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FREQUENCY REUSE
Cellular Concepts
Frequency Reuse (I)
Frequency Reuse (II)
Frequency Reuse How many cells must intervene
between two cells using the same frequency?D: Minimum distance between centers of cells that use
the same band (co-channels)R: Radius of a celld: distance between adjacent cells (d=3 R)N: Number of cells in a repetitious pattern (reuse factor)
D/R = √(3N)or D/d = √N
Frequency Reuse is the core concept of cellular mobile radio
Users in different geographical areas (in different cells) may simultaneously use the same frequency
Frequency reuse drastically increases user capacity and spectrum efficiency
Frequence reuse causes mutual interference (trade off link quality versus subscriber capacity)
Channel Reuse The total number of channels are
divided into K groups.› K is called reuse factor or cluster size.
Each cell is assigned one of the groups. The same group can be reused by two
different cells provided that they are sufficiently far apart.
Example: K = 7
10
Frequency Reuse
F1
F2
F3
F4F5
F6
F7 F1
F2
F3
F4F5
F6
F7
F1
F2
F3
F4F5
F6
F7 F1
F2
F3
F4F5
F6
F7
F1
F1
F1
F1
Fx: Set of frequency
7 cell reuse cluster
Reuse distance D
11
Reuse Distance
F1
F2
F3
F4F5
F6
F7
F1
F2
F3
F4F5
F6
F7
F1
F1
Reuse distance D
• For hexagonal cells, the reuse distance is given by
RND 3
R
where R is cell radius and N is the reuse pattern (the cluster size or the number of cells per cluster).
NRDq 3
• Reuse factor is
Cluster
12
Reuse Distance (Cont’d)
The cluster size or the number of cells per cluster is given by
22 jijiN
where i and j are integers.
N = 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 28, …, etc.
The popular value of N being 4 and 7.
i
j
60o
13
Reuse Distance (Cont’d)
(b) Formation of a cluster for N = 7 with i=2 and j=1
60°
1 2 3 … i
j direction
i direction
(a) Finding the center of an adjacent cluster using integers i and j (direction of i and j can be interchanged).
i=2i=2j=1
j=1
j=1
j=1
j=1
j=1
i=2i=2
i=2i=2
Frequency Reuse (III)
Co-Channel Cells
Finding the Nearest Co-Channel
(1) Move i cells along any chain of hexagons
(2) Turn 600 counter-clockwise and move j cells, to reach the next cell using same frequency sets this distance D is required for a given frequency reuse
to provide enough reduced same channel interference ie, after every distance D we could reuse a set of
frequencies in a new cell
Co-Channel Cells
Cellular Frequency Reuse Concept
Prof. Sridhar Iyer Session: 22.21
Coordinate System
Use (i,j) to denote a particular cell.
Example:
Cell A is represented by (2,1).
A
Prof. Sridhar Iyer Session: 22.22
R D
Distance Formula
RK
RjijiD
3
)(3 22
22 jijiK
Note: i and j are integers
where
Reuse factor
Relations between Cluster Size and i, j
Relations between Cluster Size and i, j
25
D
L * iL * j
r
In this case: j=2, i=1
Compute D based on “law of cosine”
NijjirD
ijjiLD
jiLjLiLD
jLiLjLiLD
3)(3/
)(
)5.0(2
)3/2cos())((2)()(
22
2222
222222
222
rL 3
How frequency Reuse Increases Capacity
Example:A GSM communication system uses a frequency reuse
factor of 1/7 and 416 channels available. If 21 channels are allocated as control channels, compute its system capacity. Assume a channel supports 20 users
Channels available for allocation = 416 - 21 = 395Number of cells = 395 / 7 = 57Number of simultaneous users per cell = 20 x 57 = 1140
Number of simultaneous users in system = 7 x 1140 = 7980
Cell Planning Example Suppose you have 33 MHz bandwidth
available, an FM system using 25 kHz channels, how many channels per cell for 4,7,12 cell re-use?
total channels = 33,000/25 = 1320 N=4 channels per cell = 1320/4 = 330 N=7 channels per cell = 1320/7 = 188 N=12 channels per cell = 1320/12 = 110
Smaller clusters can carry more traffic However, smaller clusters result in larger
co-channel interference
28
Practical deployment issues Location to setup antenna
› Antenna towers are expensive› Local people do not like BSs
Antenna/BS does not look like antenna/BS Antenna
› Omni-directional› Directional antenna
Remarks on Reuse Ratio
30
Cochannel Interference
Mobile Station
Serving Base Station
First tier cochannel Base StationSecond tier cochannel
Base Station
R
D1
D2
D3
D4
D5
D6
31
Cochannel Interference
Cochannel interference ratio is given by
M
kkI
CceInterferen
CarrierIC
1
where I is co-channel interference and M is the maximum number of co-channel interfering cells.For M = 6, C/I is given by
÷ø
öçè
æ
M
k
kR
D
C
I
C
1
gwhere g is the propagation path loss slope and g = 2~5.
32
Worst Case of Cochannel Interference
Mobile Station
Serving Base Station Co-channel Base Station
R
D1
D2
D3
D4
D5
D6
Next Topic
HAND’S OFF
33
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