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FIGURE 5.14. 2D presentation of the multislit street model with the width a.

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The dielectric properties of a building s walls are usually described by the surface impedance: ZEM $ er 2 ;

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In a real city scenario, the screen and the slit lengths are much greater than the radiation wavelength l, that is, Ln ) l, ln ) l. In this case we can make use of approximations provided to us from GTD. According to the GTD, the re ected and diffracted waves have the same nature, and the total eld can be presented as a superposition of direct (incident) elds from the source and waves re ected and diffracted from the screens. Path Loss Along the Straight Streets. Following the previously constructed model [69 71], we consider the resulting re ected and diffracted elds as a sum of elds reaching the observer from the virtual image sources (for the re ections from n plate z a) and (for the re ections from plate z 0), as shown in Figure 5.14. n Using some straightforward derivations presented in References [69 71], we can obtain the approximate expression for the path loss of the radio wave intensity at large ranges from the source (r ) a): L % 32:1 20 log10 f0 20 log10 8:6 j ln wjRn jj ( a " 1 wjRn j 2

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Kn kZEM Here, Rn Kn kZEM is the coef cient of re ection for normal modes in the waveguide, jn is its phase, and jRn j is its modulus

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Here, w L L l is the parameter of slit density. The expression for the ground re ection coef cient Gg is presented by (4.50) in 4. For a perfectly conductive waveguide, ZEM 0; jRn j 1; jn 0 and L % 32:1 20 log10 f0 20 log10 " 1 w 2 1 w 2 # hp i r n 17:8 log10 r 8:6 j ln wj 0 a rn a (

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Like classical waveguides, most of the energy is conveyed by the rst mode. Hence, taking n 1 gives an accurate estimation of the resulting path loss along the street in LOS conditions. Using the two-ray model (see Section 5.3), we can also obtain from the proposed waveguide model the break point rb , which determines the attenuation of the path loss as r 2 , for r < rb, and varying as r 4 , for r > rb [69 71]. The formula for the break point rb , that depends on the geometry of the streets and their structures, is given by: rb 4hT hR 1 wjRn j = 1 wjRn j 1 hb =a hT hR =a2 l jRn j2 5:67

In all the above formulas we assumed that the absolute values of the diffraction coef cients Dmn from the buildings corners are close to unity. Analyzing formula (5.67), one can see that for wide avenues, when a > hb > hT ; hR , and w ! 0, for jRn j % 1, the break point is rb 4hT hR , that is, the same formula obtained from the l two-ray model. Beyond the break point the eld intensity attenuates exponentially [69 71]. This law of attenuation, obtained experimentally, states that the attenuation mode of eld intensity beyond the break point is $ r q , q 5 7. This result does not follow from the two-ray model but can be explained using the waveguide model. In the case of narrow streets, when a < hT , hR < hb and w ! 1, the range of the break point tends to go to in nity for the observed wavelength bandwidth