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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ContentsContents
• Problem definition• Discrete optimization• Continuous optimization• Hybrid method• Conclusions and perspectives
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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
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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
• Graph coloring problem– NP-hard
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Problem definitionProblem definition
• Interference constraints
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Binary interference Cumulative interference
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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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• Matlab’s solver fmincon
Continuous optimizationContinuous optimization
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• Matlab’s solver fmincon
Continuous optimizationContinuous optimization
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• Matlab’s solver fmincon
Continuous optimizationContinuous optimization
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• Matlab’s solver fmincon
Continuous optimizationContinuous optimization
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• 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
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