Cooperation and Fairness of Wireless Networking using Game Theoretical Approaches

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Cooperation and Fairness of Wireless Networking
using Game Theoretical Approaches

• Zhu Han
• UNIK
• June 5th, 2008

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Outline

• Motivation and game theoretical approaches
• OFDMA Resource Allocation
• Power control, bit loading and channel assignment
  problem
• Simple high efficient bargaining solution
• Cooperative transmission new communication
  paradigm
• Distributed implementation with less signaling
• Broader impact other than that in physical layer
• Packet forwarding wireless networks with selfish
  nodes
• Curse of boundary nodes
• Cooperative game using cooperative transmission
• Other topics
• Summary

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Resource Allocation over Wireless Networks

• Resource Allocation over Wireless Networks
• Limited radio resources, conflict interests among
  users
• Different parameters and constraints in different
  layers
• New Perspectives Compared to Traditional
  Communications
• System optimality instead of individual link
  optimality
• Interactions among users in addition to overcome
  nature
• Cross layer approaches instead of layered design
• Challenges
• Traditional approach for resource allocation
  centralized control
• Excessive measurement, signaling, and feedback
• Network and MAC layer
• Distributive resource allocation user autonomy
• Pro local information, less signaling/overhead,
  flexible
• Con low system efficiency and unfairness

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Enforcing Cooperation

• Enforcing Cooperation in Wireless Networks
• Greedy usage of system resources by the
  autonomous distributive users reducing system
  efficiency
• Current Approaches for Enforcing Cooperation
• Pricing anarchy using price/tax to control
  resource usage
• Pro no incentive to overuse the resources
• Con price itself hard to calculate continuous
  parameters only hard for cross-layer
  optimization, heterogeneous networks, multicell
  networks, ad hoc/sensor networks
• Tradeoff system efficiency and individual
  fairness
• Game Theoretical Approaches
• Natural conflict between parties equilibrium of
  competition
• Flexible rich mathematical tools different ways
  to enforce cooperation incentive, threat,
  referee, negotiation

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Rich Game Theoretical Approaches

• Non-cooperative
• static game
• Play once
• Prison dilemma
• Zero sum game OH1
• Dynamic game play multiple times
• Threat of punishment by repeated game. MAD Nobel
  prize 2005.
• Tit-for-Tat
• Cooperative game
• Startup company everybody wants IPO, while
  competing for more stock shares.
• Coalition game M (OH)1, where O and H belongs
  to the same party
• Auction Theory and Mechanism Design (Nobel Prize
  2007)

An eye for eye makes the world blind.
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Single Cell OFDMA Networks

• Orthogonal Frequency Division Modulation (OFDM)
• Frequency selective fading. No ISI. High speed
• CSMA RTS/CTS for multiuser system, TDMA system
• Why OFDMA systems?
• Frequency, time, and multiuser diversity.
• Challenges difficult mixed resource allocation
  assignment problems need to consider fairness

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Single Cell System Descriptions (Example)

• Single cell uplink case
• M subcarriers, K users
• Optimization overall rate
• Subcarrier assignment only one user per
  subcarrier.
• Conflict the same subcarrier may be good for
  many users.
• Constraints
• Minimal requirement Rmin
• Maximal power from mobile unit Pmax

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Basic Problem (An Example)

• Problem Formulation (an example for single cell
  uplink case)
• Optimization Goals U maximal rate and max-min
• Channel Assignment
• User i occupies subcarrier j
• AijAij ? 0,1
• Bit Loading
• Rate for user i at subcarrier j
• Adaptive modulation
• Power Allocation
• Complicated Integer Non-convex Assignment
  Problem.

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Motivations Using Game Theory for OFDMA

• Existing Work
• Relaxation and then back to integer
• Finding the lowest point in the basin or valley
  does not mean finding the lower village (which is
  discrete in nature). NP hard
• Hungarian method complexity
• Two Step Solution Integer heuristic first, then
  programming
• Local optima
• Cooperative game for single cell OFDMA system
• Competition each subcarrier can be occupied by
  one user.
• Exist a central node base station, similar to
  the market in reality where negotiations and
  exchanges between mobiles can take place.
• Distributed users can negotiate via base station
  to cooperate in making the decisions on the
  subcarrier usage, such that each will operate at
  its optimum and joint mutual benefits are made
  about their operating points.

