Mobile Wireless Communications in .NET Generating Code128 in .NET Mobile Wireless Communications

Mobile Wireless Communications using .net vs 2010 topaint code 128 code set c on web,windows application ISBN - 10 R 3R Figure 3.4 Hexagon circles rather than hexa Visual Studio .NET Code-128 gons are sometimes used in subsequent chapters to simplify the analysis. Given the hexagonal radius R, the following values of the center-to-center spacing between the closest interfering cells, indicated in Figs.

3.2 and 3.3, are readily as established: D3 = 3R = 3 3 R; D4 = 2 3R = 3.

46R = 3 4 R; D7 = 3 R = 7 4.58R. In general, for cluster sizes C, as given by (3.

4), we shall show that DC /R = 3C. Hence as the cell cluster increases, the spacing between interfering cells increases, reducing the interference. But the channel assignment per cell decreases as well, as already noted, reducing the effectiveness of the channel reuse, the reason for introducing a cellular structure.

Consider the AMPS and IS-54/136 examples again. Say N cells constitute a geographic area. The number of frequency channels available for this area is then 832N/C.

The number per cell is 832/C. For a 7-reuse system the number per cell is 832/7 118 = channels. For a 3-reuse system, the number is 832/3 277 channels per cell, as already = noted in the earlier one-dimensional example of the previous chapter.

We have yet to establish the validity of the magic numbers given by (3.4) and DC /R = 3C. Consider the latter condition rst.

We adopt an approach used in Yacoub (1993). Note from Fig. 3.

2 that the cluster consisting of seven cells may itself be approximated by a hexagon of the form shown more generally in Fig. 3.5.

This larger hexagon has as its distance between edges just the distance D7 indicated in Fig. 3.2.

In the general case this would be DC , the distance between closest interferers, as indicated in Fig. 3.5.

A hexagon with this distance between edges has a radius RC = DC / 3. Its area is then 2 2 AC = 3 3RC /2 = 3DC /2. The number of cells within a cluster is given by the ratio of the cluster area to the cell area.

The cell area a = 3 3 R2 Taking the ratio of areas, /2. we nd C = AC /a = DC 2 /3R2 , from which we get DC /R = 3C. Now consider (3.

4). The speci c form of this expression is a property of the hexagonal tessellation of the two-dimensional space. To demonstrate this property, consider the set of hexagons of radius R shown in Fig.

3.6. The location of the centers of the hexagons may be speci ed by drawing two axes labeled u and v as shown.

Axis v is chosen to be vertical; axis u is chosen to be at an angle of 30 ( /6 rad) with respect to the horizontal. Starting at an arbitrary hexagon whose center is taken to be (0, 0), axes u and v intersect. Yacoub, M. D. 1993. Foundations of Mobile Radio Engineering, Boca Raton, FL, CRC Press. Cellular concept and channel allocation Rc Dc Figure 3.5 Larger hexagon (u,v) u (0,0). Figure 3.6 Hexagonal space tessellation the centers of adjacent Visual Studio .NET Code 128A hexagons as indicated in the gure. Consider the distance D now to the center of a hexagon whose location is at point (u,v).

From the Pythagorian Theorem this is given by D 2 = (v + u sin 30 )2 + (u cos 30 )2 = u 2 + v2 + uv (3.5) But note that u and v each increment by multiples of 3 R, the distance between edges of a hexagon. Thus u = i 3 R and v = j 3 R, i and j = 0, 1, 2, .

. . .

We thus have, from (3.5) D 2 = 3R 2 (i 2 + j 2 + i j) (3.5a).

2 Combining this equatio n with the relation C = DC /3R 2 , we get (3.4). Given this introduction to two-dimensional cell clusters, hexagonal geometry, and the spacing of rst-tier interferers, we are in a position to calculate the two-dimensional SIR, just as was done in the previous section for the one-dimensional case.

Note rst that, given any cell, there will be six rst-tier interferers located about it. This is apparent from the cluster constructions of Figs. 3.

2 and 3.3. These six interferers are drawn schematically in Fig.

3.7. The actual location of these interferers depends on the cluster size C.

Assume, for simplicity, that that they fall along the six hexagonal axes spaced 60 apart as shown in Fig. 3.7.

For the worst-case SIR calculation, let the mobile be placed at point P, a corner of the cell, as shown in Fig. 3.7.

Its distance from its own base station at the center of the cell is R. Its distance from the closest interferer, the base station at another cell at.
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