A Bargaining Approach to Power Control in Networks of Autonomous Wireless Entities

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A Bargaining Approach to Power Control in
Networks of Autonomous Wireless Entities

• Vaggelis G. Douros
• George C. Polyzos
• Stavros Toumpis

ACM MOBIWAC 17 Oct. 2010,
Bodrum, Turkey
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Motivation (1)
This is urgent!
Deadline is today!
The food is delicious
Fantastic shirt!
Some couples may not communicate efficiently ?
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Motivation (2)

• N pairs of wireless nodes (e.g., BSs-MNs,
  APs-Clients) transmit their data sharing the same
  wireless medium
• Each pair aims at achieving a (different) (SINR)
  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 multiple players,
where the influence from each player is different
Weighted Congestion Game
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Fundamentals of SINR-Based Power Control (1)

• Power control is a standard radio resource
  management method for interference mitigation
• Analogy A person that increases/ reduces his
  level of voice
• The Simplified Foschini-Miljanic Formula (FM)
  FM, TVT 93, Bambos, IEEE Pers.
  Comm. 98
• () fully distributed algorithm
• no need for cooperation among the nodes to apply
  FM
• At steady state, for each node i Pi(k1)Pi(k)
• each node i has either achieved its SINR target
  ?i or it is below its target and transmits with
  Pmax

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Fundamentals of SINR-Based Power Control (2)

• The problem Even in small topologies, there are
  cases that it is impossible for all wireless
  nodes to achieve their SINR targets
• One solution One/ many nodes need to power
  off.
• E.g. Trunc(ated) Power Control Zander, TVT 92
• N-1 links apply a power control algorithm
• the one that is furthest from its SINR target
  powers off
• (-) Unfair for this node no opportunity to
  achieve its target
• More importantly, how to oblige an autonomous
  entity to power off?

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The Bargaining Foschini-Miljanic Scheme (BFM)

• A heuristic approach that aims at maximizing the
  number of links that have achieved their targets
• Should be at most N-1 (N-1)-feasible
  solution
• Bargaining as an incentive tool for negotiations
  among unsatisfied nodes (those that are below
  their SINR targets)
• BFM works on top of FM, starting from its steady
  state
• Links that have achieved their targets apply FM
• Unsatisfied links negotiate in pairs. Each one
  uses part of its budget to make an offer to the
  other
• I offer you X credits if you reduce your power Y
  
• These virtual credits may be used for future
  networking functions Blazevic et al., IEEE Comm.
  Mag. 01

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Fundamentals of BFM (1)

• How to choose who makes an offer?
• How to choose to whom it offers?
• Choose randomly one among the set of unsatisfied
  nodes
• (-) This demands an external entity
• A distributed approach Each unsatisfied link
  decides independently whether it is a Seller
  or a Buyer and broadcasts its status to the
  network
• Which is the desired percentage reduction Pred?
• The minimum needed to achieve its target in the
  next round (but if, e.g., the node is distant
  this may be impossible)

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Fundamentals of BFM (2)

• Tx1 computes the reward R1?2 that is willing to
  offer to Tx2
• If Tx2 accepts its offer, then Tx1 updates its
  power according to the FM scheme and achieves its
  target
• If Tx2 rejects its offer, then Tx1 voluntarily
  reduces a bit its current transmission power
  (0ltclt1)
• Otherwise, all nodes may stay at the same state

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Fundamentals of BFM (3)

• Tx2 computes through the reward R2?1 that would
  have given if Tx2 had asked for the same Pred
• If R2?1 R1?2,Tx2 accepts the offer and
  transmits at PredP2(k)
• If R2?1 gt R1?2,Tx2 rejects the offer and updates
  its power using the FM algorithm
• Can you show us an example to see how this works?
• Just raise your hand during the questions -)

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On the Number of (N-1)-feasible Solutions

• Number of (N-1)-feasible solutions after the
  application of both BFM and Trunc FM for 50000
  different scenarios
• Similar Performance with Trunc FM
• But Trunc FM is not suitable for autonomous nodes
  and it is unfair

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On the Long Term Fairness of BFM (1)

• Application of BFM for the same set of nodes for
  10000 transmission rounds
• The budget at the start of the (m1)th round is
  the one at the end of the mth round
• For every period of 100 transmission rounds, we
  count how many times Tx5 and Tx6 (the only
  unsatisfied nodes in this particular example) do
  not achieve their targets

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On the Long Term Fairness of BFM (2)

• There is an average ratio 32 per period
• () This ratio represents well every transmission
  period
• () All nodes get the opportunity to transmit
  their data
• (-) In Trunc FM, the weakest node always powers
  off
• () This ratio is independent of the initial
  budget of the nodes
• Due to the dynamically adjusting mechanism that
  nodes follow when they either make or evaluate an
  offer

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The Meat

• BFM A heuristic approach for joint power control
  and bargaining that aims at maximizing the number
  of satisfied entities, in cases that it is
  impossible for all of them to achieve their SINR
  targets
• () distributed implementation
• () efficient finds out a large number of
  solutions
• () fair statistical rotation of unsatisfied
  nodes
• Ongoing Work To cast this problem as a weighted
  congestion game and apply findings from recent
  works of the algorithmic game theory

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? Tesekkür ederim ?

• Vaggelis G. Douros
• Mobile Multimedia Laboratory
• Department of Informatics
• Athens University of Economics and Business
• douros_at_aueb.gr
• http//mm.aueb.gr/douros

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BACKUP
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Performance Evaluation of FM
Even in small topologies, where few entities
coexist, there are many cases where at least one
node cannot achieve its SINR target
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Topology
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FM SINR Evolution
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Trunc FM SINR Evolution
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Trunc FM Power Evolution
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BFM SINR Evolution
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BFM Power Evolution
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Simulation Parameters (1)
Parameter Value
Links of each Topology 4, 7, 10
Scenarios per Topology 50000
Max Iterations per Algorithm 1000
Simulation Terrain A square of size 100
Transmitters (Tx) Distribution Uniform
Receivers (Rx) Distribution Rx is placed randomly in the interior of a circle of radius 5 from its associated Tx
Path Loss Model G f(d-4), d distance between Tx and Rx
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Simulation Parameters (2)
Parameter Value
Mobility Model Quasi-static model
Noise 10-6
Pmax 5.0
SINR Targets (in dB) 11,15
Initial Transmission Powers Randomly selected at (0, Pmax
Parameter c (Voluntarily Power Reduction) 0.9
Initial Budget B Randomly value at 100, 200