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Point #51. Terrain Factor n = 0.1, 1, 10; Transmitter Antenna hT = 93m
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FIGURE 5.19. Distribution of F hR versus the receiver antenna height hR (for a transmitter antenna hT 93 m), for various parameters n 0:1, 1, 10.
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In Figure 5.19, we examined the role of the parameter n on F hT ; hR ; n at a constant transmitter antenna height hT 93 m. The values chosen were n 0:1, 1, 10 that describe predominantly tall buildings, uniformly distributed heights, and predominantly low building heights, respectively. This provides a transition of the built-up area from that of typically residential area with predominantly small buildings (the bottom curve in Fig. 5.19 corresponding to n 10), to that of a dense city center with predominantly tall buildings (the top curve in Fig. 5.19 corresponding to n 0:1). We therefore can state that the proposed method of characterizing the terrain and its associated building overlay provide good information regarding the nature of the pro les vis-a-vis the pertinent evaluation of terminal antennas, the transmitter, and the receiver. Dimensions of the Re ected Surface Sections. Let us consider the case when LOS visibility exists between two points r1 and r2 (Fig. 5.16). Let us now determine the probability that given a point A r1 , the horizontal segment inside the building (as a nontransparent screen) can be observed (see Fig. 5.20). If a horizontal segment with length l could be seen from point r1 , a vertical segment with width l can be seen from this point as well. The vertical screen forms an angle with line AB. After
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FIGURE 5.20. The screen at the building s wall with horizontal and vertical segments of length l, illuminated under the angle c by the source located at the point A r1 .
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Here, the multiplier X in the integrand of (5.77) determines the probability of the event when the projection of the point r(x, y, z) on the plane z 0 hits inside an arbitrary building (as shown in Fig. 5.15). When X 1 and z > z1 ; z2 , Equation (5.77) becomes to:
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The Spatial Distribution of Scattering Points. The role of the single scattering case is very important when one of the antennas (mainly, the base station antenna)
fS yS
FIGURE 5.21. 2D-model of scattering from a nontransparent screen.
is above the roof level, and the other one is below it. This case is presented in Figure 5.21, where the re ected point C is inside the building contour of height h. The building orientation is determined by the angle s and the vector (rs r1 ). The receiver (or transmitter) is placed at point B r2 ), and the transmitter (or receiver) is placed at point A r1 ). If we now introduce the polar coordinate system (r, j) with point B as a base point on the plane z 0 (Fig. 5.21), then for discrete distributed sources, the density of the scattered point distribution can be presented as follows [57 59]: a) for z1 ; z2 < h m r; j 0:5ng0 sin2 a=2 r e expf g0 r e g r r
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0:5n sin2 a=2 f z2 h e exp g0 r =hg m1 r; j m2 r; j r
where e d 2 r 2 2rd cos j 1=2 ; and h is the average building height. r Comparing formulas (5.79) and (5.80b), one can see that the rst summand in