Optimization of Cellular Operators in Shared Spectrum: Game Theory Approaches and Simulations

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

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

4. Modeling

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 Shared Spectrum, March 2006

6. Definitions • Signal-to-Interference-plus-Noise-Ratio: • Interference from one Base Station: • Interference from whole Network ws,B,A Shared Spectrum, March 2006

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

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

9. Modeling Second Attempt: node-deletion Base Station A Base Station B Interference B1 A1 A2 B2 A3 B3 Shared Spectrum, March 2006

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

11. Modeling Early results in first version (IMax): • quality of a "uniform setting" ( infinite b ) • response by "chunks" ( when decreasing b ) • "almost" equivalent solutions ( N0=0 ) • effect of changing one base station's setting • coverage constraint & inactive base stations  introduce second version (SMax) Shared Spectrum, March 2006

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

13. Modeling Interference over A Shared Spectrum, March 2006

14. Game Theory

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

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

17. Program

18. Program • Initialization: • network • upper-bound constraint b (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 • choose a base station • choose a strategy for this base station • update the best strategy profile encountered (if necessary) • simultaneously: • play game • run optimization • heuristic } change of strategy = MOVE 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: • RAN RandomSearch • SEQ SequenceSearch • GTS GlobalTabuSearch • DTS DistributedTabuSearch Shared Spectrum, March 2006

20. Simulations &Results

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

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

24. Results b = ∞ 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 g 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 • Example • 3 utility functions with • g = 0.2 • tabu = 5 • range = free • initial s. = PRan 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 Shared Spectrum, March 2006

26. Further Research

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

28. Conclusion

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 b and new utility functions. This could be done theoretically and by using the developed simulator. 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) Shared Spectrum, March 2006

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