Frequency assignment for satellite communication systems Kata KIATMANAROJ Supervisors: Christian ARTIGUES, Laurent HOUSSIN 1

Problem definition Current state of the art Contributions Conclusions and perspectives 2

Problem definition 3

To assign a limited number of frequencies to as many users as possible within a service area 4

Frequency is a limited resource! – Frequency reuse -> co-channel interference – Intra-system interference 5

Simplified beam SDMA: Spatial Division Multiple Access 6 j k i

To assign a limited number of frequencies to as many users as possible within a service area Frequency is a limited resource! – Frequency reuse -> co-channel interference – Intra-system interference Graph coloring problem – NP-hard 7

Interference constraints 8 i j i j k Binary interferenceCumulative interference Acceptable interference threshold Interference coefficients

Assignment – Logical boxes (superframes) – Demand = |F|x|T| – No overlapping within the superframe – Overlapping between superframes (simultaneous)  may create interference 9 0 ≤ o ij ≤ 1 1 2

Superframe structure 10

Frames and satellite beams 11

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Current state of the art 13

Distance FAPs – Maximum Service FAP – Minimum Order FAP – Minimum Span FAP – Minimum Interference FAP Solving methods – Exact method – Heuristics and metaheuristics 14

Two branches – Inter-system interference – Intra-system interference Inter-system interference – Two or more adjacent satellites – Minimize co-channel interference (multiple carriers) Intra-system interference – Multi-spot beams – Geographical zones assuming the same propagation condition 15

Contributions 16

Part 1: Single carrier models Part 2: Multiple carrier models Part 3: Industrial application 17

Single carrier models 18 K. Kiatmanaroj, C. Artigues, L. Houssin, and F. Messine, Frequency assignment in a SDMA satellite communication system with beam decentring feature, submitted to Computational Optimization and Applications (COA) K. Kiatmanaroj, C. Artigues, L. Houssin, and F. Messine, Frequency allocation in a SDMA satellite communication system with beam moving, IEEE International Conference on Communications (ICC), 2012 K. Kiatmanaroj, C. Artigues, L. Houssin, and F. Messine, Hybrid discrete-continuous optimization for the frequency assignment problem in satellite communication system, IFAC symposium on Information Control in Manufacturing (INCOM), 2012

1 frequency over the total duration Same frequency + located too close -> Interference 3 models (supplied by Thales Alenia Space) 19

Model 1 (fixed-beam binary interference) – 40 fixed-beams – 2 frequencies / beam even no user – Interference matrix (binary interference) – Graph coloring: DSAT algorithm -> 4 colors 20 8 frequencies in total

Model 2 (fixed-beam varying frequency) – 40 fixed-beams – 8 frequencies (different within the same beam) – Cumulative interference – Greedy vs. ILP 21

Model 3 (SDMA-beam varying frequency) – SDMA (beam-centered) – 8 frequencies (different within the same beam) – Cumulative interference – Greedy vs. ILP 22

Greedy algorithms – User selection rules – Frequency selection rules 23

Greedy algorithms – User selection rules – Frequency selection rules 24

Integer Linear Programming (ILP) 25

26 Performance comparison ILP 60 sec

27 ILP performances

Continuous optimization 28 * Collaboration with Frédéric Mezzine, IRIT, Toulouse

Beam moving algorithm – For each unassigned user Continuously move the interferers’ beams from their center positions Non-linear antenna gain Minimize the move Not violating interference constraints 29

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

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

32 i j k x User iGainαiαi Δ ix i↓↓↓↓ j k x- Matlab’s solver fmincon

33 i j k x User iGainαiαi Δ ix i↓↓↓↓- j k x- Matlab’s solver fmincon

34 i j k x User iGainαiαi Δ ix i↓↓↓↓ j↓↓↓↓ k↓↓↓↓ x+ Matlab’s solver fmincon

35 Matlab’s solver fmincon k: number of beams to be moved MAXINEG: margin from the interference threshold UTVAR: whether to include user x to the move

36 Matlab’s solver fmincon Parameters: k, MAXINEG, UTVAR

37 Beam moving results with k-MAXINEG-UTVAR = 7-2-0

38 Beam moving results with k-MAXINEG-UTVAR = 7-2-0

39 Closed-loop implementation

Greedy algorithm: efficient and fast ILP: optimal but long calculation time Beam moving: performance improvement Column generation for ILP Fast heuristics for continuous problem Non-linear integer programming 40

Multiple carrier models 41

Binary interference Cumulative interference 42

Binary interference – LF: loading factor 43

Binary interference – A user as a task or an operation – User demand (frequencies) as processing time – Interference pairs as non-overlapping constraints – Disjunctive scheduling problem without precedence constraints – Max. number of scheduled tasks with a common deadline 44

Binary interference – Disjunctive graph and clique – {1,2}, {2,3}, {2,4}, {3,5}, {4,5,6} vs. 7 interference pairs – CP optimizer 45

Binary interference 46

Binary interference 47

Binary interference 48

Cumulative interference – Overlapping duration should be considered 49

Cumulative interference: ILP1 50

Cumulative interference: ILP2 51

Cumulative interference: ILP3 52

Scheduling (CP) vs. ILP (CPLEX) 53

Cumulative interference vs. binary interference 54

Cumulative interference vs. binary interference 55

FAP as scheduling problem Outperform ILP Cumulative -> Binary interference Pattern-based ILP with column generation Heuristics based on interval graph coloring Local search technique 56

Industrial application 57 K. Kiatmanaroj, C. Artigues, L. Houssin, and E. Corbel, Greedy algorithms for time-frequency allocation in a SDMA satellite communication system, International conference on Modeling, Optimization and Simulation (MOSIM), 2012

Terminal types – 50 dBW, 45 dBW – Max. 24 Mbps, 10 Mbps Traffic types – Guaranteed, Non-guaranteed User priority level and handling 58

Symbol rate - Modulation - Coding scheme (RsModCod) – 16 ModCod – 4 symbol rates (Rs) corr. to 5, 10, 15 and 20 MHz – Support bitrate (Mbps) – Different acceptable interference thresholds (alpha) 59

Beam positioning methods – Fixed-beam – SDMA beams 60

Greedy algorithms 61

Fast Flexible Extensive hierarchical search MI (Minimum Interference) MB (Minimum Bandwidth) No performance guarantee 62

Minimum Interference (MI) Superframe 1Superframe 2 63 MI New superframe when the old one is utilized.

Minimum Bandwidth (MB) 64 New superframe before increasing bandwidth

Experimental results 65

Test instances 66

Assignment time (seconds) 67 BC longer time than FB BC30 longer than BC25 MI about the same time as MB

Number of rejected users 68 Largely depended on demand / BW

Highly complex problem and fast calculation time requirement ILP impractical MI: least interference MB: least bandwidth Lower bounds on the number of rejected users Local search heuristics 69

Conclusions and further study 70

Solved FAP in a satellite communication system Binary and cumulative interference Single, multiple carrier, realistic models Greedy algorithm, ILP, scheduling Hyper-heuristics Non-linear integer programming Column generation Local search: math-heuristics 71

Thank you 72

Frame structure constraints 73

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User priority level and handling – – Weighted-Round-Robin ordering 75

Uplink power control – After the resource assignment – PCMargin – Overall interference reduction 76

NbS (superframe) m-n (bin configurations) y1-y2 (low – high frequencies) x1-x2 (leftmost – rightmost time bin) Interference calculation repeats * Use control parameters to limit the search space 77

Number of optima for ILPs 78

Frequency utilization (MHz) 79 Note: system maximum bandwidth 300 MHz

Total interference gap 80