1. Capacity Analysis of GSM Systems using Slow Frequency
Hopping and Multiple Beam Smart Antennas
Mohamed H. Ahmed and Samy A. Mahmoud
Department of Systems and Computer Engineering
E-Mail: [mhahmed, mahmoud]@sce.carleton.ca
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2. I. Introduction
A. GSM Basic Features
1- GSM (Global System for Mobile communications) is the European standard and
the most popular cellular radio system allover the world.
2- TDMA (or more accurately) Hybrid FDMA/TDMA
Time Frame (4.614 msec)
0 1 2 3 4 5 6 7
Frequency
200 KHz
Time 0.577msec
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3. 3- 8 time slots per carrier, 200KHz carrier spacing, 270.833 Kbps aggregate bit rate
per carrier.
4- Modulation scheme: GMSK with a BT product of 0.3.
5- Coding and Interleaving: Cyclic block code (with a minimum free distance
dmin=2) + 1/2 rate convolutional coding (with constraint length K=5) + 456 data
bits are separated into 8 blocks and then spaced 8 bits apart within the interleaved
block.
6- FDD at 900 MHz and 1900 MHz.
7- The raw data rate is 13 Kbps (full rate coded speech), 7 Kbps (half rate coded
speech).
8- Slow frequency hopping is optional.
9- Power control is used with 20 dB and 30 dB dynamic range in the uplink and
downlink respectively and with a 2 dB power step size.
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4. B. Slow Frequency Hopping
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
........
fi fi fi
No Frequency Hopping
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
........
fi fj fk
Slow Frequency Hopping
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5. • Slow since the hopping rate is much slower than the symbol rate
• Cyclic or Random
• Frequency Diversity:
It combats the frequency selective fading since the frequency is changing every
time frame (4.614 msec)
• Interference Diversity (Averaging):
A different set of cochannel interferes is encountered every frame with different
displacement and propagation parameters
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6. C. Fractional Loading
• A tight frequency planning (e.g. 1/3) is used
• Only a certain FRACTION of the assigned channels to each cell (sector) can be used
simultaneously to preserve the signal quality.
• A Call Admission Control (CAC) algorithm is employed to control the cell loading.
• Less blocking and dropping rates compared to those of the conventional frequency
planning (e.g. 4/12 or 5/15).
System Capacity System Capacity
Blocking limit
Interference limit Interference limit
Blocking limit
System capacity with conventional frequency planning System capacity with fractional loading
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7. D. System Capacity
• The maximum system capacity (C) is given by
C = Nch . LFmax
Where Nch is the number of channels per cell and LFmax is the maximum cell loading
factor.
• The maximum loading factor is determined from the blocking limit using the Erlang-B
formula (for the blocking-limited capacity) and from the outage probability (for the
interference-limited capacity).
• The average system capacity (Cavg) is given by
Cavg = C . (1-Pb) . (1-Pd)
Where Pb is the call blocking probability and Pd is the call dropping probability
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8. E. Smart Antennas
• Switched-Beam Antennas with 12 beams (30o beamwidth each) are utilized
90
1 0
120 60
0.75
−20
150 0.5 30
−40
0.25
−60
180 0
Gain dB
−80
210 330
−100
240 300
−120
−4 −3 −2 −1 0 1 2 3 4
270 Angle
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9. II. Simulation Description
A wireless simulator has been developed with the following features and characteristics:
• It is designed as a time-driven simulator to include the dynamic behavior of the wire-
less network.
• It includes 16 Macrocells (each consists of 3 sectors) with width W=12 Km and length
L=14 Km.
• To avoid the boundary effect a wrap around grid is employed.
• Mobiles are generated uniformly through the covered area.
• The time resolution of the simulation is the frame duration.
• The hand over criterion is based on the absolute received power (the distance or CIR
can be also used).
• Discontinues Transmission (DTX) and Power Control (PC) are included in the model.
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10. A snapshot of the simulator output
16
14
12
10
8
6
Y (Km)
4
2
0
−2 Blocking probability=0.013 Dropping probability=0.009
−4 Macro Base Stations x Mobile Station
−6
−2 0 2 4 6 8 10 12 14
X (Km)
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11. III. Analytical Solution
A. Without Power Control
The cochannel interference from the BS in jth cell at the MS in cell 0
λj
-----
-
–n 10 (1)
I j = A j P l j 10 g ( θ i, θ bj )
t
Because of the frequency hopping we are interested in the average interference which is given by
λj
 -----
- N
 10 – n b
I j = E ( I j ) = qP t E  10  l j ∑ g ( θ i, θ bj = φ k ) f ( θ bj = φ k ) (2)
  k=1
 
It is straightforward to show that
λj
 -----
-
 10  ( ασ ) 2
E  10  = exp  --------------- (3)
   2 
 
