12/10/[email protected] 1 power control under best response dynamics for interference mitigation in...
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19/04/23 [email protected] 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
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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
http://mm.aueb.gr/~douros