Systematic Design of Space-Time

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					Cooperation and Fairness of Wireless Networking
     using Game Theoretical Approaches

                   Zhu Han
                   June 5th, 2008
    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
UNIK talk 6/5/08
        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

UNIK talk 6/5/08
                       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…
UNIK talk 6/5/08
            Rich Game Theoretical Approaches
   Non-cooperative
static game:
      – Play once
      – Prison dilemma
      – Zero sum game: O+H=1

   Dynamic game: play multiple times
                                                                          Kill Bill
      – Threat of punishment by repeated game. MAD: Nobel prize 2005.
      – Tit-for-Tat: An eye for eye makes the world blind.

   Cooperative game
      – Startup company: everybody wants IPO, while competing for more stock shares.
      – Coalition game: M +(O+H)=1, where O and H belongs to the same party

   Auction Theory and Mechanism Design (Nobel Prize 2007)

UNIK talk 6/5/08
                   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.

                                  User 3

                                                           User 5
                                                  User 4
                                  User 2

                                 User 1      User 6

      Challenges: difficult mixed fairness allocation assignment
       problems; need to consider
UNIK talk 6/5/08
    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

UNIK talk 6/5/08
                   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           max U   Ri or min Ri
                                                        i 1
       [A]ij=Aij  {0,1}                                               K

        Bit Loading:
                                            Channel Assignment:  Aijij  1, j;
                                                                      i 1

       Rate for user i at subcarrier j                            M
                                       s.t. Minimal Rate: Ri   rij  Rmin , i;
                                                                           j   i
       Adaptive modulation                                       j 1

                         cPi j Gi j                           M

         ri j  w log 2 1 
                                           Power Constraint : Piij  Pmax , i.
                            2                               j 1

           Power Allocation: P ij  P j
           Complicated Integer Non-convex Assignment Problem.
UNIK talk 6/5/08
 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 O ( M )
      – 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.

UNIK talk 6/5/08
 New Optimization Goal Using Game Theory
   New Optimization Goal:
                   Nash Bargaining Solutions
                       max U   ( Ri  Rm in )
                                 i 1

                      s.t. other constraints
      −   Why product form? Why not max-min or maximal rates?
      −   Minimal Rate Requirement Ri  Rm in , i

      −   Nash Six Axioms: Unique optimal solution
      −   NBS Fairness: Generalized proportional fairness
      −   Efficiency: Little overall performance loss
      −   Any Simple Algorithm?
UNIK talk 6/5/08
                            Two-User Algorithm
      Two band partition algorithm: Two users exchange subcarriers.
                                                                        User 1 channel gain in
              Initialization: Merge subcarrier sets
                                                                                                    G 
                                                                                                          j 1
                                                                            jth subcarrier

       2.     Sort the combined subcarrier set by the ratio of channel gains                             1

       3.     For j=1,…,M-1                                             User 2 channel gain in
                                                                            jth subcarrier
                                                                                                    G  2
                                                                                                          j 2

                   User 1 occupies and water-fills subcarrier 1 to j                                        1
                                                                                                 i 
                   User 2 occupies and water-fills subcarrier j+1 to M                                  Ri  Rmin

                   Calculate U=(R1-Rmin)(R2-Rmin)
             End                                                        user1              user2

                                                        Channel Gain
       4.     Choose the j that generates the
       largest U that satisfies all constraints.

              Update:  i
                             4       3             2
                                                   4                   5
                                                                       5        66
                                 4       3          2                   5
            Continue 
       6. Preference until convergence                                            Preference
                                                                             Sorted Channel Index
UNIK talk 6/5/08

      low complexity O(MlogM)
      Theorem 1:
             When Rmin  0, i , 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
UNIK talk 6/5/08
        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 O( K 2 M log M )             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)?
UNIK talk 6/5/08
              Cooperative Game Approach:
         Multiple 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.
                                                                  K   K
     −   Benefit Table b: negotiation effect               max  X ij bij
                                                                 i 1 j 1
         bij: benefit via negotiation between
         user i and user j.                           K X ij  1 j  1, 2,..., K , i;
                                                      i 1
                                                      K
     −   Assignment Table X:                    s.t.  j 1 X ij  1 i  1, 2,..., K , j;
         Xij=1: negotiation between i and j          
            =0: no negotiation                        X ij  {0,1} i, j
UNIK talk 6/5/08
                    Hungarian Algorithm
     A~E Brides and H~L Grooms:
       – Brides rank grooms 1~5                                       Homeless,
                                       Millionaire                     Slave, or
     Maximize the overall             Professor                     Ph.D. student

 happiness                                 B\G       H   I   J   K        L
                                              A      1   2   3   4        5
  Complexity                                 B      2   3   1   5        4

