Frequency assignment for satellite communication
systems
Kata KIATMANAROJ
Supervisors: Christian ARTIGUES, Laurent HOUSSIN
1
Contents
•
•
•
•
Problem definition
Current state of the art
Contributions
Conclusions and perspectives
2
Problem definition
3
Problem definition
• To assign a limited number of frequencies to as many users as
possible within a service area
4
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
5
Problem definition
• Simplified beam
• SDMA: Spatial Division Multiple Access
j
i
k
6
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
7
Problem definition
• Interference constraints
Binary interference
Cumulative interference
i
i
j
j
k
Acceptable
interference
threshold
Interference
coefficients
8
Problem definition
• Assignment
–
–
–
–
Logical boxes (superframes)
Demand = |F|x|T|
No overlapping within the superframe
Overlapping between superframes (simultaneous)  may create
interference
1
2
0 ≤ oij ≤ 1
9
Problem definition
• Superframe structure
10
Problem definition
• Frames and satellite beams
11
Problem definition
12
Current state of the art
13
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
14
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
15
Contributions
16
Contributions
• Part 1: Single carrier models
• Part 2: Multiple carrier models
• Part 3: Industrial application
17
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
18
Single carrier models
• 1 frequency over the total duration
• Same frequency + located too close -> Interference
• 3 models (supplied by Thales Alenia Space)
19
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
20
Single carrier models
• Model 2 (fixed-beam varying frequency)
–
–
–
–
40 fixed-beams
8 frequencies (different within the same beam)
Cumulative interference
Greedy vs. ILP
21
Single carrier models
• Model 3 (SDMA-beam varying frequency)
–
–
–
–
SDMA (beam-centered)
8 frequencies (different within the same beam)
Cumulative interference
Greedy vs. ILP
22
Single carrier models
• Greedy algorithms
– User selection rules
– Frequency selection rules
23
Single carrier models
• Greedy algorithms
– User selection rules
– Frequency selection rules
24
Single carrier models
• Integer Linear Programming (ILP)
25
Single carrier models
• Performance comparison
180
Model 1
Number of acceped users
160
Model 2 Greedy
140
Model 2 ILP
120
Model 3 Greedy
Model 3 ILP
100
80
60
40
20
0
20
40
60
80
100
120
140
160
180
200
Number of users
ILP 60 sec
26
Single carrier models
• ILP performances
27
Continuous optimization
* Collaboration with Frédéric Mezzine, IRIT, Toulouse
28
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
29
Continuous optimization
• Matlab’s solver fmincon
User i
Gain
αi
Δix
i
x
k
j
i
Δix
+
j
Δjx
+
k
Δkx
+
x
0
-
30
Continuous optimization
• Matlab’s solver fmincon
User i
Gain
αi
Δix
↓
↓
↓
i
x
j
i
↓+
j
k
k
x
-
31
Continuous optimization
• Matlab’s solver fmincon
User i
Gain
αi
Δix
↓
↓
↓
i
x
j
i
↓
j
k
k
x
-
32
Continuous optimization
• Matlab’s solver fmincon
User i
Gain
αi
Δix
↓
↓
↓
i
x
j
i
↓-
j
k
k
x
-
33
Continuous optimization
• Matlab’s solver fmincon
User i
Gain
αi
Δix
i
↓
↓
↓
↓
j
↓
↓
↓
↓
k
↓
↓
↓
↓
i
x
k
j
x
+
34
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
35
Continuous optimization
• Matlab’s solver fmincon
• Parameters: k, MAXINEG, UTVAR
180
6.0
160
140
5.0
120
4.0
100
3.0
80
60
2.0
40
1.0
20
0.0
0
3
4
5
6
7
8
9
10
k (Number of Interferers)
7.0
160
6.0
140
5.0
120
100
4.0
80
3.0
60
2.0
40
1.0
20
0.0
0
3
4
5
6
7
8
9
10
k (Number of Interferers)
Users (MAXINEG = 1)
Users (MAGINEG = 2)
Users (MAXINEG = 1)
Users (MAGINEG = 2)
Time (MAXINEG = 1)
Time (MAXINEG = 2)
Time (MAXINEG = 1)
Time (MAXINEG = 2)
36
Cal. Time / Resggined User (s)
7.0
Number of Reassigned Users
Beam Decentring with UTVAR = 1
Cal. Time / Resggined User (s)
Number of Reassigned Users
Beam Decentring with UTVAR = 0
Continuous optimization
180
180
160
160
140
140
Number of accepted users
Number of accepted users
• Beam moving results with k-MAXINEG-UTVAR = 7-2-0
120
100
80
60
Greedy
40
ILP (60s)
Greedy + Beam Decentring
20
ILP + Beam Decentring
0
20
40
60
80
100 120 140
Number of users
160
180
200
120
100
80
60
Greedy
40
ILP (180s)
20
Greedy + Beam Decentring
ILP + Beam Decentring
0
20
40
60
80
100 120 140
Number of users
160
180
200
37
Continuous optimization
• Beam moving results with k-MAXINEG-UTVAR = 7-2-0
38
Continuous optimization
• Closed-loop implementation
39
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
40
Multiple carrier models
41
Multiple carrier models
• Binary interference
• Cumulative interference
42
Multiple carrier models
• Binary interference
– LF: loading factor
43
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
44
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
45
Multiple carrier models
• Binary interference
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Multiple carrier models
• Binary interference
47
Multiple carrier models
• Binary interference
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Multiple carrier models
• Cumulative interference
– Overlapping duration should be considered
fi  d i
fi
fj  d j
fj
fi  d i
fi
fj
fj  d j
o ij  f i  d i  f j
o ij  d j
49
Multiple carrier models
• Cumulative interference: ILP1
50
Multiple carrier models
• Cumulative interference: ILP2
51
Multiple carrier models
• Cumulative interference: ILP3
52
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
55
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
56
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
57
Industrial application
• Terminal types
– 50 dBW, 45 dBW
– Max. 24 Mbps, 10 Mbps
• Traffic types
– Guaranteed, Non-guaranteed
• User priority level and handling
58
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)
59
Industrial application
• Beam positioning methods
– Fixed-beam
– SDMA beams
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Greedy algorithms
61
Greedy algorithms
• Fast
• Flexible
• Extensive hierarchical search
• MI (Minimum Interference)
• MB (Minimum Bandwidth)
• No performance guarantee
62
Greedy algorithms: MI
• Minimum Interference (MI)
New superframe when the old one is utilized.
MI
Superframe 1
Superframe 2
63
Greedy algorithms
• Minimum Bandwidth (MB)
New superframe before increasing bandwidth
64
Experimental results
65
Computational experiments
• Test instances
66
Experimental results
• Assignment time (seconds)
BC longer time than FB
BC30 longer than BC25
MI about the same time as MB
67
Experimental results
• Number of rejected users
Largely depended on demand / BW
68
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
69
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
71
Thank you
72