frequency assignment for satellite communication systems kata kiatmanaroj supervisors: christian...

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Frequency assignment for satellite communication systems

Kata KIATMANAROJ

Supervisors: Christian ARTIGUES, Laurent HOUSSIN

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Contents

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

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Problem definition

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Problem definition

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

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Problem definition

• 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

Problem definition

• Simplified beam• SDMA: Spatial Division Multiple Access

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j

ki

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Problem definition

• 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

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Problem definition

• Interference constraints

ij

i

j

k

Binary interference Cumulative interference

Acceptable interference threshold

Interference coefficients

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Problem definition

• Assignment– Logical boxes (superframes)– Demand = |F|x|T|– No overlapping within the superframe– Overlapping between superframes (simultaneous) may create

interference

0 ≤ oij ≤ 1

1 2

Problem definition

• Superframe structure

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Problem definition

• Frames and satellite beams

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Problem definition

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Current state of the art

Current state of the art - FAP

• Distance FAPs– Maximum Service FAP– Minimum Order FAP– Minimum Span FAP– Minimum Interference FAP

• Solving methods– Exact method– Heuristics and metaheuristics

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Current state of the art – satellite FAP

• 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

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Contributions

Contributions

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

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Single carrier models

• 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

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Single carrier models

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

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Single carrier models

• 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

8 frequencies in total

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Single carrier models

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

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Single carrier models

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

Single carrier models

• Greedy algorithms– User selection rules– Frequency selection rules

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Single carrier models

• Greedy algorithms– User selection rules– Frequency selection rules

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Single carrier models

• Integer Linear Programming (ILP)

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Single carrier models

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• Performance comparison

20 40 60 80 100 120 140 160 180 2000

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40

60

80

100

120

140

160

180

Model 1Model 2 GreedyModel 2 ILPModel 3 GreedyModel 3 ILP

Number of users

Num

ber o

f acc

eped

use

rs

ILP 60 sec

Single carrier models

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• ILP performances

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Continuous optimization

* Collaboration with Frédéric Mezzine, IRIT, Toulouse

Continuous optimization

• 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

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Continuous optimization

i

j

k

x

User i Gain αi Δix

i Δix +

j Δjx +

k Δkx +

x 0 -

• Matlab’s solver fmincon

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Continuous optimization

i

j

k

x

User i Gain αi Δix

i ↓ ↓ ↓ ↓+

j

k

x -

• Matlab’s solver fmincon

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Continuous optimization

i

j

k

x

User i Gain αi Δix

i ↓ ↓ ↓ ↓

j

k

x -

• Matlab’s solver fmincon

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Continuous optimization

i

j

k

x

User i Gain αi Δix

i ↓ ↓ ↓ ↓-

j

k

x -

• Matlab’s solver fmincon

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Continuous optimization

i

j

k

x

User i Gain αi Δix

i ↓ ↓ ↓ ↓

j ↓ ↓ ↓ ↓

k ↓ ↓ ↓ ↓

x +

• Matlab’s solver fmincon

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Continuous optimization

• 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

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Continuous optimization

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

3 4 5 6 7 8 9 100.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0

20

40

60

80

100

120

140

160

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Beam Decentring with UTVAR = 0

Users (MAXINEG = 1) Users (MAGINEG = 2)Time (MAXINEG = 1) Time (MAXINEG = 2)

k (Number of Interferers)

Num

ber o

f Rea

ssig

ned

User

s

Cal.

Tim

e /

Resg

gine

d Us

er (s

)

3 4 5 6 7 8 9 100.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0

20

40

60

80

100

120

140

160

Beam Decentring with UTVAR = 1

Users (MAXINEG = 1) Users (MAGINEG = 2)Time (MAXINEG = 1) Time (MAXINEG = 2)

k (Number of Interferers)

Num

ber o

f Rea

ssig

ned

User

s

Cal.

Tim

e /

Resg

gine

d Us

er (s

)

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Continuous optimization

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

20 40 60 80 100 120 140 160 180 2000

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40

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80

100

120

140

160

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Greedy

ILP (180s)

Greedy + Beam Decentring

ILP + Beam Decentring

Number of users

Num

ber o

f acc

epte

d us

ers

20 40 60 80 100 120 140 160 180 2000

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40

60

80

100

120

140

160

180

Greedy

ILP (60s)

Greedy + Beam Decentring

ILP + Beam Decentring

Number of users

Num

ber o

f acc

epte

d us

ers

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Continuous optimization

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

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Continuous optimization

• Closed-loop implementation

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Conclusions and further study – Part 1

• 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

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Multiple carrier models

Multiple carrier models

• Binary interference

• Cumulative interference

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Multiple carrier models

• Binary interference

– LF: loading factor

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Multiple carrier models

• 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

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Multiple carrier models

• Binary interference

– Disjunctive graph and clique

– {1,2}, {2,3}, {2,4}, {3,5}, {4,5,6} vs. 7 interference pairs

– CP optimizer

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Multiple carrier models

• Binary interference

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Multiple carrier models

• Binary interference

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Multiple carrier models

• Binary interference

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Multiple carrier models

• Cumulative interference

– Overlapping duration should be considered

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if ii df jf jj df

jiiij fdfo

if ii df jf jj df

jij do

Multiple carrier models

• Cumulative interference: ILP1

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Multiple carrier models

• Cumulative interference: ILP2

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Multiple carrier models

• Cumulative interference: ILP3

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Multiple carrier models

• Scheduling (CP) vs. ILP (CPLEX)

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Multiple carrier models

• Cumulative interference vs. binary interference

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Multiple carrier models

• Cumulative interference vs. binary interference

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Conclusions and further study – Part 2

• FAP as scheduling problem• Outperform ILP• Cumulative -> Binary interference

• Pattern-based ILP with column generation• Heuristics based on interval graph coloring• Local search technique

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Industrial application

• 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

Industrial application

• Terminal types– 50 dBW, 45 dBW– Max. 24 Mbps, 10 Mbps

• Traffic types– Guaranteed, Non-guaranteed

• User priority level and handling

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Industrial application

• 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)

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Industrial application

• Beam positioning methods– Fixed-beam– SDMA beams

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Greedy algorithms

Greedy algorithms

• Fast• Flexible

• Extensive hierarchical search• MI (Minimum Interference)• MB (Minimum Bandwidth)

• No performance guarantee

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Greedy algorithms: MI

• Minimum Interference (MI)

Superframe 1 Superframe 2

MI

New superframe when the old one is utilized.

Greedy algorithms

• Minimum Bandwidth (MB)

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New superframe before increasing bandwidth

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Experimental results

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Computational experiments

• Test instances

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Experimental results

• Assignment time (seconds)

BC longer time than FBBC30 longer than BC25MI about the same time as MB

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Experimental results

• Number of rejected users

Largely depended on demand / BW

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Conclusions and further study – Part 3

• 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

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Conclusions and further study

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Conclusions and further study

• 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

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Thank you