Vaggelis G. Douros Stavros Toumpis George C. Polyzos

1. Power control under best response dynamics for interference mitigation in a two-tier femtocell network Vaggelis G. Douros Stavros Toumpis George C. Polyzos @ RAWNET 2012 Paderborn, Germany, 18 May 2012 douros@aueb.gr

2. Motivation (1) Deadline is today! This is urgent! The food is delicious Fantastic shirt! The problem: Some couples may not communicate efficiently 

3. Motivation (2) • N couples of friends discuss in the same cafeteria • Each couple aims at achieving a (different) “minimum quality of discussion” • Discussions of other couples may prevent an efficient communication • N pairs of wireless nodes (e.g., BSs-MNs, FBSs-FMNs) transmit their data sharing the same wireless medium • Each pair aims at achieving a (different) QoS target • Interference among wireless devices may prevent an efficient communication Competition for resources among players≡ Non-Cooperative Game Interference mitigation through power control

4. Which is the wireless network? A two-tier femtocell network Chandrasekhar et al., IEEE Comm. Mag., 2008

5. Why Femtocells? (1) • Femtocells: • low-power access points • connect to the service provider’s network via broadband • provide voice and broadband services • allow a small number of simultaneous calls and data sessions http://www.smallcellforum.org

6. Why Femtocells? (2) • (+) dense deployment increase spectrum reuse • (+) better indoor coverage superior indoor reception • (+) low(er) cost (than macrocell deployment) • (+) plug and play installation • … • (-) interference: This is the challenge! Source: InformaTelecoms & Media, October 2011

7. A two-tier femtocell network power control game (1) • Players N transmitters share the same portion of the spectrum (CDMA Network) • N1Macrocell Mobile Nodes (MNs) • N2 Femtocell Mobile Nodes (FMNs) • Strategy Selection of the transmission power • MN: Pi  [0,Pmax] • FMN: Pi [0,FPmax] • Utility (Payoff)…

8. A two-tier femtocell network power control game (2) • N1MNs • will be mostly used for voice, inelastic traffic • high(er) priority to be served by the operators • low(er) QoS demands (than FMNs) • N2 FMNs • are deployed by indoor users for their self interest • should not create high interference to MNs • focus on data serviceshigh(er) QoS demands • Conclusion: Difficult to describe their needs and restrictions with the same utility function

9. A two-tier femtocell network power control game (3) • … Our choices… • MN Utility Function: • FMN Utility Function:

10. A two-tier femtocell network power control game (4) • N1 MNs • will be mostly used for voice, inelastic traffic • high(er) priority to be served by the operators • use any transmission power up to Pmax without pricing • low(er) QoS demands (than femtocells) • SINRmax • N2 FMNs • FMNs should not create high interference to MNs • pricing is used to discourage them from creating high interference to the macrocell users • focus on data serviceshigh(er) QoS demands • No SINRmax

11. Nash Equilibrium Existence • Q1: Has the game G at least one NE? • Yes! • Debreu-Fan-Glicksberg(1952)

12. Best Response Dynamics Power Control (1) • Q2: How can we devise an algorithm that converges toa NE? • The two-tier femtocell game G is a collection of N parallel optimization problems • each (F)MN aims at maximizing its own utility function Ui • Best Response Dynamics Scheme…

13. Best Response Dynamics Power Control (2) • MN Optimization problem • which leads to: (1) • See also [Foschini & Miljanic, TVT’93] [Grandhi et al., WPC’94] • So, the best response dynamics scheme is: (2)

14. Best Response Dynamics Power Control (3) • FMN Optimization problem • which leads to: (3) • See also [Alpcan, Basar, Srikant, Altman, Wireless Netw.‘02] • So, the best response dynamics scheme is: (4)

15. Best Response Dynamics Power Control (4) • Equations (2) and (4) form a best response dynamics power control scheme • (+) simple scheme • (+) distributed algorithm

16. Uniqueness of the Nash Equilibrium (1) • Q3: Does the best response dynamics power control scheme based on equations (2) and (4) converge to the NE that is defined by equations (1) and (3) respectively? • In general, there are games where the best response dynamics do not always* lead to a NE • *from every initial strategy

17. Uniqueness of the Nash Equilibrium (2) • Q4: Is this the unique NE of the game G? • Answers: Yes & Yes! • Theorem: Let L be the spread factor of the system and be the maximum SINR target among all the MNs. If , then: • The two-tier femtocell network game has a unique NE • The power control scheme under best response dynamics for FMNs and MNs converges to this NE

18. Topology/Scenarios • Topology parameters are based on an extensive study by the smallcellforum • Symmetric topologies, vary (F)MN-(F)BS positions and/or SINR targets

19. Some Results (1) • Fixed positions • The target SINR of each MN increases with a step equal to 0.5 dB Voice is feasible

20. Some Results (2) • Each FMN gradually moves away from its associated FBS. All other parameters are fixed

21. Some Results (3) • Each FMN gradually moves away from its associated FBS. All other parameters are fixed Voice is feasible

22. “The Meat” • Two-tier femtocell networks • heterogeneous needs • heterogeneous targets • interference remains a big challenge • We show the existence and uniqueness of a NE and devise an algorithm based on best response dynamics that converges to it • Interference mitigation in various scenarios is achieved • Things to do: Stackelberg game formulation, maximize total revenue, maximize social welfare…

23.  Dankeschön! Vaggelis G. Douros Mobile Multimedia Laboratory Department of Informatics Athens University of Economics and Business douros@aueb.gr http://mm.aueb.gr/~douros