1. 1 CODING FOR MULTIPLE ANTENNAS WITH LINEAR AND NONLINEAR (BLAST) INTERFACES DIMACS WORKSHOP, OCTOBER 2002 EZIO BIGLIERI (work done with A. Nordio, G. Taricco, and A. Tulino)

2. 2 OUTLINE  SYSTEM MODEL AND BASIC ASSUMPTIONS  LINEAR AND NONLINEAR RECEIVERS  ZERO-FORCING AND MMSE BLAST  ITERATIVE RECEIVER  CODING FOR NONLINEAR RECEIVERS  SIMULATION RESULTS

3. 3 SYSTEM MODEL  mimo channel with t transmit and r receive antennas  fading constant over N symbol intervals  independent rayleigh fading channel  perfect csi at receiver

4. 4 H TX RX

5. 5 SYSTEM MODEL

6. 6 INTRODUCING AN INTERLEAVER Pairwise error probability with ML detection: E E

7. 7 INTRODUCING AN INTERLEAVER Spatial interference

8. 8 INTRODUCING AN INTERLEAVER

9. 9 OPTIONS FOR REMOVING  1 : r  

10. 10 INTRODUCING AN INTERLEAVER OPTIONS FOR REMOVING  1 : r   Alamouti-type coding

11. 11 INTRODUCING AN INTERLEAVER OPTIONS FOR REMOVING  1 : r   Alamouti-type coding Introducing a row-interleaver

12. 12 INTRODUCING AN INTERLEAVER A random row interleaver yields

13. 13 LINEAR INTERFACE A Metric used:

14. 14 NONLINEAR INTERFACE G + L decoder + – reduce spatial interference L has zero diagonal elements

15. 15 NONLINEAR INTERFACE G + L decoder + – reduce spatial interference L strictly upper triangular: Allows t iterations  BLAST L with zero diagonal elements  ITERATIVE RECEIVER

16. 16 Use a soft estimate of the transmitted code word X in the form BLAST INTERFACE

17. 17 BLAST algorithm: step 1

18. 18 BLAST algorithm: step 1

19. 19 BLAST algorithm: step 1

20. 20 BLAST algorithm: step 1

21. 21 BLAST algorithm: step 2

22. 22 ZF BLAST

23. 23 ZF BLAST

24. 24 MMSE BLAST

25. 25 MMSE BLAST

26. 26 NONLINEAR ITERATIVE INTERFACE A + L decoder + – estimate of spatial interference L has zero diagonal elements: L = AH - diag(AH)

27. 27 NONLINEAR ITERATIVE INTERFACE estimate of spatial interference:

28. 28 CODING FOR NONLINEAR INTERFACES...... encoder vertical coding: coded symbols are spread across TX antennas

29. 29...... horizontal coding: each TX antenna is encoded separately encoder CODING FOR NONLINEAR INTERFACES

30. 30...... encoder vertical coding: no preliminary decisions available to increase the reliability of symbols detected and used for cancellation CODING FOR NONLINEAR INTERFACES

31. 31 horizontal coding: interference cancellation is limited by the weakest code...... encoder CODING FOR NONLINEAR INTERFACES

32. 32 horizontal + vertical coding: each TX antenna transmits a subcode of a larger code...... encoder CODING FOR NONLINEAR INTERFACES

33. 33 SIMULATION RESULTS (8,4,4) Extended Hamming code

34. 34

35. 35

36. 36

37. 37

38. 38

39. 39

40. 40

41. 41