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FIGURE 12.9. Frequency reuse plan with reuse factor N 7.
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use the repeat frequency set in the other clusters. Between D and the cell radius Rcell there is a relationship that is called the reuse ratio. This parameter, denoted by Q, for a hexagonal cell is a function of the cluster size, that is [16 19], Q p D 3N Rcell 12:3
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Within other cells in a cluster, interference inside the communication channel can be expected at the same frequencies. Hence, for a 7-cell cluster there could be up to six immediate interferers, as it is shown in Figure 12.9. So, it is apparent that the cellular system concept is closely connected with the so-called co-channel interference caused by the frequent reuse of channels within the cellular communication system. To illustrate the concept of the co-channel interference, let us consider a pair of cells with radius R, separated by a reuse distance D, as shown in Figure 12.9. As the co-channel site is located far from the transmitter (D ) R), which is located within the initial cell, its signal at the servicing site will suffer multipath attenuation. To predict the degree of co-channel interference in such a situation with moving subscribers within the cellular system, a new parameter, carrier-to-interference ratio C=I, is introduced in References [10 19]. A co-channel interferer has the same nominal frequency as the desired frequency. It arises from multiple use of the same frequency band. For omnidirectional or isotropic antennas (see de nitions in 2) located inside each site, the theoretical co-channel interference in decibal is given by References [16 19]  ! C 1 D g 10 log I j R 12:4
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where j is the number of co-channel interferers ( j 1, 2, . . . , 6), g is the path-loss slope constant introduced and de ned in 5. It determines the signal decay in various propagation environments. For a typical seven-cell cluster (N 7) with one cell as basic (with the transmitter inside it) and with six other interferers ( j 6, as seen from Fig. 12.9) as the co-channel sites, this parameter depends on the conditions of wave propagation within the urban communication channel. As a simple example, presented in Reference [19] for two-ray propagation model above a at terrain with g 4 (see also 5), we can rewrite (12.4) as "   # C 1 D 4 10 log 12:5 I 6 R Namely, for N 7, that is D=Rcell (12.3), we can simplify (12.5) as p 3N 4:58, we get C=I 18:6 dB. Using 12:6
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! C 1 2 10 log 3 N 10 log 1:5 N 2 I 6
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meaning that the carrier-to-interference ratio is also a function of the cluster size N and increases with the increase in the number of cells in each cluster or with the decrease of the cell radius Rcell . Now we will discuss the problem of how to predict the optimal cell size. That is we will discuss how to de ne its radius and how to ef ciently design a cellular map based on the law of signal decay as was shown in 5. The law of signal decay is changed for different propagation situations in the urban scene and for different land wireless communication channels, outdoor and indoor. 12.2.2. Methods of Cellular Map Design To arrange the effective splitting of a tested built-up area at cells, the designers need strict information about the law of signal power decay for the concrete situation in the site of consideration. Speci cally, they need the strict link budget analysis of propagation situation within each communication channel, as well as full radio coverage of each subscriber located at LOS or NLOS conditions in areas of service, giving exact clearance between subscribers within each cell. On the basis of precise knowledge of the propagation phenomena inside the cellular communication channels, it is easy to optimize cellular characteristics, such as the radius of a cell, reuse factor Q, channel interference parameter C/I, and so on. Standard De nition of the Radius of Cells. As follows from 5, a better clearance between the base station (BS) and the moving subscribers (MS) in cluttered conditions may be reached only for LOS conditions (or direct visibility) between them. In this case, as follows from the two-ray model and the waveguide street model (see 5), the cell size, Rcell , cannot be larger than the break point range, rB , at which the decay of the signal is changed from g 2 (as in free space propagation) to g 4 (propagation above at terrain). If so, the law of signal decay between BS and each MS in the cell of radius Rcell rB is R 2 . Generally cell speaking, beyond the break point the law of signal decays versus the range between terminal antennas, described by path-loss slope parameter g, depends on the concrete situation in the urban scene and may be proportional to R g with g > 2 g 4 7, see discussions in 5). Such a distance dependence of signal decay law inside and outside the cell is shown in Figures 12.10a and 12.10b for two typical situations in regular cell splitting. So, we can conclude that the best clearance between each BS and any subscriber inside the cell determines the minimum radius of the concrete cell. Wave propagation phenomena in urban environments with both antennas in NLOS (clutter) conditions were described earlier in 5 by using two physical statistical models, street waveguide, and multiparametric stochastic. As follows from the models described there, in rural and mixed residential areas with a rare building distribution, the path-loss slope parameter g describing the received signal decay is changed from g 2:5 to g 4:0 (see 5). In other words, in such an area eld attenuation is faster than that in LOS conditions of free space.
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