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indoor communication systems. In particular, it has been observed that the eld diffusion due to the edges of penetrable objects introduces an additional attenuation of the echoes of the radio signal with respect to the empty environment. Because of its numerical accuracy and limited computational requirements, the UTD raytracing model can be successfully employed to estimate the channel performance and the total eld distribution (radio coverage) directly during the design phase of indoor wireless communication. 8.2.2. Physical Waveguide Model of Radio Propagation Along the Corridor This model is an analytic model of radio wave propagation along an impedance corridor as a waveguide. This model, which differs from other models [14,18], allows us to analyze the electromagnetic eld distribution inside a building corridor to obtain an expression for the attenuation (extinction) length and the path loss. The Geometry of the Problem. Below we brie y present the guiding effects of the corridor on the basis of same theoretical approach that was followed for the outdoor street scene [2], that is, we model the corridor by a two-dimensional impedance parallel waveguide (Fig. 8.4). As d ) l, where d is the corridor s width and l is the wavelength, we can use the approximation of geometrical theory of diffraction (GTD). This approximation is valid as long as the rst Fresnel zone $(lx)1/2 equals or does not exceed the width of corridor d. In this case, x 30 50 m, l 3 10 cm (L/X-band); d 2 3 m; (lx)1/2 d. The electrical properties of walls are de ned by the surface impedance ZTE $ e 1=2 ; e e0 j 4ps=o , where e is the dielectric permittivity of the wall s surface, e0 is the dielectric constant of the vacuum, s is the conductivity, and o 2pf is the angular frequency of the radiated wave. We consider the 2D problem of wave re ection without taking into account the re ection from the corridor s oor and ceiling because the corridor s height H and the position of the transmitter/receiver h 2 3 m are usually larger values than l. Let us also assume, according to the geometry presented in Figure 8.4, that a vertical electric dipole is placed at the point (0, w, h) at the (y, z) plane, as it is shown in Figure 8.5. To convert the problem to a 2D case, we must consider the dipole oriented along the y-axis, that is, the horizontal dipole with respect to the (x, y) plane, which
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FIGURE 8.4. The corridor waveguide model; a view from the top.
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FIGURE 8.5. The corridor in the 2D case.
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corresponds to the well-known electromagnetic eld equation described by the Hertzian potential vector iy x; y [2]: r2 iy x; y k2 iy x; y 4pi p d x d y w o y 8:6
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The solution of such an equation can be presented using the Green s function [2]: iy x; y i eikr p o y r 8:7
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Here, the electric momentum of a point horizontal electric dipole, p py is r x2 y2 is the distance from the source. Total Field in 2D Unbroken Impedance Waveguide. The re ected eld in an unbroken waveguide can be determined according to Reference [2] as the sum of re ected modes replaced by the image sources (as shown in Fig. 8.6). The straight computations made according to Reference [2] give the normal mode expression inside the impedance wave guide (called the discrete spectrum of the total eld): ( ) 0 j ln jRn k pn irn x exp 0 x 8:8 n x; y D1 e d rn d where r 0 n q r np2 2 k2 Kn k2 d
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and Rn Kn kZEM ; D1 2DRn ; Kn np is the wave number of normal modes of 0 Kn kZEM d irn d number n that propagate along the waveguide with width d, k 2p, D is the l parameter of electrical dipole including its momentum p [2].
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