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Cooperation and Fairness of Wireless Networking using Game Theoretical Approaches

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Title: Cooperation and Fairness of Wireless Networking using Game Theoretical Approaches


1
Cooperation and Fairness of Wireless Networking
using Game Theoretical Approaches
  • Zhu Han
  • UNIK
  • June 5th, 2008

2
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

3
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

4
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

5
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.
6
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

7
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

8
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.

9
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.

10
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?

11
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
12
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

13
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)?
14
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

15
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
16
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

17
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

18
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
19
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.

20
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

21
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

22
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

23
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

24
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

25
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

26
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)

27
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

28
Joint Repeated Game and Coalition Game
29
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.

30
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.

31
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

32
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?
33
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

34
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
35
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

36
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

37
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

38
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

39
Questions?
Thank you very much
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