    – K user                                  C      3   5   1   2        4
                                              D      1   3   2   4        5
O( K 4  K 2 M log M )                        E      4   2   5   1        3

       – Much lower than O ( M 4 )         B\G       H   I   J   K        L
                                              A      0   1   0   0        0
     Find most effective negotiation         B      0   0   0   0        1
                                              C      0   0   1   0        0
 for each round.             table            D      1   0   0   0        0
                                              E      0   0   0   1        0
     Con: limited central control
UNIK talk 6/5/08
                          Two User Simulations
   Setup :User1 locates at 100m
    from base station. User2 moves

                                                 Overall Rate (MHz)
   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

    UNIK talk 6/5/08
    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
UNIK talk 6/5/08
              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
                             Destination                                Destination

                   Phase 1                                    Phase 2

     Sender                                        Sender
                             Relay                                      Relay

      – Most popular research in current wireless communication
      – Industrial standard: IEEE WiMAX 802.16J
UNIK talk 6/5/08
                           System Model (1)
     System model:
        – One source-destination node pair; N relay nodes, amplify-and-forward
          cooperation protocol.

                                                  Ys ,ri  PGs ,ri X s ,ri  

        – 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.
UNIK talk 6/5/08
                          System Model (2)
     Maximal achievable rate of direct transmission is

     Maximal achievable rate at the destination output with relay node ri helping is

     with  i 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
UNIK talk 6/5/08
          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 node’s 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
UNIK talk 6/5/08
                   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
      – Any feasible solution can be enforced by repeated game

UNIK talk 6/5/08
                           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

UNIK talk 6/5/08
               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

UNIK talk 6/5/08
    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-

      – Maximal ration combining at the receiver of backbone node

      – To achieve same SNR, power saving for backbone nodes P0<Pd

UNIK talk 6/5/08
                                        Main Idea
Poor guy’s daughter got bullied by sons of an influential man
 Punishment could not be taken by law or revenge, then he
  asked for help from Don. Don ordered to beat the sons,
       and asked for payback when his son was dead

       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)
   UNIK talk 6/5/08
    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
UNIK talk 6/5/08
   Joint Repeated Game and Coalition Game

UNIK talk 6/5/08
                   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.

UNIK talk 6/5/08
                   Simulation Results
   Connectivity: any
    node can reach any
    other node in the
   More than 50%
    network connectivity
   Conclusion: using
    transmission and
    cooperative game,
    we solve a well
    known problem in
    wireless networking.

UNIK talk 6/5/08
    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
UNIK talk 6/5/08
            Non-cooperative Game Approach:
       Referee-Based Approach for Multicell OFDMA

    Algorithm                                   R: required rate
1. Initialization                           S: occupied subcarrier set

2. Non-cooperative game
3. Desired Nash Equilibrium?
4. Subcarrier removal/
   rate reduction
    Implementation
1.   Where is referee
2.   Small overhead            Candidate?
3.   No more measurement
4.   Complexity O(MlogM)
5.   Synchronization
 UNIK talk 6/5/08
                          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
UNIK talk 6/5/08
                     Sensor Networks
    Energy and Lifetime                                 Direct Transmission

    Security Problem                                 Cooperative Transmission

    Key idea
      – Use cooperative                                 0
      transmission to bypass                                               Sink

      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
UNIK talk 6/5/08
 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
                                                                  Per Power

                                                      Per Power

UNIK talk 6/5/08
    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
UNIK talk 6/5/08
                         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

UNIK talk 6/5/08
    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

UNIK talk 6/5/08

UNIK talk 6/5/08

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