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Here, following Reference [38] we take a simple two-ray propagation model with g 4 (see 5). Notice that all notations are changed here from those used in References [32,34,38] to be uni ed with those used in this section. Here Ri is a radius of cell i; Mi is the set of all the cells (excluding cell i) that uses the same bandwidths (channels) as cell i; dij is the worst-case distance between interfering cell j and cell i. The latter can be found as [38] q xi xj 2 yi yj 2 Ri
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FIGURE 12.12. Nonuniform cell pattern. (Source [31]: Reprinted with permission # 2004 IEEE)
where xi ; yi and xj ; yj are the Cartesian coordinates of the base stations (BSs) of cells i and j. Using the simplest propagation model, in Reference [38] the co-channel interference constraint was obtained for C=I threshold a 1=b 18 dB
4 X dij j2Mi
R 4 i
In Reference [32], suf cient improvements of the model [38] were obtained by introducing adjacent channel interference adj factork a 1 log2 k : Where k is the bandwidth separation (in number of channels) between the adjacent channel frequency and central frequency of the corresponding lter (see the strict explanations in Reference [32]). A typical value for a is 18 dB (as a 18 dB in Reference [38]), and for k 1 an adjacent channel is attenuated by a factor equal to 0.015 [32]. Channel Assignment Strategy Accounting for the Propagation Loss Law. Using such de nitions, the co-channel interference constraint (12.16), accounting for the simple law of the received power attenuation PRi / PTi d 4 , can be rewritten as [32]
4 X PTj dij
P R 4 j2Mi Ti i
n X k 1
adj factork
X PTk d 4
P R 4 j2Mi Ti i
Using the two-ray model presentation (see 5), we can also express this constraint as [32] X PTj L dij ; f PTi L Ri ; f
n X k 1
adj factork
X PTk L dik ; f
PTi L Ri ; f
In Reference [32], the Wal sch Ikegami propagation model (WIM) with a slopeattenuation parameter of g 2:6 (i.e., PRi / PTi d 2:6 ), was also taken into consideration. Let us now compare results obtained according to Reference [32], using a simple two-ray model and the WIM model, with those obtained using the stochastic approach with a slope-attenuation parameter of g 3:0 (i.e., PRi / PTi d 3:0 ). To compare the effects of these three laws of propagation loss on the strategy of frequency assignment, in computations, following References [31 33], we take into account the interference effects of rst (n 1) and second (n 2) adjacent channels. During computations we considered only co-channel interference (n 0) and also considered a practical example of a 21 cell network, by varying the radii of the cells without changing the base station locations in order to produce three different con gurations: a) nonoverlapping cells; b) adjacent cells; and c) overlapping cells. Finally, the channel assignment, span and order, which guarantees a C/I of at least 18 dB in every point in an urban environment, was computed and presented in Figures 12.13(a,b) 12.15(a,b) for span (a) and order (b) assignment. Here, three kinds of laws of path loss according to two-ray d 4:0 , WIM d 2:6 and stochastic
Frequency assignment span (Radius 100 m) nonoverlapping cells 240 L~d-3 L~d-4 WIM Number of channels 235
231 230 229
231 230 229
231 230 229
1 2 Interference considered
Frequency assignment order (Radius 250 m) nonoverlapping cells
200 186 186 186 L~d-3 L~d-4 WIM
Number of channels
113 100 105
113 105
113 105
1 2 Interference considered
FIGURE 12.13. Frequency assignment for nonoverlapping cells.
d 3:0 models for nonoverlapping (Fig. 12.13), adjacent (Fig. 12.14), and overlapping (Fig. 12.15) con gurations of nonuniform cellular patterns are shown. As it is clearly seen from the presented illustrations, the multiparametric model and the Wal sch Ikagami model (WIM) give higher channel (frequency)