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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

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Problem definition Discrete optimization Continuous optimization Hybrid method Conclusions and perspectives 2INCOM-2012

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To assign a limited number of frequencies to as many users as possible within the service area 3INCOM-2012

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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

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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 5INCOM-2012

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Interference constraints 6 i j i j k Binary interferenceCumulative interference INCOM-2012

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Satellite beam & antenna gain 7 INCOM-2012

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Discrete optimization 8INCOM-2012

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Integer Linear Programming Greedy algorithms 9 INCOM-2012

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Integer Linear Programming (ILP) 10 INCOM-2012

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Greedy algorithms – User selection rules – Frequency selection rules 11 INCOM-2012

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Greedy algorithms – User selection rules – Frequency selection rules 12 INCOM-2012

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13 INCOM-2012 Performance comparison: ILP vs. Greedy

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14 INCOM-2012 ILP performances

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Continuous optimization 15INCOM-2012

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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 16 INCOM-2012

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17 i j k x User iGainαiαi Δ ix i + jΔ jx + kΔ kx + x0- INCOM-2012 Matlab’s solver fmincon

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18 i j k x User iGainαiαi Δ ix i↓↓↓↓+ j k x- INCOM-2012 Matlab’s solver fmincon

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19 i j k x User iGainαiαi Δ ix i↓↓↓↓ j k x- INCOM-2012 Matlab’s solver fmincon

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20 i j k x User iGainαiαi Δ ix i↓↓↓↓- j k x- INCOM-2012 Matlab’s solver fmincon

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21 i j k x User iGainαiαi Δ ix i↓↓↓↓ j↓↓↓↓ k↓↓↓↓ x+ INCOM-2012 Matlab’s solver fmincon

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22INCOM-2012 Matlab’s solver fmincon Parameters: k, MAXINEG, UTVAR

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Hybrid discrete-continuous optimization 23INCOM-2012

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24INCOM-2012 Beam moving results with k-MAXINEG-UTVAR = 7-2-0

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25INCOM-2012 Beam moving results with k-MAXINEG-UTVAR = 7-2-0

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26INCOM-2012 Closed-loop implementation

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Greedy algorithm vs. ILP Beam Moving algorithm benefit Closed-loop implementation benefit vs. time Further improvements 27INCOM-2012

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Thank you 28INCOM-2012

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