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Hybrid Discrete-Continuous Optimization for the Frequency Assignment Problem in Satellite Communications System Kata KIATMANAROJ, Christian ARTIGUES, Laurent HOUSSIN (LAAS), Fr édéric MESSINE (IRIT). Contents. Problem definition Discrete optimization Continuous optimization Hybrid method - PowerPoint PPT Presentation
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Hybrid Discrete-Continuous Optimization for the Frequency Assignment Problem in Satellite
Communications System
Kata KIATMANAROJ, Christian ARTIGUES, Laurent HOUSSIN (LAAS), Frédéric MESSINE (IRIT)
1INCOM-2012
ContentsContents
• Problem definition• Discrete optimization• Continuous optimization• Hybrid method• Conclusions and perspectives
2INCOM-2012
Problem definitionProblem definition
• To assign a limited number of frequencies to as many users as possible within the service area
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Problem definitionProblem 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
4INCOM-2012
Problem definitionProblem 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 definitionProblem definition
• Interference constraints
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k
Binary interference Cumulative interference
INCOM-2012
Problem definitionProblem definition
• Satellite beam & antenna gain
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Discrete optimization
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Discrete optimizationDiscrete optimization
• Integer Linear Programming• Greedy algorithms
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Discrete optimizationDiscrete optimization
• Integer Linear Programming (ILP)
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Discrete optimizationDiscrete optimization
• Greedy algorithms– User selection rules– Frequency selection rules
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Discrete optimizationDiscrete optimization
• Greedy algorithms– User selection rules– Frequency selection rules
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Discrete optimizationDiscrete optimization
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• Performance comparison: ILP vs. Greedy
Discrete optimizationDiscrete optimization
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• ILP performances
Continuous optimization
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Continuous optimizationContinuous 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 optimizationContinuous optimization
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i
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k
x
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• Matlab’s solver fmincon
Continuous optimizationContinuous optimization
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k
x
INCOM-2012
• Matlab’s solver fmincon
Continuous optimizationContinuous optimization
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i
j
k
x
INCOM-2012
• Matlab’s solver fmincon
Continuous optimizationContinuous optimization
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i
j
k
x
INCOM-2012
• Matlab’s solver fmincon
Continuous optimizationContinuous optimization
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i
j
k
x
INCOM-2012
• Matlab’s solver fmincon
Continuous optimizationContinuous optimization
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• Matlab’s solver fmincon• Parameters: k, MAXINEG, UTVAR
Hybrid discrete-continuous optimization
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Hybrid methodHybrid method
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• Beam moving results with k-MAXINEG-UTVAR = 7-2-0
Hybrid methodHybrid method
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• Beam moving results with k-MAXINEG-UTVAR = 7-2-0
Hybrid methodHybrid method
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• Closed-loop implementation
Conclusions and further studyConclusions 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
28INCOM-2012