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					An Optimal Link Layer Model for Multi-hop
            MIMO Networks

                       Yi Shi
            Virginia Tech, Dept. of ECE

    (with Jia Liu, Canming Jiang, Cunhao Gao, and 
                      Thomas Hou)




           IEEE INFOCOM 2011 – Shanghai, China
                              MIMO
l Multiple antennas at both 
  transmitter and receiver

l Benefits
  n Increase throughput, mitigate 
    interference
  n Without additional bandwidth 
    or transmit power




 IEEE INFOCOM 2011                   2
                     Current Status
l Two modeling approaches
  n Matrix-based model
  n Degree of freedom (DoF)-based model

l Matrix-based model                   l DoF-based model 
  n Accurate: Characterize MIMO          n Simple: Use DoF to identify a 
    channel by a matrix                    feasible rate region
  n High complexity: Due to              n Not optimal: Existing DoF-
    matrix manipulations                   based models cannot achieve 
                                           the maximum rate region


 An optimal DoF-based model for multi-hop MIMO networks


 IEEE INFOCOM 2011                 3
                         ZFBF Scheme
l DoF-based model is for the zero-force beam-forming 
  (ZFBF) scheme
  n An effective MIMO technique


l Two benefits associated with ZFBF
  n Spatial multiplexing (SM)
      uEnables multiple data streams on the same link
  n Interference cancellation (IC)
      uEnables more links to transmit at the same time




 IEEE INFOCOM 2011                    4
        Spatial Multiplexing – An Example
 




                         



                                    1   0
                             



                                    0   1
    IEEE INFOCOM 2011           5
Interference Cancellation – An Example




 




                         




                            0
    IEEE INFOCOM 2011           6
                     Matrix-Based Model
l 




 IEEE INFOCOM 2011           7
     Troubles with Matrix-Based Model
l 




Networking research using matrix-based model has very limited success



 IEEE INFOCOM 2011                 8
                     Understanding DoF
l DoF is associated with each transmit/receive vector

l Initially, each vector has no constraint
   n Each element in a vector can be adjusted to optimize network 
     performance
   n Feasible region of this vector includes all possible values
   n # of DoFs of this feasible region is equal to # of elements in a vector 
     (or # of antennas at the node)




 IEEE INFOCOM 2011                    9
       Understanding DoF Consumption
              - An Example -
l 




 IEEE INFOCOM 2011   10
       Understanding DoF Consumption
           - A Second Example -
l 




      # of consumed DoFs due to a set of constraints is equal to
      # of independent constraints


 IEEE INFOCOM 2011                  11
                    DoF Consumption by SM
l 




 




 




    IEEE INFOCOM 2011         12
                    DoF Consumption by IC




l Interference can be cancelled by either transmit or receive 
  vector

l Which vector?
    n To answer this question, we need an order among vectors




IEEE INFOCOM 2011                13
 IC DoF Consumption Under An Order
l 




 IEEE INFOCOM 2011   14
             Vector-Level to Node-Level
                - A Transformation -
l 




 IEEE INFOCOM 2011       15
      Total DoFs Consumed by SM & IC
l Is the total number of consumed DoFs a simple sum of 
  those by SM and IC?

  n The answer is Yes!
  n Show that there is no dependency among SM and IC constraints




 IEEE INFOCOM 2011               16
                     DoF-Based Model
l Half-duplex constraint

l Constraints for node activity




l Ordering constraints




 IEEE INFOCOM 2011                17
               DoF-Based Model (Cont’d)
l DoF consumption constraints




 IEEE INFOCOM 2011          18
Matrix-Based Model vs. New DoF-Based model

l Consider a three
  -link network
l Two models 
  achieve the 
  same rate 
  region 
l Complexity 
  comparison




  IEEE INFOCOM 2011   19
                     An Application Example
l Objective: Maximize 
  the sum of weighted 
  session rates

l A linear optimization 
  problem
   n Similar complexity to that 
     for single-antenna 
     networks




 IEEE INFOCOM 2011                 20
Node Ordering Results in Each Time Slot




 IEEE INFOCOM 2011   21
                           Summary
l The matrix-based MIMO model is too complex for network 
  performance analysis
  n Results based on the matrix-based model are very limited


l Developed an optimal DoF-based model 
  n Retains the similar simplicity as single-antenna networks
  n Offers the same achievable rate region as that by the matrix-based 
    model


l Showed how to use our optimal DoF-based model for a 
  multi-hop MIMO network problem


 IEEE INFOCOM 2011                 22

				
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