TERRESTRIAL RADIO COMMUNICATIONS

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5.6.2. Comparison with Other Models The stochastic model described in the previous section is compared with Tamir s model [48 50]. The total eld intensity for the range 0 < r < 1 2 km in [48 50] is proportional to r 2:5 r 3 . The same result can also be obtained from formulas (5.48) (5.50). In fact, for zones far from the transmitter, the two last terms in (5.48) are the dominant terms and they predict a eld intensity attenuation from exp g0 r to r exp g0 r that can be expanded to r 1:5 r 3:5 [60]. Thus, the results obtained in r3=2 References [48,50] are predicted by results of the stochastic model presented here. A good agreement was also with Weissberger s empirical model [64], that is based on numerous experiments in different forest environments. Comparisons with other statistical models have also shown that the stochastic model described here is more precise and covers the case of single scattering with a signal decay law of r 2 obtained in References [65 67] using the Born s approximation. 5.7. PROPAGATION IN MIXED RESIDENTIAL AREAS Let us consider an array of houses and trees as blocks and cylinders with randomly distributed surfaces which are placed on a at terrain. Such obstructions are mainly present in mixed residential areas. The characterization of the propagation properties of such environments has been thoroughly investigated in Reference [68] and brie y discussed in Reference [59]. 5.7.1. Statistical Description of Mixed Residential Area We assume that the re ecting properties of houses and trees are randomly and independently distributed, but they are statistically the same. The values of the re ection coef cients are complex with a uniformly distributed phase in the range 0; 2p . Thus, we consider each house or tree as a phase-amplitude screen (see Fig. 5.11). The re ection properties of these screens are described by the complex re ection coef cient with a uniform distributed phase in the range 0; 2p and with correlation scales in horizontal, h , and vertical, v , directions, respectively. Both scales characterize the correlation function of the re ection coef cient, which can be presented as [68]: & ' jxj jZj 0 5:52 KG rS ; rS G jS exp v h G jS is the amplitude distribution of the re ection coef cient over angles jS . The absolute value of G jS is de ned by (4.50) in 4. In (5.52), to obtain KG rS ; rS 0 , we introduce a new variable x jrS 0 rS j and construct, at the surface of the re ected rough screen (Fig. 5.11), the local coordinate system fx; Zg with origin at point rS and with axis 0x. The geometry of the problem is shown in Figure 5.12, where A r1 is the point of the transmitting antenna location at height z1 and B r2 is the point of the receiving antenna location at height z2 . As was shown in

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PROPAGATION IN MIXED RESIDENTIAL AREAS

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FIGURE 5.11. The pro le of mixed residential area.

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Reference [68], to derive an average measure of the eld intensity for waves passing through the mixed layers of houses and trees, one needs to use the single scattering approach and take into account diffraction from building roofs. In this case, we consider that one of the antennas is higher than the average mixed-layer height, " h, h that is z2 > " > z1 . The eld component which passes through such a layer after multiple-scattering is smaller than that of the single scattering case. Thus, only a single-scattering problem with diffraction from the mixed layer tops should be considered here. Moreover, because in residential areas the height of the trees and houses are at the same level (i.e., uniformly distributed in the vertical plane), we can

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