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12. Sector 1
MS
rm
θ bm
θm
θj
l j ( r m, θ m )
Cell 0
Dj
MS
θi rj θ ij
θ bj
Cell j
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13. Then total interference is given by
N int
I tot ( r m, θ ) =
m ∑ Ij (4)
i=1
While the carrier power from the BS to the MS at cell 0 is given by
λ
-----
-
–n 10 (5)
C = P t r m 10 g ( θ m, θ bm )
Thus the CIR can be expressed as
λ
-----
-
– n 10
P t r m 10 g ( θ m, θ bm )
CIR = ---------------------------------------------------------
- (6)
I tot
After some manipulations the outage probability can be given by
2π
-----
-
3 R
β
-
P ( CI R < γ ) = ∫ ∫  1 – Q  --   f ( r m, θ m )r m dr m dθ m (7)
  σ 
0 0
 γ I ( r , θ )r n 
 tot m m m
-
where β=10 log  ------------------------------------------ 

 P t g  θ m, θ bm  
 
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14. B. With Power Control
Here the transmitted power is adjusted such that the received power at the BS from each MS is
constant S. Thus the interference from the BS at jth cell at the MS in cell 0 is
( λ j – λ jj )
-
----------------------- g ( θ , θ ) (8)
 r j n 10 i bj
-
I j = A j S  ---- 10 -------------------------
-
 l j g ( θ ij, θ bj )
Thus the mean value is
2π
-----
-
3 R
–n 2 n g ( θ i, θ bj )
-r
I j = E ( I j ) = q l j S exp ( ( ασ ) ) ∫ ∫ r j f ( r j, θ ij ) ------------------------- j dr j dθ ij (9)
g ( θ ij, θ bj )
0 0
After some manipulation the outage probability can be expressed as
2π
-----
-
3 R
S
-
P ( CI R < γ ) = ∫ ∫ u  I tot ( r m, θ m ) – -- f ( r m, θ m )r m dr m dθ m (10)
 γ
0 0
Where u( ) is the unit step function
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15. IV. Results
CDF(CIR) at 20% loading
0 0
10 10
−1 −1
10 10
−2 −2
10 10
CDF
CDF
−3 −3
10 10
−4 −4
10 10
SC−Simulation SC−Simulation
MB−Simulation MB−Simulation
SC−Analysis SC−Analysis
MB−Analysis MB−Analysis
−5 −5
10 10
4 6 8 10 12 14 16 18 4 6 8 10 12 14 16 18
CIR (dB) CIR (dB)
Without PC With PC
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16. CDF(CIR) at 40% loading
0 0
10 10
−1 −1
10 10
−2 −2
10 10
CDF
CDF
−3 −3
10 10
−4 −4
10 10
SC−Simulation SC−Simulation
MB−Simulation MB−Simulation
SC−Analysis SC−Analysis
MB−Analysis MB−Analysis
−5 −5
10 10
4 6 8 10 12 14 16 18 4 6 8 10 12 14 16 18
CIR (dB) CIR (dB)
Without PC With PC
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17. CDF(CIR) at 60% loading
0 0
10 10
−1 −1
10 10
−2 −2
10 10
CDF
CDF
−3 −3
10 10
−4 −4
10 10
SC−Simulation SC−Simulation
MB−Simulation MB−Simulation
SC−Analysis SC−Analysis
MB−Analysis MB−Analysis
−5 −5
10 10
4 6 8 10 12 14 16 18 4 6 8 10 12 14 16 18
CIR (dB) CIR (dB)
Without PC With PC
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18. 0
10
MB+No PC
SC+No PC
MB+PC
SC+PC
−1
10
−2
10
−3
10
Outage Probability (CDF(CIR=9dB))
−4
10
−5
10
5 10 15 20 25 30 35 40 45 50 55 60 65 70
Loading Factor LF%
Outage Probability versus Loading Factor
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19. Table 1 Outage Probability (CDF(CIR = 9 dB)) for uplink at different loading factor values
Antenna CDF (CIR = 9 dB)
Type
LF = 10% LF = 20% LF = 30% LF = 40% LF = 50% LF = 60%
3 sectors 2.9x10-02 5.7x10-02 8.1x10-02 9.0x10-02 1.0x10-01 1.2x10-01
no PC Multiple 7.5x10-03 1.9x10-02 3.3x10-02 4.5x10-02 5.6x10-02 6.7x10-02
Beam
3 sectors 1.0x10-05 6.0x10-02 1.3x10-01 2.5x10-01 4.1x10-01 6.3x10-01
with PC Multiple 1.0x10-05 1.0x10-05 1.0x10-05 1.0x10-05 1.0x10-05 2.0x10-02
Beam
Table 2 Maximum loading factor for the uplink with various outage probability requirements
Maximum Loading Factor (LFmax)
Antenna type pmax=2% pmax=4% pmax=10% Outage
with PC No PC with PC No PC with PC No PC
3 sectors 18% 7% 19% 15% 26% 40%
Multiple Beam 60% 20% 70% 36% 100% 90%
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20. V. Conclusions
1-The Network Capacity of FH-GSM can be determined analytically with a high degree of
accuracy and with less computational time compared to the simulation approach.
2-The dependence of the signal quality (in terms of the CDF(CIR)) on the loading factor is
derived analytically and by simulation
3- The dependence of the CDF(CIR) on the loading factor shows the importance of the
CAC algorithms to enhance the system capacity without degrading the signal quality.
4-The use of multiple beam antennas in FH-GSM systems can enhance the system capac-
ity by 100-150%.
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