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INDOOR RADIO PROPAGATION
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Ea 0 1 4 2 5 Eb Ed Ec Ee
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FIGURE 8.2. A structure illuminated by an incident electric eld; points 0 and 7 indicate the source and the observation points, respectively [30].
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b) re ected ray- eld Eb r7 R1 Ei r1 c) transmitted and re ected ray- eld Ec r7 R3 T2 Ei r2 d) diffracted ray- eld s S04 Ed r7 D4 E r4 e jks47 ; S47 S04 S47
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S01 e jks17 ; S01 S17
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e) diffracted and re ected ray- eld s S05 e jk s56 s67 Ee r7 R6 D5 E r5 S56 S67 S05 S56 S67
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where k is the wave number and Sij is the optical length between the points ri and rj . Let us now use the broadcast beam-tracing algorithm [30] used for the computation of the electromagnetic eld and the characteristics of the radio channel. The broadcast technique has a computation burden that does not strongly depend on the number of surfaces describing the environment, and it is particularly ef cient when the number of the eld computation points is large.
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MODELING OF LOSS CHARACTERISTICS IN VARIOUS INDOOR ENVIRONMENTS
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FIGURE 8.3(a). Beams emanating from the antenna towards all directions [30].
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The Beam-Tracing Algorithm. This numerical algorithm consists of two parts. The rst, determines the ray optical paths, while the second evaluates the electromagnetic eld distribution. The eld radiated from the antenna is modeled by means of beams shooting from the antenna location towards all space directions, independently of the observation point (see Fig. 8.3a [30]). During the propagation, the beam can impinge, totally or partially, on a surface describing the environment (see Fig. 8.3b, extracted from Reference [30]), it can capture the observation point,
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Incident beam Reflected beam
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A B Transmitted beam
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FIGURE 8.3(b). The beam impinges on a surface [30].
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INDOOR RADIO PROPAGATION
Diffraction Beams
A 1st Keller s cone 2nd Keller s cone B
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FIGURE 8.3(c). Division of the diffracted ray tube [30].
or nally it may not intercept any of the environment elements. In the rst case, using Snell s law, the transmitted and the re ected beams are evaluated. If the beam partially impinges on the surface, it is splitted in new beams in a way that they totally intercept, or not, the surface under construction. Then, the ray optical paths of the diffracted eld are determined. To this end, a subdivision of the diffracted ray tube, identi ed by the two Keller s cones whose tips coincide with the extremes of the segment excited by the incident ray beam, is performed (see Fig. 8.3c [30]). If the beam does not intercept any obstructions, it does not produce any secondary beams, and, consequently, it is removed from the eld computation procedure. The same happens when the beam has a cross section less than a de nite size area, or it carries a eld amplitude less than a speci c threshold, or, nally, it exceeds a maximum number of permissible bounces. For each observation point lighted by the beam, the exact ray path is computed by means of the image method. In this way, the computation technique does not suffer either from multipath count error or from the error generated by the eld approximation based on the computation of the beam median ray. In the second part of the beam-tracing algorithm, the GO and diffracted elds are evaluated using the re ection, transmission, and diffraction matrices at the points where the incident eld impinges. In the numerical procedure, only the edge diffraction processes excited by the GO eld have been taken into account. To increase the numerical accuracy of the computation, one can take into account the GO eld contribution that has experienced up to ve re ections/transmissions. The diffracted eld arising from any scattering object is considered to be excited either by the line-of-sight GO eld or by the GO contributions that have experienced up to three re ections/transmissions. Finally, the diffracted eld contribution is taken into account whether it reaches the observation point directly or after three re ections/transmissions processes. The complete analysis is carried out in References [1,28 30], and on the basis of experimental data and numerical results of the UTD ray model, it has been shown that the presence of furniture in the LOS region gives rise to greater eld diffusion and additional attenuation of the received signal. This effect decreases ef ciency of the channel performance in wireless