Vaggelis G. Douros Stavros Toumpis George C. Polyzos

22/04/23 douros@aueb.gr 1

Power control under best response dynamics for interference mitigation

in a two-tier femtocell network

Vaggelis G. DourosStavros Toumpis

George C. Polyzos

@ RAWNET 2012Paderborn, Germany,

18 May 2012

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Motivation (1)

The food is delicious

Fantastic shirt!

This is urgent!Deadline is today!

The problem: Some couples may not communicate efficiently

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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

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Which is the wireless network?

A two-tier femtocell network

Chandrasekhar et al., IEEE Comm. Mag., 2008

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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

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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

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A two-tier femtocell network power control game (1)

Players N transmitters share the same portion of the spectrum (CDMA Network)

– N1 Macrocell Mobile Nodes (MNs)

– N2 Femtocell Mobile Nodes (FMNs)

Strategy Selection of the transmission power– MN: Pi [0,Pmax]

– FMN: Pi [0,FPmax]

Utility (Payoff)…

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A two-tier femtocell network power control game (2)

N1 MNs– 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 serviceshigh(er) QoS demands

Conclusion: Difficult to describe their needs and restrictions with the same utility function

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… Our choices… MN Utility Function:

FMN Utility Function:

A two-tier femtocell network power control game (3)

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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 serviceshigh(er) QoS demands– No SINRmax

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Nash Equilibrium Existence

Q1: Has the game G at least one NE? Yes! Debreu-Fan-Glicksberg (1952)

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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 Ui

Best Response Dynamics Scheme…

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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)

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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)

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Best Response Dynamics Power Control (4)

Equations (2) and (4) form a best response dynamics power control scheme

(+) simple scheme (+) distributed algorithm

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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

max max{ }i

1 1max

max ,L

N L

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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

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Some Results (1)

Fixed positions The target SINR of each MN increases with a step

equal to 0.5 dB

Voice is feasible

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Some Results (2)

Each FMN gradually moves away from its associated FBS. All other parameters are fixed

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Some Results (3)

Each FMN gradually moves away from its associated FBS. All other parameters are fixed

Voice is feasible

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“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…

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Danke schön!

Vaggelis G. Douros

Mobile Multimedia Laboratory

Department of Informatics

Athens University of Economics and Business

douros@aueb.gr

http://mm.aueb.gr/~douros