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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

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  1. Hybrid Discrete-Continuous Optimization for the Frequency Assignment Problem in Satellite Communications System Kata KIATMANAROJ, Christian ARTIGUES, Laurent HOUSSIN (LAAS), Frédéric MESSINE (IRIT)

  2. Contents • Problem definition • Discrete optimization • Continuous optimization • Hybrid method • Conclusions and perspectives

  3. Problem definition • To assign a limited number of frequencies to as many users as possible within the service area

  4. 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

  5. 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

  6. Problem definition • Interferenceconstraints Binary interference Cumulative interference i i j j k

  7. Problem definition • Satellite beam & antenna gain

  8. Discrete optimization

  9. Discrete optimization • Integer Linear Programming • Greedy algorithms

  10. Discrete optimization • Integer Linear Programming (ILP)

  11. Discrete optimization • Greedy algorithms • User selection rules • Frequency selection rules

  12. Discrete optimization • Greedy algorithms • User selection rules • Frequency selection rules

  13. Discrete optimization • Performance comparison: ILP vs. Greedy

  14. Discrete optimization • ILP performances

  15. Continuous optimization

  16. 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

  17. Continuous optimization • Matlab’s solver fmincon i j x k

  18. Continuous optimization • Matlab’s solver fmincon i j x k

  19. Continuous optimization • Matlab’s solver fmincon i j x k

  20. Continuous optimization • Matlab’s solver fmincon i j x k

  21. Continuous optimization • Matlab’s solver fmincon i j x k

  22. Continuous optimization • Matlab’s solver fmincon • Parameters: k, MAXINEG, UTVAR

  23. Hybrid discrete-continuous optimization

  24. Hybrid method • Beam moving results with k-MAXINEG-UTVAR = 7-2-0

  25. Hybrid method • Beam moving results with k-MAXINEG-UTVAR = 7-2-0

  26. Hybrid method • Closed-loop implementation

  27. Conclusions and further study • Greedy algorithm vs. ILP • Beam Moving algorithm benefit • Closed-loop implementation benefit vs. time • Further improvements

  28. Thank you

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