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In Section 5.8.1, we start with the multislit waveguide model, which was found to be in good agreement with experimental data for wave propagation in urban areas with regular cross-street grid layouts [69 71]. In Section 5.8.2, we discuss the situation when an array of buildings is randomly distributed at a rough terrain surface and we present the 3D stochastic multiparametric model obtained in Reference [76,77]. Then, in Section 5.8.3, we compare the stochastic model with the frequently used empirical, semi empirical and deterministic analytical models for predicting loss in various built-up areas [72 75, 78 83]. In order to understand the effect of a built-up environment on radio propagation in land communication links, researchers, rst of all, have analyzed the role of concrete buildings on radio wave propagation relative to LOS propagation above both smooth and rough terrains. It was shown both theoretically and experimentally that the total eld distribution surrounding a single, non transparent building is caused by rays diffracted and re ected from the building s corners and walls, as well as, by the waves bounced from the ground and then re ected from the walls [69 83] (see also discussions in Section 5.5). In this case, the number of rays caused by diffraction is larger than the number of rays caused by re ection. The estimation of these diffracted rays has been carried out using several approaches [32 40] based on Keller s GTD [28 31] described in Section 5.5 for diffraction from wedges with different shapes and material. Using the results of these investigations, we can now tackle the problem of how an array of buildings affects the radio propagation in urban communication channels.
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5.8.1. Propagation in Urban Areas with Regularly Distributed Rows of Buildings Here, we consider several urban propagation environments. We start with the simplest case of EM-wave propagation in the urban scene, where both antennas are placed above a at ground surface in conditions of LOS and below the rooftop level. As was shown in Section 5.3, in LOS, all propagation characteristics, as path loss and radio coverage, can be determined using the well known two-ray model. We will brie y discuss below the multislit waveguide model (for LOS propagation), which was found to be in good agreement with experimental data of wave propagation in urban areas with a regular cross-street grid layout [69 71]. Street Waveguide Model. As mentioned in References [59,69 71], the conditions of LOS propagation along a straight street on which a base station is located is of great importance in de ning the coverage area for antennas located below because of the low path loss as compared to propagation over the rooftops. At the same time, a multislit waveguide model has been introduced recently for describing the propagation of EM-waves in a city scene with regularly planned streets, that is a model of straight streets with buildings lined up on the sides [69 71]. The street is seen as a planar multislit waveguide with a Poisson distribution of screens (building walls) and slits (intervals between buildings). The dielectric properties of the buildings
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FIGURE 5.13. 3D presentation of the street waveguide model.
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walls are taken into account by introducing the electrical impedance as a function of their surface permittivity and conductivity. In Figure 5.13, a 3D-waveguide model of a city region with regularly planned buildings, and with a receiver and transmitter is shown. We notice that the condition hT , hR < hb is the main condition for the validity of the proposed street waveguide model [69 71]. Here, hb is the height of the buildings lining up the street, and hT and hR are the transmitter and receiver antenna heights, respectively. The re ection from the ground surface is also considered using an imaginary source. The projection of the waveguide on the zy-plane presents the 2D impedance parallel multislit waveguide with randomly distributed screens and can be considered as a model of a city street (see Fig. 5.14). One waveguide plane is placed at the waveguide (street) side z 0, and the second one at z a, where a is a street width (Fig. 5.14). The screen length Ln and slit length ln are distributed according to Poisson s distribution with the average values of hLi L and hli l, respectively [59,69 71] & ' Ln ; f Ln L 1 exp L & ' ln f ln l 1 exp l
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