Page 38 - Integrated Wireless Propagation Models

16 C h a p t e r 0 n e

We also studied the case with more than one interfering tier and created an interfer­
k
ence ratio of Ik of kth tier to I of the first interfering tier, � for k = 2, 3, 4. The center cell
1
1
of the first-tier co-channel cells is the same center cell of the second- and third-tier co-
channel cells. Thus, starting from Eq. (1.7.1.3), the C/I of the center cell from only the
first-tier co-channel interfering cells for the frequency reuse factor K = 7 (i.e., a total
bandwidth will be divided evenly in a cluster of seven cells) is
(1.7.1.6)
where Z is the number of co-channel interfering cells in the first tier. From Eq. (1.7.1.1),
1
1
D/R = .J3K = 4.7 for K = 7 ( . 7.1.7)
The distance Dk from kth-tier co-channel interfering cell to the center cell is
1
1
Dk = k · D 1 ( . 7. . 8)
and Zk is the number of total co-channel interfering cells at the kth tier:
k
1
1
zk = . Z 1 ( . 7. . 9)
Then the co-channel interference for the kth-tier co-channel cells is
1
C/Ik = Zk (DJR)4 = k Z (k D/R)4 ( . 7.1.10)
1
Thus, IJI can be found from Eqs. ( . 7. . 6 ) and ( . 7.1.10) as
1
1
1
1
IJI = k-5 ( . 7. . 1 1)
1
1
1
I z
T= 2-5 = 0.0312 = -15 dB (interference by the second tier)
1
I
3
T = 3-5 = 0.004115 = -24 dB (interference by the third tier)
1
The total interference (first tier and second tier) versus the first-tier interference is
1
1
(I + I ) / I = 1 + 0.0312 = . 0312 = 0.133 dB ( . 7. . 1 2)
1
1
1 2
The total interference (first and second and third tier) versus the first-tier interference is
1
1
(I + I + I)/I = 1 + 0.0312 + 0.004115 = 1.0353 = 0.15 dB ( . 7. . 13)
1
1 2
1
1
From the results from Eqs. ( . 7. . 1 2) and (1.7.1.13), we can conclude that the co-channel
interference caused by the second and third tiers is very small and can be neglected.
As frequency reuse factor K increases, the frequency reuse distance D increases, and
the interference is reduced. The cell size becomes insignificant larger compared with
the reuse distance D for large K. Then we can approximate each cell by its center. Usu­
ally, the ratio of interference caused by the second tier and the first tier is the largest.
One way to reduce co-channel interference is to divide the cell into sectors and a use
1
directional antenna in each sector, as shown in Fig. . 7.1.2. A directional antenna pro­
vides a very low gain in the back lobe and will interfere with the cells only in the front
1
(shown in Fig. . 7.1.2). Thus, the interference caused by the co-channel cells to the cen­
ter cell will be reduced by more than one-half.