Hybrid Discrete-Continuous Optimization for the
Frequency Assignment Problem in Satellite
Communications System
Kata KIATMANAROJ, Christian ARTIGUES, Laurent HOUSSIN (LAAS),
Frédéric MESSINE (IRIT)
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Contents
•
•
•
•
•
Problem definition
Discrete optimization
Continuous optimization
Hybrid method
Conclusions and perspectives
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Problem definition
• To assign a limited number of frequencies to as many users as
possible within the service area
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Problem definition
• To assign a limited number of frequencies to as many users as
possible within the service area
• Frequency is a limited resource!
– Frequency reuse -> co-channel interference
– Intra-system interference
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Problem definition
• To assign a limited number of frequencies to as many users as
possible within the service area
• Frequency is a limited resource!
– Frequency reuse -> co-channel interference
– Intra-system interference
• Graph coloring problem
– NP-hard
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Problem definition
• Interference constraints
Binary interference
Cumulative interference
i
i
j
j
k
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Problem definition
• Satellite beam & antenna gain
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Discrete optimization
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Discrete optimization
• Integer Linear Programming
• Greedy algorithms
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Discrete optimization
• Integer Linear Programming (ILP)
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Discrete optimization
• Greedy algorithms
– User selection rules
– Frequency selection rules
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Discrete optimization
• Greedy algorithms
– User selection rules
– Frequency selection rules
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Discrete optimization
• Performance comparison: ILP vs. Greedy
180
160
140
120
100
80
60
40
Greedy
ILP (60s)
20
0
20
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60
80
100
120
140
160
180
200
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Discrete optimization
• ILP performances
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Continuous optimization
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Continuous optimization
• Beam moving algorithm
– For each unassigned user
• Continuously move the interferers’ beams from their center positions-> reduce
interference
• Non-linear antenna gain
• Minimize the move
• Not violating interference constraints
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Continuous optimization
• Matlab’s solver fmincon
User i
Gain
αi
Δix
i
x
k
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i
Δix
+
j
Δjx
+
k
Δkx
+
x
0
-
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Continuous optimization
• Matlab’s solver fmincon
User i
Gain
αi
Δix
↓
↓
↓
i
x
j
i
↓+
j
k
k
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-
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Continuous optimization
• Matlab’s solver fmincon
User i
Gain
αi
Δix
↓
↓
↓
i
x
j
i
↓
j
k
k
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-
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Continuous optimization
• Matlab’s solver fmincon
User i
Gain
αi
Δix
↓
↓
↓
i
x
j
i
↓-
j
k
k
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-
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Continuous optimization
• Matlab’s solver fmincon
User i
Gain
αi
Δix
i
↓
↓
↓
↓
j
↓
↓
↓
↓
k
↓
↓
↓
↓
i
x
k
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x
+
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Continuous optimization
• Matlab’s solver fmincon
• Parameters: k, MAXINEG, UTVAR
180
6.0
160
140
5.0
120
4.0
100
3.0
80
60
2.0
40
1.0
20
0.0
0
3
4
5
6
7
8
9
10
k (Number of Interferers)
7.0
160
6.0
140
5.0
120
100
4.0
80
3.0
60
2.0
40
1.0
20
0.0
0
3
4
5
6
7
8
9
10
k (Number of Interferers)
Users (MAXINEG = 1)
Users (MAGINEG = 2)
Users (MAXINEG = 1)
Users (MAGINEG = 2)
Time (MAXINEG = 1)
Time (MAXINEG = 2)
Time (MAXINEG = 1)
Time (MAXINEG = 2)
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Cal. Time / Resggined User (s)
7.0
Number of Reassigned Users
Beam Decentring with UTVAR = 1
Cal. Time / Resggined User (s)
Number of Reassigned Users
Beam Decentring with UTVAR = 0
Hybrid discrete-continuous optimization
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Hybrid method
• Beam moving results with k-MAXINEG-UTVAR = 7-2-0
180
160
140
120
100
80
60
Greedy
40
ILP (60s)
Greedy + Beam Decentring
20
ILP + Beam Decentring
0
20
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60
80
100
120
140
160
180
200
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Hybrid method
• Beam moving results with k-MAXINEG-UTVAR = 7-2-0
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Hybrid method
• Closed-loop implementation
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Conclusions and further study
• Greedy algorithm vs. ILP
• Beam Moving algorithm benefit
• Closed-loop implementation benefit vs. time
• Further improvements
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Thank you
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