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g 2 g; g ! 1) and on the cellular map splitting strategy (on parameters N and Rcell ). In fact, from the formulas presented above, the C=I performance is enhanced if the cell radius Rcell is within the break point range and the reuse distance D is beyond this range. At the same time, stated differently, for a given C=I-ratio, a channel can be reused more often, enhancing the cellular system capacity. This is a pure engineering subject as the same engineering questions of cellular system performance, which lie outside the purpose and main goal of this book. The reader can nd all these questions described in detail in References [16 19]. 12.2.3. Strategy of Non Uniform Cellular Maps Design In the previous section, we considered the classical strategy of how to split the radio map into regular cell lattice using hexagon-cell con guration with periodic constant frequency reuse pattern, that is cluster layout concept by using the same frequencies at those cells, the ranges of which between their BS equal the reused distance D. This concept is good for uniform distribution of users/subscribers and calls, for uniform traf c (see Section 12.1). However, due to the demand to keep on increasing the network traf c capacity, designers of the most modern cellular networks started looking for new strategies and some alternative concepts to deal with inhomogeneous traf c. Moreover, in such modern approaches the base station positioning within the cell pattern was stated to be nonuniform with relocation in real time according to propagation conditions within the traf c hot spots, as shown in Figure 12.11. The corresponding approaches and models are fully discussed in References [27 36]. Below, we brie y will show how to introduce a exible concept of cell splitting and propagation effects in a new strategy of cellular maps design. Then, we base on a speci c experiment, described in Reference [28], and use for comparison with theoretical predicting model proposed in References [31 33]. We compare the obtained theoretical and experimental results with those obtained by using the proposed stochastic approach of radio propagation in different scenarios in the urban scene.
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FIGURE 12.11. Non-homogeneous cellular pattern.
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A Heuristic Approach for Channel Assignment Performance. Let us brie y introduce a modern heuristic algorithm developed in References [31 33] on how to obtain C=I-ratio based on mathematical models proposed in References [27 30,34 36] by accounting for the Wal sch Ikegami model (WIM) of signal power decay in the urban environment [37]. The frequency assignment problem, was represented in References [31 33] in the form of the heuristic algorithm developed on the basis of cell con guration, which does not follow the classical hexagonal-cell homogeneous concept with a periodic frequency reuse pattern. This algorithm is based on the binary constraints between a pair of the transmitters presented in References [31 33] that appear in the following form: jfi fj j > k; k!0 12:14
where fi and fj are the frequencies assigned to transmitters i and j. In References [31 38], different con gurations of the cellular pattern were analyzed for channel (frequency) assignment with applications to real nonregular, nonuniform radio networks, mobile and stationary, considering cellular maps with different dimensions of cells; cellular maps with irregular shapes of cells; cellular maps with certain level of intercell overlapping. An example of nonuniform cell pattern distribution with different shapes and sizes of cells is presented in Reference [38] for a city in Germany [34], where the location of the BS, the cell-shape, and dimensions of each cell were taken to be nonregular. It was then redesigned in References [31 33] by using the new heuristic approach. In its redesigned form, this nonregular cell pattern is shown in Figure 12.12, according to References [31 33]. For such a con guration of cells we need to use the following formula:   C R 4 P i 4 I i dij
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