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New Optimization Goal Using Game Theory

• New Optimization Goal
• Nash Bargaining Solutions
• Why product form? Why not max-min or maximal
  rates?
• Minimal Rate Requirement
• Nash Six Axioms Unique optimal solution
• NBS Fairness Generalized proportional fairness
• Efficiency Little overall performance loss
• Any Simple Algorithm?

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Two-User Algorithm

• Two band partition algorithm Two users exchange
  subcarriers.
• Initialization Merge subcarrier sets
• Sort the combined subcarrier set by the ratio of
  channel gains
• For j1,,M-1
• User 1 occupies and water-fills subcarrier 1 to
  j
• User 2 occupies and water-fills subcarrier j1
  to M
• Calculate U(R1-Rmin)(R2-Rmin)
• End
• Choose the j that generates the
• largest U that satisfies all constraints.
• 5. Update
• 6. Continue until convergence

User 1 channel gain in jth subcarrier
User 2 channel gain in jth subcarrier
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Properties

• low complexity O(MlogM)
• Theorem 1
• When , NBS fairness is the proportional
  fairness.
• NBS fairness is a generalized proportional
  fairness.
• Theorem 2
• There exists a unique and optimal solution for
  the formulated multi-user problem.
• Theorem 3
• The algorithm can find the unique and optimal
  solution for two user case, when SNR is high.
• Theorem 4 Convergence

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N-Person OFDMA Resource Allocation

• Proposed N-person cooperative games
• Scheme
• 1. Initialization
• 2. Grouping users to pairs, which is called
  coalitions
• 3. Apply two-user algorithm to each pair
• 4. Go to 2, stop until no improvement can be
  achieved
• Low complexity K number of users
• Key Difference
• Traditional scheme in Subcarrier level with
  dimension of M
• Optimization in user domain. Complexity of with
  order of K
• Iterative improvement Soul of interior-point
  method

How to group users into pairs (coalitions)?
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Cooperative Game ApproachMultiple User Scheme
Grouping Users

• Random Method free market.
• Negotiate between arbitrary two users to exchange
  subcarrier
• Converge slowly and achieve local optima
• Hungarian Method
• Select optimal coalition pairs to maximize payoff
  for each negotiation round.
• Benefit Table b negotiation effect
• bij benefit via negotiation between
• user i and user j.
• Assignment Table X
• Xij1 negotiation between i and j
• 0 no negotiation

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Hungarian Algorithm

• AE Brides and HL Grooms
• Brides rank grooms 15
• Maximize the overall
• happiness
• Complexity
• K user
• Much lower than
• Find most effective negotiation
• for each round.
• Con limited central control

Homeless, Slave, or Ph.D. student
Millionaire Professor
Assignment table
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Two User Simulations

• Setup User1 locates at 100m from base station.
  User2 moves
• Fairness and efficiency
• Rates for different user 2
• location D2
• Fairness, compared with
• maximal rate algorithm
• Little rate loss to maximal rate algorithm, but
  great rate gain over max-min algorithm.
• Open Issue beyond cognitive, dynamic spectrum
  access, mesh, video, what else to extend the
  ideas to and could it be used in standards

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Transition

• Motivation and game theoretical approaches
• OFDMA Resource Allocation
• Power control, bit loading and channel assignment
  problem
• Simple high efficient bargaining solution
• Cooperative transmission new communication
  paradigm
• Distributed implementation with less signaling
• Broader impact other than that in physical layer
• Packet forwarding wireless networks with selfish
  nodes
• Curse of boundary nodes
• Cooperative game using cooperative transmission
• Other topics
• Summary

