Basics of Cellular Communications
Grade of Service, Interference, & Capacity
The Cellular Concept

Early Mobile Communications


Single, high powered transmitter with an antenna mounted on a tall
tower
The Cellular Concept

© Tallal Elshabrawy
Replace a single high power transmitter (large cell) with many low
power transmitters (small cells) each providing coverage to only a
small portion of the service area
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Frequency Reuse


Each base station is allocated
a group radio channels to be
used within a small geographic
area
Base station in adjacent cells
are assigned channel groups
which contain completely
different channels than
neighboring cells
Cluster
Cluster
G
F
B
A
E
C
D
G
F
G
F
B
A
E
B
A
E
C
D
C
D
Cluster
A Cluster: A Group of N cells that
which collectively use the
complete set of available
frequencies
© Tallal Elshabrawy
Total Number of Channels in the
System:
C=MkN=MS
M: Number of clusters within the system
K: Number of channels per cell
N: Cluster Size
S: Number of available physical channels
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Locating Co-channel Cells


Number of Cells per Cluster N = i2+ij+j2, i, j are non-negative integers
To find nearest co-channel neighbor of a given cell


Move i cells along any chain of hexagons
Turn 600 counter clockwise and move j cells
i=3, j=2, N=19
© Tallal Elshabrawy
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Grade of Service and Capacity
(i.e., Blocking Probability)
Trunking & Grade of Service
Trunked Radio System:
Each user is allocated a channel on per call basis, and upon
termination of the call, the previously occupied channel is
immediately returned to the pool of available channels.
Grade of Service:
A measure of the ability of a user to access the trunked system
GOS measures in cellular networks


Probability that a call is blocked
Probability a call experiences a delay greater than a certain queuing
time
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Traffic Intensity
Traffic intensity generated by each user: Au Erlangs
Au = H
H : average duration of the call
λ : average number of call requests per unit time
For a system containing U users and unspecified number of
channels, Total offered traffic intensity: A Erlangs
A = UAu
In C channel trunked system, if the traffic is equally
distributed among the channels, Traffic intensity per channel
: Ac Erlangs
Ac = UAu/C
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Types of Trunked Systems
Calls Blocked Cleared
Trunking System
Calls Blocked Delayed
Trunking System
No queuing provided for call
requests and calls are blocked if no
available channels
Queuing is provided to hold call
requests. Calls are blocked if no
available channels for a certain
delay
Assumptions:
 Calls arrive as determined by Poisson distribution
 Infinite number of users
 Memoryless arrivals of requests : all users can request channel at any
time
 Probability of user occupying a channel is exponentially distributed
 Finite number of channels available in the trunking pool
© Tallal Elshabrawy
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Erlang B Formula
AC
Pr blocking  C C! k  GOS (Calls Blocked Cleared)
A

k 1 k !
M/M/C/C Queuing System
Inter-arrival time
distribution
Service time
distribution
Queue
Size
Number of
Servers
C Servers and Exponential
Service Times
Exponential Interarrival Time
(Poisson Arrival Process)
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Erlang B Curves
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Erlang C Formula
Pr delay  0  
AC
A  C1 Ak

A  C!  1   
C  k 0 k !

Pr delay  t =Pr delay  0 Pr delay  t delay  0 
C
-
 C-A  t
Pr delay  t =Pr delay  0  e H =GOS (Calls Blocked Delayed)
Average Delay for Calls in Queued System
H
D=Pr delay  0 
CA
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Erlang C Curves
Pr[delay>0]
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Interference and Capacity in
Cellular Systems
Interference & System Capacity
The wireless environment constitutes a shared
medium
Interference is the major limiting factor in
performance of wireless systems in general
Types of Interference:
 Co-channel interference
 Adjacent channel interference
© Tallal Elshabrawy
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Co-channel Interference
Frequency reuse implies that several cells use the same set of channels
G
F
G
F
B
A
E
B
A
E
C
D
G
F
C
D
G
F
B
A
E
G
F
B
A
E
C
D
B
A
E
C
D
G
F
C
D
G
F
B
A
E
B
A
E
C
D
C
D
Frequency reuse = 7
Co-channel interfering cells for cell allocated with channel group A
© Tallal Elshabrawy
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Co-channel Interference, SIR & System Capacity
Co-channel
Interfering Cells
BS 1
H21
H12
P1
H11
R
P2
H22
D
BS 2
R
MT 2
P1H11
SIR1 
P2H21
SIR2 
P2H22
P1H12
MT 1
BS: Base Station
MT: Mobile Terminal
Px: Transmitter power by base station x
Hxy: Small-scale & Large-scale channel between base station x and mobile terminal y
SIRy: Signal-to-Interference Ratio at mobile terminal y
Improving SIR1 by increasing P1 would result in a decrease in SIR2
Improving BOTH SIR1 & SIR2 is possible by increasing the
distance separation between BS1 and BS2
© Tallal Elshabrawy
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Distance Separation between Base Stations
3
R
2
where R is the Cell Radius
R' 
D
j(2R’)
i(2R’)
Q: Co-channel reuse Ratio
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SIR Computations
Assume interference from first tier (ring)
of co-channel interferers
 d
Pr  P0 

d
 0
SIR 
n
D
P0 R d0 
k
 P D
i1
0

 SIR 
i
n
d0 
3N
NB
n

R n
NB
D
i1

D
D
R
n
i
X
D
D
n
Qn

NB
D
Di: interfering distance from
ith co-channel interference
NB No. of co-channel
interfering sites
© Tallal Elshabrawy
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SIR Computations
Assume interference from first tier (ring)
of co-channel interferers
 d
Pr  P0 

d
 0
SIR 
n
D+R
P0 R d0 
k
 P D
i1
0
n
d0 
i
n

R
D+R
n
NB
D
D
n
i
i1
X
Worst Case SIR
 SIR 
 SIR 
D-R
2 D  R 
 2 D  R 
n
 2 D 
n
1
2  Q  1
© Tallal Elshabrawy
n
 2  Q  1
D
D-R
R n
n
R
n
 2  Q
n
Di: interfering distance from
ith co-channel interference
NB No. of co-channel
interfering sites
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SIR & System Capacity
n
SIR  Q , Q=D R  3N
Improving SIR means increasing cluster size, which
corresponds to a decrease in system capacity
Decreasing the cell size does not affect the SIR as
Q=D/R remains constant. A decrease in cell size
corresponds to an increase in system capacity
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Example
In First Generation cellular systems, sufficient voice
quality is achieved when SIR = 18 dB
SIR 
1
2  Q  1
n
 2  Q  1
n
 2  Q
n
N=7Q=4.6. Worst Case SIR = 49.56 (17 dB)
To design cellular system with worst performance better than
18 dB, N=9
 Capacity reduction = 7/9
© Tallal Elshabrawy
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Adjacent Channel Interference
Adjacent channel interference results from imperfect
receiver which allows nearby frequencies to leak into the
passband
Adjacent channel interference can be minimized through
careful filtering and channel assignments
© Tallal Elshabrawy
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Improving Coverage and Capacity in Cellular
Systems: Cell Splitting
Subdividing a congested cell into smaller cells, each with
its own base station and a corresponding reduction in
antenna height and transmitter power
Cell splitting Increasing system capacity by increasing
the number of clusters in a given area
Decreasing Transmitter Power
SIR  Qn , Q=D R  3N
The SIR is independent of
transmitted power as long as it
is the same for all base stations
Why not make Transmitter Power as low as possible?
SNR  Pr Noise
© Tallal Elshabrawy
The SNR must be a above a minimum
threshold controlled by Pr
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