1. ç ç Cellular Operators in a Shared Spectrum Sivan Altinakar Supervisors: Tinaz Ekim-Asici Márk Félegyházi

2. S. Altinakar Shared Spectrum, March 2006 2 Summary  Introduction  Modeling  Game Theory  Program  Simulations  Results  Further Research  Conclusion

3. S. Altinakar Shared Spectrum, March 2006 3 Introduction In a given network with non-cooperative operators on a shared frequency band: we are interested in optimizing the interference from the point of view of the network, by setting each base station's transmission power.

4. Modeling

5. S. Altinakar Shared Spectrum, March 2006 5 Modeling Cellular Network  components operators base stations (BS) threshold distance of interference  our approach shared frequency band notion of Interference (related to SINR) finite number of power settings

6. S. Altinakar Shared Spectrum, March 2006 6 Definitions  Signal-to-Interference-plus-Noise-Ratio:  Interference from one Base Station:  Interference from whole Network w s,B,A

7. S. Altinakar Shared Spectrum, March 2006 7 Modeling First Attempt: edge-deletion Mutual Disturbance

8. S. Altinakar Shared Spectrum, March 2006 8  Modeling First Attempt: edge-deletion    B D A C Difficult to interpret

9. S. Altinakar Shared Spectrum, March 2006 9 Modeling Second Attempt: node-deletion Base Station A A1A1 A2A2 A3A3 B1B1 B2B2 B3B3 Base Station B Interference

10. S. Altinakar Shared Spectrum, March 2006 10 Modeling Second Attempt: node-deletion Threshold = 60 59 61 59 pairwise threshold NP-complete

11. S. Altinakar Shared Spectrum, March 2006 11 Modeling Early results in first version (IMax):  quality of a "uniform setting" ( infinite  )  response by "chunks" ( when decreasing )  "almost" equivalent solutions ( N 0 =0 )  effect of changing one base station's setting  coverage constraint & inactive base stations  introduce second version (SMax)

12. S. Altinakar Shared Spectrum, March 2006 12 Modeling A B C X Network Final Model w s,X,C w s,X,A w s,B,A w s,C,A w s,A,C w s,A,B w s,X,B Individual Interference of B over A (w/ setting s) noise factor of B (w/ setting s) Interference over A (w/ setting s) SUM

13. S. Altinakar Shared Spectrum, March 2006 13 Modeling Interference over A

14. Game Theory

15. S. Altinakar Shared Spectrum, March 2006 15 Definition  strategic-form game playerbase station strategypower level utility function(based on Interference )  Nash equilibrium (=stable strategy profile)  price of anarchy Game Theory simultaneous sequential game choice of a strategy No need of an objective function

16. S. Altinakar Shared Spectrum, March 2006 16 Game Theory Utility functions used (for a base station A ): simulations related to the SINR of a virtual user very close to the base station (BA) (BWFS) (BPON)

17. Program

18. S. Altinakar Shared Spectrum, March 2006 18 Program  Initialization: network upper-bound constraint  (if defined) initial strategy profile (=power setting) objective function choice of the next base stations utility function  Result: the final strategy profile reached (result of the game) the best strategy profile encountered (result of the heuristic)  Procedure: While a stopping criteria is not met, perform the steps 1.choose a base station 2.choose a strategy for this base station 3.update the best strategy profile encountered (if necessary) change of strategy = MOVE simultaneously: play game run optimization heuristic }

19. S. Altinakar Shared Spectrum, March 2006 19 Program Stopping criteria: Nash equilibria max # of iterations without move max # of iterations Additional fine-tuning capabilities: limited range of strategies tabu list Choice of the next base station: RANRandomSearch SEQSequenceSearch GTSGlobalTabuSearch DTSDistributedTabuSearch

20. Simulations & Results

21. S. Altinakar Shared Spectrum, March 2006 21 Simulations It's time for a demo…?

22. S. Altinakar Shared Spectrum, March 2006 22 Program Software & Hardware Java 1.5 Dell with 600MHz Intel Pentium III and 128 MB RAM Matlab Implementation: 3 types of classes model representation  model parameters  base stations, operators, network,… algorithms  brute force search  game  tabu search interfaces  SharedSpectrumSolver  MultipleRunLauncher  SSS

23. S. Altinakar Shared Spectrum, March 2006 23 Simulations Environment parameters N = 0.0001  = 4 d thresh = 10 km Network parameters  = ∞ set of power levels = {6.25, 12.5, 25, 50, 100} Experiment variables objective function (IMin, SMax) utility function (Base, BWFS, BPON, ) initial setting (PMin, PMax, PRan) range (free, 1-step) tabu list length (no list, 1, 3, 5, 7) procedure (RAN, SEQ, GTS, DTS)

