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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 Networks

Yi Shi

Virginia Tech, Dept. of ECE

(with Jia Liu, CanmingJiang, CunhaoGao, and

Thomas Hou)

IEEE INFOCOM 2011 – Shanghai, China

- Multiple antennas at both transmitter and receiver
- Benefits
- Increase throughput, mitigate interference
- Without additional bandwidth or transmit power

IEEE INFOCOM 20112

- 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

- 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

- Spatial multiplexing(SM)

IEEE INFOCOM 20114

- 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

- Link causes interference at link
- Interference for stream on link is

0

IEEE INFOCOM 20116

- 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

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

- 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

- 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

# 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

- 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

- 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

- 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

- 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

- 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

Half-duplex constraint

Constraints for node activity

Ordering constraints

IEEE INFOCOM 201117

DoFconsumption constraints

IEEE INFOCOM 201118

Consider a three-link network

Two models achieve the same rate region

Complexity comparison

IEEE INFOCOM 201119

- Objective: Maximize the sum of weighted session rates
- A linear optimization problem
- Similar complexity to that for single-antenna networks

IEEE INFOCOM 201120

IEEE INFOCOM 201121

- 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