Game Theory and Cognitive Radio

1
Game Theory and Cognitive Radio

• James (Jody) Neel
• Friday, Nov. 19, 2004

2
Work Sponsors

• Office of Naval Research
• Grant Number N00014-03-1-0629
• National Science Foundation
• Integrated Research and Education in Advanced
  Networking an IGERT program
• MPRG Affiliates Program

Lucent Technologies Motorola Qualcomm SBC
Laboratories Texas Instruments
Analog Devices Army Research Office DRS
Technologies General Dynamics Huawei Technologies
Company
3
Presentation Objectives

• Describe how/when game theory applies to
  cognitive radio.
• Give a brief example.

4
Cognition Cycle

• Level
• 0 SDR
• 1 Goal Driven
• 2 Context Aware
• 3 Radio Aware
• 4 Planning
• 5 Negotiating
• 6 Learns Environment
• 7 Adapts Plans
• 8 Adapts Protocols

Select Alternate Goals
Generate Alternate Goals
Establish Priority
Immediate
Normal
Urgent
Determine Best Known Waveform
Generate Best Waveform
Negotiate
Negotiate Protocols
Adapted From Mitola, Cognitive Radio for
Flexible Mobile Multimedia Communications , IEEE
Mobile Multimedia Conference, 1999, pp 3-10.
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Analyzing Distributed Dynamic Behavior

• Dynamic benefits
• Improved spectrum utilization
• Improve QoS
• Many decisions may have to be localized
• Distributed behavior
• Adaptations of one radio can impact adaptations
  of others
• Interactive decisions
• Difficult to predict performance

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Is this a game?
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Games

• A game is a model (mathematical representation)
  of an interactive decision process.
• Its purpose is to create a formal framework that
  captures the processs relevant information in
  such a way that is suitable for analysis.
• Different situations indicate the use of
  different game models.

Normal Form Game Model

• A set of 2 or more players, N
• A set of actions for each player, Ai
• A set of utility functions, ui, that describe
  the players preferences over the outcome space

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How a Normal Form Game Works
Player 1
Player 2
Actions
Actions
Action Space
Decision Rules
Decision Rules
Outcome Space
u1
u2
-1
1
1 WINS!
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The Cognition Cycle is a Player

• Level
• 0 SDR
• 1 Goal Driven
• 2 Context Aware
• 3 Radio Aware
• 4 Planning
• 5 Negotiating
• 6 Learns Environment
• 7 Adapts Plans
• 8 Adapts Protocols

Utility Function
Utility function Arguments
Select Alternate Goals
Generate Alternate Goals
Establish Priority
Immediate
Normal
Urgent
Outcome Space
Decision Rules
Determine Best Known Waveform
Generate Best Waveform
Action Sets
Negotiate
Negotiate Protocols
Adapted From Mitola, Cognitive Radio for
Flexible Mobile Multimedia Communications , IEEE
Mobile Multimedia Conference, 1999, pp 3-10.
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Cognitive Radio Network as a Game
Radio 1
Radio 2
Actions
Actions
Action Space
Decision Rules
Decision Rules
Informed by Communications Theory
u2
Outcome Space
u1
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When Game Theory can be Applied

• Level
• 0 SDR
• 1 Goal Driven
• 2 Context Aware
• 3 Radio Aware
• 4 Planning
• 5 Negotiating
• 6 Learns Environment
• 7 Adapts Plans
• 8 Adapts Protocols

Select Alternate Goals
Establish Priority
Generate Alternate Goals
Immediate
Normal
Urgent
Generate Best Waveform
Determine Best Known Waveform
Game Theory applies to 1. Adaptive aware radios
2.
Cognitive radios that learn about
their environment
Negotiate
Negotiate Protocols
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Example Application
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Ad-hoc Power Control as a Game
1

• Player Set N
• Set of decision making radios
• Individual nodes i, j ? N
• Actions
• Pi power levels available to node i
• May be continuous or discrete
• P power space
• p power tuple (vector)
• pi power level chosen by player i
• Nodes of interest
• Each node has a node or set of nodes at which it
  measures performance
• ?i the set of nodes of interest of node i.
• Utility function
• Target SINR at node of interest

?5
5
?0
2
0
?1
?4
?3
?2
4
3
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Specific Scenario

• Two cluster ad-hoc network
• 11 nodes
• DS-SS N 63
• Path loss exponent n 4
• Power levels -120, 20 dBm
• Step size 0.1 dBm
• Synchronous updating
• Target SINR ? 8.4 dB
• Objective Function

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Potential Game Model

• Existence of a potential function V such that

• Identification
• NE Properties (assuming compact spaces)
• NE Existence All potential games have a NE
• NE Identification Maximizers of V are NE
• Convergence
• Better response algorithms converge.

• Stability
• Game is stable (Lyapunov)
• V is a Lyapunov function
• Design note
• If V is designed so that its maximizers are
  coincident with your design objective function,
  then NE are also optimal.

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Simulation Results
Noisy Simulation
Noiseless Simulation
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Example Potential Games

• Menon Fair Interference Avoidance (Session 1.4)
• Neel SDR02 specialized ad-hoc power control
  and waveform adaptations
• Single Cell Power Control target SINR
• Ad-hoc power control target SINR (fixed
  assignment)
• Hicks Globecom04 Littoral combat interference
  avoidance
• Lau - Aloha

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Conclusions

• Game theory applies to cognitive radio levels
  1-6.
• Use of game models can greatly simplify analysis.
• Choice of goal and allowable adaptations largely
  determine applicable models.