Spatial Reuse in Spectrum Access: A Matrix Spatial Congestion Games Approach

1. Spatial Reuse in Spectrum Access:A Matrix Spatial Congestion Games Approach Kai Zhou, Gaofei Sun, Xinbing WangDepartment of Electronic Engineering Shanghai Jiao Tong University Zhiyong Feng Key Lab. of Universal Wireless Commun. Beijing University of Posts and Telecommunications

2. Outline • Introduction • Motivations • Related work • Objectives • System Model and Problem Formation • Potential Game Approach • Matrix Spatial Congestion Games • Discussion Based on Numeric Results • Conclusion and Future Work

3. Motivations • How to allocate spectrum in CRNs efficiently? • system throughput • fairness issue • … …

4. Motivations • Spatial reuse is a key feature in wireless networks • Interference model • … …

5. Related works Congestion ! [3]R. Rosenthal, “A class of games possessing pure-strategy nash equilibria,” INTERNATIONAL JOURNAL OF GAME THEORY, vol. 2, no. 1, pp. 65–67, 1973. [8] R. Southwell and J. Huang, “Convergence dynamics of resource homogeneous congestion games,” in Proc. International Conference on Game Theory for Networks (GameNets). Shanghai, China, Apr. 2011. [9] L. Law, J. Huang, M. Liu, S. Li et al., “Price of anarchy for cognitive mac games,” in Proc. Global Telecommunications Conference. Hawaii, Dec. 2009. • Model distributed spectrum competition as Congestion Games • Congestion games [3] • Convergence speed [8] • Price of anarchy [9]

6. Related works directed or undirected weighted or unweighted [11]C. Tekin, M. Liu, R. Southwell, J. Huang, and S. H. A. Ahmad, “Atomic congestion games on graphs and its applications in networking,” IEEE Transactions on Networking, In Press. [12] M. Liu and Y. Wu, “Spectum sharing as congestion games,” in Proc. the 46th Annual Allerton Conference on Communication, Control, and Computing. IAllerton House, Illinois, Sept. 2008. [13] S. Ahmad, C. Tekin, M. Liu, R. Southwell, and J. Huang, “Spectrum sharing as spatial congestion games,” Arxiv preprint arXiv:1011.5384,2010. • Extend congestion games to consider spatial reuse • Virtual resource [13] • Conflict graph [11] [12]

7. Objectives Converge Local Updates Equilibrium ? • Will SUs’ local selfish updates of channel selection finally converge to an Equilibrium ? Multi-radios for each SU Weighted interference level

8. Outline • Introduction • System Model and Problem Formation • System model • Problem formation • Potential Game Approach • Matrix Spatial Congestion Games • Discussion Based on Numeric Results • Conclusion and Future Work

9. System model • User set : • Resource (channel) set : • Homogeneous • Heterogeneous • Payoff functions : • User-specific • Non-user-specific • Non-increasing with n • Utility :

10. Problem formation User number (N=4) Channel number (R=3,m=2) User number User number Channel selection matrix Interference level matrix • Channel selection matrix • Each user can access channels simultaneously ( ) • Interference level matrix

11. Problem formation • Strategy profile: • Matrix Spatial Congestion Games (MSCG) • Four types of MSCG according to payoff function: • non-resource-specific and non-user-specific • non-resource-specific and user-specific • resource-specific and non-user-specific • resource-specific and user-specific

12. Outline Introduction System Model and Problem Formation Potential Game Approach Matrix Spatial Congestion Games Discussion Based on Numeric Results Conclusion and Future Work

13. Potential game approach • Potential function [3]: • Basic idea : • for each user : • the value of potential function changes correlating to the change of each user’s payoff e.g. • potential function is bounded • users can’t update infinitely to increase payoffs [3] R. Rosenthal, “A class of games possessing pure-strategy nash equilibria,”INTERNATIONAL JOURNAL OF GAME THEORY, vol. 2, no. 1,pp. 65–67, 1973.

14. Potential game approach Local updates FIP PNE • Finite improvement property (FIP) • Improvement steps • Improvement steps are finite • Pure Nash Equilibrium (PNE)

15. Outline Introduction System Model and Problem Formation Potential Game Approach Matrix Spatial Congestion Games Discussion Based on Numeric Results Conclusion and Future Work

16. MSCG –I/IV • MSCG with non-user-specific & non-resource specific payoff functions • payoff function : • utility : • potential function : • proved:

17. MSCG – I/IV • Theorem 1:For matrix spatial congestion games with non-resource-specific and non-user-specific payoff functions, every asynchronous improvement step path is finite and converges to a pure Nash Equilibrium (PNE). Furthermore, any change of the strategy profile can not result in a grater value of potential function , which indicating that this PNE is also a local optimum in potential function. • FIP PNE • Local optimum in potential function

18. MSCG – II/IV • MSCG with user-specific & non-resource specific payoff functions • payoff function : • utility : • potential function : , where

19. MSCG – II/IV • Proved: with increasing and non-increasing with when increases, decreases accordingly • Theorem 2: For matrix spatial congestion games with non-resource-specific and user-specific payoff functions, every asynchronous improvement path is finite and converges to a pure Nash Equilibrium (PNE).

20. MSCG – III,IV/IV • Proposition 1: For MSCG with resource-specific and non-user-specific payoff functions, FIP does not hold. • PNE ? • Proposition 2: For MSCG with resource-specific and user-specific payoff functions, FIP does not hold. Moreover, a PNE dose not necessarily exist.

21. Outline • Introduction • System Model and Problem Formation • Potential Game Approach • Matrix Spatial Congestion Games • Discussion Based on Numeric Results • user number • channel utilization proportion • updating mechanism • Conclusion and Future Work

22. User number Average improvement steps total improvement steps User number User number • using updating steps indicating convergence speed • users update in a predefined order

23. Channel utilization proportion Average improvement steps Channel utilization proportion Channel utilization proportion: more radios better ?

24. Updating mechanism improvement steps User number Mechanism 1: updating in a predefined order Mechanism 2: maximum improvement first [8] [8] R. Southwell and J. Huang, “Convergence dynamics of resource homogeneous congestion games,” in Proc. International Conference on Game Theory for Networks (GameNets). Shanghai, China, Apr. 2011.

25. Outline • Introduction • System Model and Problem Formation • Potential Game Approach • Matrix Spatial Congestion Games • Discussion Based on Numeric Results • Conclusion and Future Work • Conclusion • Future work

26. Conclusion • MSCG model • Multi-radio • Spatial reuse with weighted interference level • Four types of MSCG • General payoff functions • FIP • PNE • Convergence speed analysis

27. Future work • More work on later two types of MSCG • achieve PNE? • Network topology • Charging scheme • Performance of PNE • POA analysis • Fairness issue • Distributed algorithm to achieve global optimality • Convergence speed

28. Thank you !