frequency assignment for satellite communication systems kata kiatmanaroj supervisors: christian...
TRANSCRIPT
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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
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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
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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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120
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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
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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