# Ex.2 Celluar Concepts

```Electronics and Electrical Communications Engineering Department
Cairo University
ELCN 436 Mobile Communications
Assignment # 2
Problem 1:
If 20MHz of total spectrum is allocated for a duplex wireless cellular system and each simplex
channel has 25 kHz RF bandwidth, find:
(a) The number of duplex channels
(b) The total number of channels per cell site, if N=4 reuse is used.
Problem 2:
The US AMPS system is allocated 50 MHz of spectrum in the 800 MHz range and provides 832
channels. Forty-two of those channels are control channels. The forward channel frequency is
exactly 45 MHz greater than the reverse channel frequency.
(a) Is the AMPS system simplex, half-duplex or duplex? What is the bandwidth of each
channel and how is it distributed between the base station and the subscriber?
(b) Assume a base station transmits control information on channel 352, operating at 880.560
MHz. What is the transmission frequency of a subscriber unit transmitting on channel
352?
(c) The A-side and B-side cellular carriers evenly split the AMPS channels. Find the number
of voice channels and the number of control channels for each carrier. A-side and B-side
cellular carriers are two cellular service providers that evenly split the AMPS channels.
(d) For an ideal hexagonal cellular layout which is identical cell coverage, what is the
distance (as a function of the cell radius R) between the centers of two nearest co-channel
cells for seven-cell reuse? For four-cell reuse?
Problem 3:
Consider the hexagonal cell structure in Figure 1, where each cell has a radius R. Define two axes
r
r
u and v as shown and define the center of cell A as the origin (0,0). Denote the location of each
r
cell by a pair (i, j ) where the location relative to (0,0) is obtained by moving i cells along the u
o
r
axis, then turning 60 counterclockwise and moving j cells along the v axis. For example, cell G
is located at (0,1) , cell S at (1,1) , cell P is located at (−2,2) , and cell M is located at (−1,−1) ,
etc.
(a) Show that the distance between cell centers of adjacent cells is 3R .
(b) Show that the distance between the cell center of a cell located at the point (i, j ) and the
cell center of cell A is given by D = 3R i 2 + j 2 + ij .
As mentioned in class the formula for D derived in part (b) above suggests a method for assigning
frequency A to cells such that the cell separation between cells operating 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 degrees, move j cells along hexagon chains of this new heading, and
assign frequency A to the jth cell. This process is shown in Figure 2. To assign frequency A
throughout the region, this process is repeated starting at 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 3.
(c) Show that the area of a hexagonal cell is 3 3R 2 / 2
(d) Obtain the area of a cluster
(e) Deduce that the number of cells per cluster is N = D 2 /(3R 2 ) = i 2 + ij + j 2 . N is called
the reuse factor, and a small value for N indicates efficient reuse (frequencies reused
more often within a given area) at the expense of higher levels of co-channel interference.
Figure 1
Figure 2
Figure 3
Problem 4:
Problem 3.7 from Textbook (see below).
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