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Cooperative Transmission

• New communication paradigm
• Exploring broadcast nature of wireless channel
• Relays can be served as virtual antenna of the
  source
• MIMO system
• Multi-user and multi-route diversity
• Most popular research in current wireless
  communication
• Industrial standard IEEE WiMAX 802.16J

Destination
Destination
Phase 1
Phase 2
Sender
Sender
Relay
Relay
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System Model (1)

• System model
• One source-destination node pair N relay nodes,
  amplify-and-forward cooperation protocol.
• Phase 1 - received signals from source node s to
  destination node d and each relay node ri
• Phase 2 - received signal at destination node d
  via relay node ri
• with
  .
• Destination combines two phases to improve
  performance.

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System Model (2)

• Maximal achievable rate of direct transmission is
  
• Maximal achievable rate at the destination output
  with relay node ri helping is
  
• with as a bandwidth factor and
• Increase of capacity region and diversity gain
  for BER
• Depending on the power control and relay
  locations
• Challenge
• Broader impact other than power control and relay
  selection
• Needs all channel information a lot of
  signalling
• Motivation for game theory

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Packet Forwarding Networks

• Characteristics of packet forwarding networks
  such as MANET
• Most likely involved multiple hops transmissions
• Require other nodes to forward packets.
• Individual node has its own autonomy
• Forwarding others packets consumes the nodes
  limited energy
• Reluctant to forward others packets
• If nodes do not cooperate
• Network can be disconnected
• Fatal effects on network as well as individual
  performances
• Nash equilibrium
• No user can achieve better if the others do not
  change strategy
• Likely nobody forwards the others information in
  our case
• To overcome this problem, we need to employ the
  repeated game

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Repeated Game Basics

• Packet forwarding network modeled as a graph
  G(L,A)
• Each node has transmission destination
• To reach the destination j in , depending
  graph contains the nodes that transmitter
  i will depend on packet forwarding.
• Repeated game average utility (power in our
  case) over time.
• Discounting factor ?
• Folk theorem
• If the nodes are mutually dependent, ensure
  cooperation by threat of future punishment.
• Any feasible solution can be enforced by repeated
  game

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Cartel Maintenance

• Enforcing Cooperation by Punishment
• Each user tries to maximize the benefit over
  time.
• Short term greedy benefit will be weighted out by
  the future punishment from others. By maintaining
  this threat of punishment, cooperation is
  enforced among greedy users.
• Cartel Maintenance Repeated Game Approach
• Initialization Cooperation
• Detect the outcome of the game
• If better than a threshold, play cooperation in
  the next time
• Else, play non-cooperation for T period, and then
  cooperate.
• Applications
• Rate control for selfish users in multiple access
  networks
• Packet forwarding for ad hoc network
• Power control for co-channel interfered networks
• Self learning algorithms

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Curse of Boundary Nodes

• Boundary nodes depend on the backbone nodes for
  transmission. but backbone nodes do not depend
  boundary nodes. (dependence graph)
• Example 1,2 backbone nodes 0,3 boundary nodes
• Very famous problem in this research community

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Cooperative Transmission Model

• No cooperation (direct transmission), backbone
  needs power
• Cooperative transmission
• Stage one direct transmission. s, source r,
  relay d, destination
• Stage two relay retransmission using orthogonal
  channels, amplified-and-forward
• Maximal ration combining at the receiver of
  backbone node
• To achieve same SNR, power saving for backbone
  nodes P0ltPd

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Main Idea

• Boundary nodes help the backbone node reduce
  transmission power using cooperative
  transmission, for future rewards of packet
  forwarding by the backbone node. The idea can be
  formulated by a coalition game.
• My own understanding of the idea
• If bullied by a Mafia, take revenge, (repeated
  game)
• If revenge cannot be taken, join the Mafia,
  (coalition game)

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Coalition Game Stability and Fairness

• Coalition S, (N,v), N is the set of nodes, v is
  the characteristic function overall benefit by
  coalition.
• Payoff function
• Group rational
• Individual rational, better than work alone
  mutual benefit
• Core no node has incentive to leave grand
  coalition
• Fairness
• Min-Max Fairness
• Average Fairness
• Market Fairness
• Key to the success collaboration
• Mutual benefits and fairness

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Joint Repeated Game and Coalition Game
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Simulation Results

• Setups source-destination 100m or 50m,
  source-relay distance varying
• 1/?i How many packets need to relay before a
  transmission reward
• Longer the distance, less effective the boundary
  nodes to help backbone node, the smaller ?i, and
  more packets the boundary nodes need to transmit
  to get rewards.

