Pt• ( 𝜆
4𝜋R )2
(4.9) Equation (4.9) can be re-written introducing a path lossL, which is measure of atten- uation factor caused by propagation mechanism and propagation media in general case.
Pr= Pr∕L (4.10)
The free-space path loss factor is L=
(4𝜋 𝜆
)2
R2 (4.11)
This is a well-known free-space equation for an isotropic antenna. When written in a logarithmic scale, it takes the form
L0=33.44+20 logf(MHz) +20 logR(km), dB (4.12) As follows from (4.12), the received power in a free space falls by 6 dB when the range is doubled; in other words, the path loss increases by 20 dB per decade. Similarly, path loss increases by 6 dB if the frequency is doubled.
In a general case, radio propagation path loss formulas are based on the free-space loss formula with additional empirical correction factors. The generic formula for path loss takes the form
L=L0(r) +𝛼 log(R−r) (4.13)
whereL0is a loss at reference distance (can be 1 m or 1 km) and the second term states that the losses are exponential with distance. This is illustrated in Figure 4.1, where the second term of equation (4.13) determines a ‘clutter loss factor’; that is, the slope of expo- nent in different environment related to land-usage. The slop is defined in dB/decade, and nominal values of slop are 20–25 dB/dec for free-space–open area loss, 30 dB/dec in a suburban area and 40 dB/dec in an urban area, respectively.
The radio signal attenuation depends on the environment the signal passes through. A rise in signal strength can be observed despite of increasing distance, when the receiver re-enters an open area after passing through a small urban cluster causing a higher attenuation exponent, see Figure 4.2. Since the received signal strength depends on the close environment of the receiver, there is no abrupt rise in signal strength but a gradual increase as the mobile enters an open area.
The total propagation path can be divided conditionally into long-distance and local propagation. Because the mobile terminal’s antenna is often much lower than the height of surrounding objects, the direct line of sight to the horizon is obscured. Typically, the received signal will comprise a number of reflected waves; that is, there is distinct multipath propagation. The base-station antenna is often in a more open location, but reflections or shadow effects from nearby buildings and the terrain configuration can sometimes affect the propagation conditions.
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fluid in
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Figure 4.1 Path loss examples with different clutter loss factors.
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20 dB/decade
32 dB/decade
41 dB/decade Signal level,
dB
10 dB 20 dB Distance, km
20 dB
Open space Suburbian Urban
Figure 4.2 Path loss in a mixed environment.
Multipath propagation gives rise to a fine structure of signal fluctuations, which results in corresponding variations (fast fading) in the input signal to the mobile unit. Averaging with respect to the fast fading structure gives the local mean of the propagation path loss or received signal strength.
In a typical propagation situation there are considerable shadow effects. The propa- gation loss with respect to the local mean is generally much greater than when there is free-space propagation, owing to the strong influence of the terrain. This influence manifests itself partly as an increase in the average (‘global’) propagation loss and partly as a varying loss due to the irregularity of the terrain. The large-scale effects can be esti- mated from data on the terrain and built up areas. The result of the calculation is the global mean. However, the detailed structure causes random variations in the local mean of the signal received by the mobile unit (called shadow fading, slow fading orlognormal fading).
Following this discussion, it is useful to divide propagation loss into three components:
theglobal meanof the propagation loss, that is the deterministic part, and two random elements resulting from shadow fading (slow fading) and multipath propagation (fast fading), see Figure 4.3. The global mean of the received signal power is typically inversely proportional to the fourth power of the propagation distanceP∼R−n(n=4), wheren is the propagation exponent.