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

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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  1. 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

  2. MIMO • Multiple antennas at both transmitter and receiver • Benefits • Increase throughput, mitigate interference • Without additional bandwidth or transmit power IEEE INFOCOM 2011 2

  3. 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 2011 3

  4. 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 2011 4

  5. 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 2011 5

  6. Interference Cancellation – An Example • Link causes interference at link • Interference for stream on link is 0 IEEE INFOCOM 2011 6

  7. 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 2011 7

  8. 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 2011 8

  9. 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 2011 9

  10. 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 2011 10

  11. 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 2011 11

  12. 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 2011 12

  13. 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 2011 13

  14. 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 2011 14

  15. 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 2011 15

  16. 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 2011 16

  17. DoF-Based Model Half-duplex constraint Constraints for node activity Ordering constraints IEEE INFOCOM 2011 17

  18. DoF-Based Model (Cont’d) DoFconsumption constraints IEEE INFOCOM 2011 18

  19. Matrix-Based Model vs. New DoF-Based model Consider a three-link network Two models achieve the same rate region Complexity comparison IEEE INFOCOM 2011 19

  20. 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 2011 20

  21. Node Ordering Results in Each Time Slot IEEE INFOCOM 2011 21

  22. 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 2011 22

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