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Simulation Results

• Connectivity any node can reach any other node
  in the network
• More than 50 network connectivity improvement.
• Conclusion using cooperative transmission and
  cooperative game, we solve a well known problem
  in wireless networking.

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Transition

• Motivation and game theoretical approaches
• OFDMA Resource Allocation
• Power control, bit loading and channel assignment
  problem
• Simple high efficient bargaining solution
• Cooperative transmission new communication
  paradigm
• Distributed implementation with less signaling
• Broader impact other than that in physical layer
• Packet forwarding wireless networks with selfish
  nodes
• Curse of boundary nodes
• Cooperative game using cooperative transmission
• Other topics
• Summary

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Non-cooperative Game ApproachReferee-Based
Approach for Multicell OFDMA

• Algorithm
• 1. Initialization
• 2. Non-cooperative game
• 3. Desired Nash Equilibrium?
• 4. Subcarrier removal/
• rate reduction
• Implementation
• Where is referee
• Small overhead
• No more measurement
• Complexity O(MlogM)
• Synchronization

R required rate S occupied subcarrier set
Candidate?
Candidate?
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Auction Theory

• Example painting auction
• Highest bidder gets the good
• and pays the bid
• Elements of auction
• Good resource
• Auctioneer (manager)
• representing seller of the good
• Bidders (users)
• buyers of the good
• Rules of auction
• Bids what the bidders submit to the auctioneer
• Allocation how auctioneer allocates the good to
  the bidders
• Payments how the bidders pay the auctioneer
• Suitable for communication resource allocation
  video

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Sensor Networks

• Energy and Lifetime
• Security Problem
• Key idea
• Use cooperative
• transmission to bypass
• the energy depleting nodes
• Reduce the transmission power for each link
• Beamforming to null the direction of malicious
  nodes
• Future works
• Cooperative routing
• Video surveillance
• Bio and medical sensor
• Car torrent

Direct Transmission
Cooperative Transmission
1
0
k
Sink
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Two Level Buy/Seller Game for Power Control and
Relay Section for Cooperative Transmission

• Buyer-Seller Game
• Sender (buyer) buying the services from the
  relays to improve its performance, such as the
  transmission rate
• Relays (sellers) selling service, such as power,
  by setting prices
• Tradeoffs price too high, sender buying others
  price too low, profit low sender deciding buy
  whose and how much to spend
• Procedures convergence to the optimal equilibrium

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Others

• MUD Network coding Cooperative transmission
• Cooperative OFDMA
• Security in cooperative transmission
• Cooperative UWB
• Coverage extension using cooperative transmission
• Cognitive radios
• Double auction and evolutional game
• Collaborative sensing
• Security in cognitive radio
• Random matrix theory for cooperative transmission
• Physical layer security

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Other Work

• Dynamic Adaptive Wireless Resource Allocation
• Ad hoc/Sensor Network Design
• Ultra Wide Band Communication
• Cognitive Radios
• Information Assurance and Network Security
• Multimedia over Wireless Networks
• Underwater Acoustic Communication
• Unmanned Air Vehicle
• Wireless Access in Vehicular Environment
• Compressed Sensing for Image Processing
• Physical Layer Security
• Bio Signal Processing and Bio Information
  Processing

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Conclusions

• Cooperation and fairness problems for wireless
  networking
• Advantages of game theory
• Examples
• OFDMA resource allocations
• Cooperative transmission for networking problem
• Many other examples
• Many future research directions
• Many collaboration opportunities

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Questions?
Thank you very much