to neighboring cells. Both intracell and intercell interference are attenuated by the processing gain of
the code [1]. Due to the large number of interferers, the performance analysis of a code-division cellular
system is fairly complex, and depends very heavily on the propagation model, cell size, mobility models,
and other system parameters [1].
15.2.2
Frequency Reuse in Time and Frequency Division Systems
The channels in frequency-division (FDMA) or time-division (TDMA) are orthogonal, so there is no
intracell interference in these systems. However, frequency reuse introduces intercell (co-channel) inter-
ference in all cells using the same channel. Thus, the received SNR for each user is determined by the
amount of interference at its receiver. If the system is not interference-limited then spectral efficiency
could be further increased by allowing more users onto the system or reusing the frequencies at smaller
distances.
Consider the cell diagram in Figure 15.2 below. Let R be the distance from the cell center to a
vertex. We denote the location of each cell by the pair (i, j) where, assuming cell A to be centered at the
origin (0, 0), the location relative to cell A is obtained by moving i cells along the u axis, then turning 60
degrees counterclockwise and moving j cells along the v axis. For example, cell G is located at (0, 1), cell
S is located at (1, 1), cell P is located at (
-2, 2), and cell M is located at (-1, -1). It is straightforward
to show that the distance between cell centers of adjacent cells is
3R, and that the distance between
the cell center of a cell located at the point (i, j) and the cell center of cell A (located at (0, 0)) is given
by
D =
3R
i
2
+ j
2
+ ij.
(15.1)
The formula (15.1) for D suggests a method for assigning frequency A to cells such that the cell
separation between cells operating at frequency A is D =
3R
i
2
+ j
2
+ ij. Starting at the origin cell
A, move i cells along any chain of hexagons, turn counterclockwise by 60 degress, move j cells along the
hexagon chain of this new heading, and assign frequency A to the jth cell. This process is shown in
Figure 15.3 below. To assign frequency A throughout the region, this process is repeated starting with
any of the new A cells as origin.
Using this process to assign all frequencies results in hexagonal cell clusters, which are repeated at
the distance D, as shown in Figure 15.4. Given that the area of a hexagonal cell is A
cell
= 3
3R
2
/2 and
the area of a hexagonal cluster is A
cluster
=
3D
2
/2, the number of cells per cluster is N = D
2
/(3R
2
) =
i
2
+ j
2
+ ij. N is also called the reuse factor, and a small value of N indicates efficient frequency reuse
(frequencies reused more often within a given area).
15.3
Dynamic Resource Allocation in Cellular Systems
Initial cellular systems were based on a fixed frequency reuse pattern designed for worst-case signal
propagation and interference assumptions. Any system using fixed frequency reuse and base station
assignment must be designed relative to worst-case interference assumptions. Dynamic resource allocation
is a more efficient strategy, where frequencies, base stations, data rates, and power levels are dynamically
assigned relative to to the current interference, propagation, and traffic conditions. Simple dynamic
channel allocation techniques have been shown to improve channel efficiency by a factor of two or more,
even for relatively simple algorithms [7]. However, this analysis was based on fairly simplistic system
assumptions. Performance improvement of dynamic resource allocation under realistic system conditions
remains an open and challenging research problem.
321