1. Rate Bounds for MIMO Relay Channels Using Precoding Caleb K. Lo, Sriram Vishwanath and Robert W. Heath, Jr. Wireless Networking and Communications Group Department of Electrical and Computer Engineering The University of Texas at Austin GLOBECOM 2005

2. Outline  Motivation  SISO vs. MIMO Relay Channels  Prior Work  Problem Statement  Message Splitting  Results  Conclusions

3. Motivation  Mesh network: self-organizing wireless nodes  Relay channel: fundamental building block SenderReceiver Intermediate Node Large Distance Shorter Distance

4. SISO Relay  Assume decode-and-forward at relay  If relay is not useful h1h1 h3h3 h2h2 Sender Relay Receiver

5. MIMO Relay  Assume decode-and-forward at relay  H 1, H 2 and H 3 generally cannot be compared H1H1 H3H3 H2H2 Relay Sender Receiver

6. Prior Work  Cover and El Gamal (ITIT ’79)  Rate bounds for general full-duplex relay channel  Wang, Zhang and Host-Madsen (ITIT ’05)  Rate bounds for Gaussian MIMO relay channel  Non-cooperative lower bound for fixed channels

7. System Model

8. Problem Statement  Want tighter lower bounds for MIMO relay  Assumptions  Fixed channel gains  Full CSI at all terminals  Full-duplex decode-and-forward relaying  Our contribution  Improved lower bounds via transmit precoding

9. Message Splitting  Relay treats V as interference H1H1 H3H3 H2H2 Relay Sender Receiver X 1 = X 1 (U,V) X 2 = X 2 (U)

10. Superposition Coding  Relay only decodes U  Rx decodes both U and V SenderReceiver Relay X 1 = U + V X 2 = X 2 (U)X 1 = U + V

11. Dirty-Paper Coding  Coding in presence of known interference (from C.B. Peel, “On Dirty-Paper Coding,” IEEE Sig. Proc. Mag., May 2003, pg. 112-113)

12. Rate Bound Results (1/6)  Cover and El Gamal result  Superposition Coding X 1 = U + V Tx Relay Rx X 1 = U + V X 2 = X 2 (U)

13. Rate Bound Results (2/6)  Superposition Coding for Gaussian MIMO

14. Rate Bound Results (3/6)  Cover and El Gamal result  Dirty-Paper Coding Tx Relay Rx X 1 = X 1 (U,V) X 2 = X 2 (U)

15. Rate Bound Results (4/6)  Dirty-Paper Coding for Gaussian MIMO

16. Rate Bound Results (5/6) H1H1 H3H3 H2H2 Relay Sender Receiver  Precoding-based bounds significantly outperform Wang et al. lower bound

17. Rate Bound Results (6/6) H2H2 H1H1 H3H3 Relay Sender Receiver  Precoding-based bounds very close to Wang et al. cut-set upper bound

18. Conclusions  Variable cooperation level yields rate benefits in MIMO relay channel  New tight lower capacity bounds achieved via transmit precoding  Considered DMC and Gaussian cases