24. S. Altinakar Shared Spectrum, March 2006 24 Results NE at the end of the procedure: RAN: 99% SEQ: 100% GTS: 30-90% DTS: 65-90% Observations: better with structured network decrease of efficiency with a limited range iterations average between 10 and 60 unusual behavior with particular utility functions Reached Nash equilibria: usually 1 point: PMax for  too high: PMaxMin solution(s) for limited range:extra Nash equilibria (!) starting from PMin:difficulties, range effect Tabu list length (free range, PRan)  no effect on RAN  longer=better (-> SEQ)  Random network: GTS useless for {0,1,3} and DTS for {0,1}  w/ list: DTS better than GTS RandomPyramidal RAN3231 SEQ20 GTS2318 DTS5044 Example 3 utility functions with  = 0.2 tabu = 5 range = free initial s. = PRan = ∞

25. S. Altinakar Shared Spectrum, March 2006 25 Results Objective function value IMin:  optimum is PMax  Nash eq. for almost all utility functions  the game always stabilizes at the optimum  Price of Anarchy = 1 SMax:  optimum is PMaxMin  Nash equ. for no utilitiy  good solutions are rare and purely accidental on the way to PMAX  Price of Anarchy not relevant

26. Further Research

27. S. Altinakar Shared Spectrum, March 2006 27 Further Research  open questions  effect of < ∞  new utility functions  simultaneous strategy choice  edge- and node-deletion

28. Conclusion

29. S. Altinakar Shared Spectrum, March 2006 29 Conclusion  Optimization of the quality of the transmissions in a wireless communication system.  We designed several models, defined a game and build a program for running simulations.  We observed that: usually our utility functions have a unique Nash equilibrium at the maximum power setting the utility functions match perfectly the objective of IMin, but absolutely not SMax other variables such as tabu list length and the range of available strategies influence a game or an algorithm.  Further research could be conducted on the proposed open questions, the influence of  and new utility functions. This could be done theoretically and by using the developed simulator.

30. S. Altinakar Shared Spectrum, March 2006 30 References  Félegyházi and Hubaux Wireless Operators in a Shared Spectrum (2005)  Halldórsson, Halpern, Li and Mirrokni On Spectrum Sharing Games (2004)

31. S. Altinakar Shared Spectrum, March 2006 31 Thank you for your Attention!

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35. S. Altinakar Shared Spectrum, March 2006 35 Thank you for your Attention!

36. S. Altinakar Shared Spectrum, March 2006 36 Results

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42. S. Altinakar Shared Spectrum, March 2006 42 Results End of the procedure: RAN: 99% (a few stopped too early) SEQ: 100% (by definition) GTS: 30-90% (cycling, dependant on utility and network) DTS: 65-90% (cycling, dependant on network) Observations: better with structured network decrease of efficiency with a limited range iterations average between 10 and 60 problems with a particular utility function Reached Nash equilibria: usually 1 point: PMax for  too high: PMaxMin solution(s) for limited range:extra Nash equilibria (!) starting from PMin:sometimes difficulties, range effect

43. S. Altinakar Shared Spectrum, March 2006 43 Results Tabu list length (free range, PRan)  no effect on RAN  longer=better (-> SEQ)  Random network: GTS useless for {0,1,3} and DTS for {0,1}  w/ list: DTS better than GTS Objective function value IMin:  optimum is PMax  Nash equ. for almost all utilities  the game always stabilizes at the optimum  Price of Anarchy = 1 SMax:  optimum is PMaxMin  Nash equ. for no utilitiy  good solutions are rare and purely accidental on the way to PMAX  Price of Anarchy not relevant RandomPyramidal RAN3231 SEQ20 GTS2318 DTS5044 Summary 3 utility functions with  = 0.2 tabu = 5 range = free initial s. = PRan

44. S. Altinakar Shared Spectrum, March 2006 44 A B C X Network

45. S. Altinakar Shared Spectrum, March 2006 45 Base Station A A1A1 A2A2 A3A3 B1B1 B2B2 B3B3 Base Station B

46. S. Altinakar Shared Spectrum, March 2006 46 Definitions Cellular Network

47. S. Altinakar Shared Spectrum, March 2006 47 Remaining Work  Algorithms define a tabu search explore the game theoretical aspect  Program implement all the new options  Simulations analysis of conjecture comparison of objective functions test different algorithms

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49. S. Altinakar Shared Spectrum, March 2006 49 Thank you for your Attention!

50. S. Altinakar Shared Spectrum, March 2006 50 Thank you for your Attention!