Contents

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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