ELECTROMAGNETIC ASPECTS OF WAVE PROPAGATION OVER TERRAIN in .NET

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ELECTROMAGNETIC ASPECTS OF WAVE PROPAGATION OVER TERRAIN
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4.4. PROPAGATION ABOVE ROUGH TERRAIN UNDER LOS CONDITIONS Now we consider EM-wave propagation above a rough terrain. Both terminal antennas, the transmitter and the receiver, are placed above the rough terrain in LOS conditions. Here the multi-scattering effects, caused by the terrain roughness, must be taken into account. The total eld arrived at the receiving antenna is a superposition of the direct wave, the wave specularly re ected from the quasi- at ground surface (which together with the direct wave form the coherent part of the signal total intensity, Ico ), and the waves scattered in all directions from the irregularities of the terrain (which form the incoherent part of the signal total intensity, Iinc ). In order to predict the propagation loss characteristics of the irregular ground surface and to estimate the role of each kind of wave in the total eld, we use the Rayleigh rough-surface criteria and nd the in uence of each part in the signal total intensity at the receiver [9 14]. Next, we present expressions for both part of the total signal intensity, the coherent and incoherent, the re ected and scattered from the rough ground surface, respectively. These expressions take into consideration the various relations between the dimension of roughness, the wavelength of operation, and the angle of incidence. The interested reader is referred to the original works [15 27] for more details. Here we give recommendations on how to use these expressions for different frequency bands, for different terrain irregularities, and various positions of the receiving and transmitting antennas. 4.4.1. Scattering from a Rough Ground Surface A rough terrain can be described, according to [9 14,16] by a relief function z S x , as shown in Figure 4.12. If the roughness of arbitrary height z is distributed according to Gauss s law, with mean value " and a variance of s2 , then the z
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FIGURE 4.12. Relief function presentation for the rough terrain.
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PROPAGATION ABOVE ROUGH TERRAIN UNDER LOS CONDITIONS
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FIGURE 4.13. Different patterns of the scattered wave from a rough terrain.
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probability density function, (PDF) (see de nitions in 1), of roughness distribution is given by: ( ) 1 z " 2 z Pz p exp 2s2 2ps 4:51
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where the standard deviation of the ground surface roughness around its mean p z height " is s hz2 i "2 . In Figure 4.13, the criterion of roughness of the terrain z is presented schematically for various values of s for a better understanding of the role of the re ected and scattered waves in the total eld pattern. Thus, the case s 0 or s ( l (l is a wavelength) describes pure re ection from a at terrain; the case s l describes weak scattering effects from a gently rough surface, where the re ected wave is the dominant contributor to the total eld pattern, that is, Ico ) Iinc . In the cases of s > l and s ) l, the terrain is rough and irregular with an increased role in generating a signi cant scattered wave as a component of the total eld pattern. The last two illustrations in Figure 4.13, show the Ico ( Iinc cases. There are several approximate methods for the total eld evaluation in radio propagation channels above a rough terrain. At present, there are three general approaches to solve the wave scattering problem that arises from the rough terrain: a) the perturbation technique that applies to a surface which is slightly rough and whose surface slope is smaller than unity [4,9,21,25]; b) the Kirchhoff approximation that is applicable to a surface whose radius of curvature is much greater than a wavelength [4,9,13 20]; c) the Rayleigh approximation that is applicable to a surface whose curvature is at the same order as the wavelength [9 12]. We describe each approach brie y in the following section. 4.4.2. The Perturbation Solution The perturbation method is applicable to a slightly rough surface that will be described herein. Let us consider the height of a rough surface to be given by some
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