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

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

3 Motivation (2)  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  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 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

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: Informa Telecoms & 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) – N 1 Macrocell Mobile Nodes (MNs) – N 2 Femtocell Mobile Nodes (FMNs) Strategy  Selection of the transmission power – MN: P i  [0,P max ] – FMN: P i  [0,FP max ] Utility (Payoff)…

8 A two-tier femtocell network power control game (2) N 1 MNs – will be mostly used for voice, inelastic traffic – high(er) priority to be served by the operators – low(er) QoS demands (than FMNs) N 2 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 … Our choices … MN Utility Function: FMN Utility Function: A two-tier femtocell network power control game (3)

10 A two-tier femtocell network power control game (4) N 1 MNs – will be mostly used for voice, inelastic traffic – high(er) priority to be served by the operators – use any transmission power up to P max without pricing – low(er) QoS demands (than femtocells) – SINR max N 2 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 SINR max

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 to a 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 U i 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

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 Danke schön ! Vaggelis G. Douros Mobile Multimedia Laboratory Department of Informatics Athens University of Economics and Business