An optimal link layer model for multi hop mimo n etworks
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An Optimal Link Layer Model for Multi-hop MIMO N etworks. Yi Shi Virginia Tech, Dept. of ECE (with Jia Liu, Canming Jiang, Cunhao Gao , and Thomas Hou ). IEEE INFOCOM 2011 – Shanghai, China. MIMO. Multiple antennas at both transmitter and receiver Benefits

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An Optimal Link Layer Model for Multi-hop MIMO N etworks

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An optimal link layer model for multi hop mimo n etworks

An Optimal Link Layer Model for Multi-hop MIMO Networks

Yi Shi

Virginia Tech, Dept. of ECE

(with Jia Liu, CanmingJiang, CunhaoGao, and

Thomas Hou)

IEEE INFOCOM 2011 – Shanghai, China


An optimal link layer model for multi hop mimo n etworks

MIMO

  • Multiple antennas at both transmitter and receiver

  • Benefits

    • Increase throughput, mitigate interference

    • Without additional bandwidth or transmit power

IEEE INFOCOM 20112


Current status

Current Status

  • Two modeling approaches

    • Matrix-based model

    • Degree of freedom (DoF)-based model

  • DoF-based model

    • Simple: Use DoF to identify a feasible rate region

    • Not optimal: Existing DoF-based models cannot achieve the maximum rate region

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

  • Matrix-based model

    • Accurate: Characterize MIMO channel by a matrix

    • High complexity: Due to matrix manipulations

IEEE INFOCOM 20113


Zfbf scheme

ZFBF Scheme

  • DoF-based model is for the zero-force beam-forming (ZFBF) scheme

    • An effective MIMO technique

  • Two benefits associated with ZFBF

    • Spatial multiplexing(SM)

      • Enables multiple data streams on the same link

    • Interference cancellation(IC)

      • Enables more links to transmit at the same time

IEEE INFOCOM 20114


Spatial multiplexing an example

Spatial Multiplexing – An Example

  • Two data streams S1 and S2

  • Transmitter uses two transmit weight vectors and

  • Transmitted signal is

  • Signal arriving at receiver is

  • Receiver uses two receive weight vectors and

1

1

0

0

IEEE INFOCOM 20115


Interference cancellation an example

Interference Cancellation – An Example

  • Link causes interference at link

  • Interference for stream on link is

0

IEEE INFOCOM 20116


Matrix based model

Matrix-Based Model

  • For a time slot based scheduling, denote # of data streams on link in time slot t as

    • Assume each data stream has one unit rate

  • Link ’s average rate is

  • For SM, we need

  • For IC (if interferes with ), we need

IEEE INFOCOM 20117


Troubles with matrix based model

Troubles with Matrix-Based Model

Networking research using matrix-based model has very limited success

  • Need to verify the feasibility of each set of values for

  • The number of these sets is exponential with L

  • Verifying the feasibility of a particular set requires to solve a bilinear problem

    • A general solution to bilinear problems remains unknown

IEEE INFOCOM 20118


Understanding dof

Understanding DoF

  • DoF is associated with each transmit/receive vector

  • Initially, each vector has no constraint

    • Each element in a vector can be adjusted to optimize network performance

    • Feasible region of this vector includes all possible values

    • # of DoFsof this feasible region is equal to # of elements in a vector(or # of antennas at the node)

IEEE INFOCOM 20119


Understanding dof consumption an example

Understanding DoF Consumption- An Example -

  • Consider a transmit vector for a node with five antennas

  • Initially, there is no constraint: DoFs = 5

  • Consider two constraints and

    • The vector becomes

    • Remaining DoFs = 3

  • Consumed DoFs = 5-3 = 2

IEEE INFOCOM 201110


Understanding dof consumption a second example

Understanding DoF Consumption- A Second Example -

# of consumed DoFsdue to a set of constraints is equal to # of independent constraints

  • Consider three constraints

  • Since (7) is a linear combination of (5) and (6), we have only two independent constraints

    • The vector becomes

    • Remaining DoFs= 3

  • Consumed DoFs = 5-3 = 2

IEEE INFOCOM 201111


Dof consumption by sm

DoF Consumption by SM

  • All constraints in (8) and (9) are independent

  • The DoFconsumption for is

  • Similarly, the DoF consumption for is also

Transmit vector needs to satisfy

IEEE INFOCOM 201112


Dof consumption by ic

DoF Consumption by IC

  • Interference can be cancelled by either transmit or receive vector

    • Which vector?

    • To answer this question, we need an order among vectors

IEEE INFOCOM 201113


Ic dof consumption under an order

IC DoFConsumption Under An Order

  • For IC, vector must satisfy

    for

  • Consider one constraint

    • If is determined before , uses one DoF

    • If is determined after , the above constraint will be satisfied by in the future -- no DoFconsumption for

  • Similar results hold for

IEEE INFOCOM 201114


Vector level to node level a transformation

Vector-Level to Node-Level- A Transformation -

  • To achieve the maximum rate region, we prove that we only need an order among nodes

    • An order among vectors is unnecessary

  • We need an order between and

    • If is behind , # of DoFsconsumed at is and is 0

    • If is behind , # of DoFs consumed at is and is 0

IEEE INFOCOM 201115


Total dofs consumed by sm ic

Total DoFs Consumed by SM & IC

  • Is the total number of consumed DoFs a simple sum of those by SM and IC?

    • The answer is Yes!

    • Show that there is no dependency among SM and IC constraints

IEEE INFOCOM 201116


Dof based model

DoF-Based Model

Half-duplex constraint

Constraints for node activity

Ordering constraints

IEEE INFOCOM 201117


Dof based model cont d

DoF-Based Model (Cont’d)

DoFconsumption constraints

IEEE INFOCOM 201118


Matrix based model vs new dof based model

Matrix-Based Model vs. New DoF-Based model

Consider a three-link network

Two models achieve the same rate region

Complexity comparison

IEEE INFOCOM 201119


An application example

An Application Example

  • Objective: Maximize the sum of weighted session rates

  • A linear optimization problem

    • Similar complexity to that for single-antenna networks

IEEE INFOCOM 201120


Node ordering results in each time slot

Node Ordering Results in Each Time Slot

IEEE INFOCOM 201121


Summary

Summary

  • The matrix-based MIMO model is too complex for network performance analysis

    • Results based on the matrix-based model are very limited

  • Developedan optimal DoF-based model

    • Retains the similar simplicity as single-antenna networks

    • Offers the same achievable rate region as that by the matrix-based model

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

IEEE INFOCOM 201122


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