1. © Imperial College LondonPage 1 WSEAS PLENARY LECTURE: The Challenges of Subspace Techniques and their Impact on Space-Time Communications. 29 th December 2004 Dr Athanassios Manikas Deputy Head Comms & Signal Processing Department of Electrical & Electronic Engineering

2. © Imperial College LondonPage 2 Outline 1.Notation 2.General Problem Formulation 3.Subspace Techniques Signal-Subspace Manifolds Performance Bounds 4.Space-Time Communications 5.Conclusions

3. © Imperial College LondonPage 3 Notation

4. © Imperial College LondonPage 4 cont. - Notation

5. © Imperial College LondonPage 5 cont. - Notation

6. © Imperial College LondonPage 6 cont. - Notation

7. © Imperial College LondonPage 7 General Problem Formulation Condition AWGN

8. © Imperial College LondonPage 8 cont. - General Problem Formulation

9. © Imperial College LondonPage 9 cont. - General Problem Formulation

10. © Imperial College LondonPage 10

11. © Imperial College LondonPage 11 Subspace Techniques

12. © Imperial College LondonPage 12 cont. - Subspace Techniques

13. © Imperial College LondonPage 13 The “Signal-Subspace” Concept

14. © Imperial College LondonPage 14 cont. - The “Signal-Subspace” Concept

15. © Imperial College LondonPage 15 cont. - The “Signal-Subspace” Concept

16. © Imperial College LondonPage 16 cont. - The “Signal-Subspace” Concept

17. © Imperial College LondonPage 17 cont. – The “Signal-Subspace” Concept

18. © Imperial College LondonPage 18 cont. – The “Signal-Subspace” Concept

19. © Imperial College LondonPage 19 The “Manifold” Concept

20. © Imperial College LondonPage 20 cont. – The “Manifold” Concept

21. © Imperial College LondonPage 21 cont. – The “Manifold” Concept

22. © Imperial College LondonPage 22 cont. – The “Manifold” Concept

23. © Imperial College LondonPage 23 cont. – The “Manifold” Concept

24. © Imperial College LondonPage 24 cont. Manifold

25. © Imperial College LondonPage 25 cont. – The “Manifold” Concept

26. © Imperial College LondonPage 26 cont. – The “Manifold” Concept

27. © Imperial College LondonPage 27 cont. – The “Manifold” Concept

28. © Imperial College LondonPage 28 cont. – The “Manifold” Concept

29. © Imperial College LondonPage 29 Performance Bounds

30. © Imperial College LondonPage 30 Space-Time Communications

31. © Imperial College LondonPage 31 cont. - Space-Time Communications

32. © Imperial College LondonPage 32 cont. - Space-Time Communications All ‘conventional’ CDMA receivers can be modified to become Space-Time CDMA receivers Enhancements would result in considerable performance gains Enhancements are not trivial however

33. © Imperial College LondonPage 33 cont. - Space-Time Communications Two classes 1.ST - Single-User Rx: requires no knowledge beyond the PN-sequence and the timing of the user it wants to demodulate/receive ('desired' user) 2.ST - Multi-User Rx: requires knowledge of the PN- sequence & the timing of every active user as well as knowledge of the received amplitudes of all users and the noise level >Can be Optimal or Sub-optimal depending on whether the decision making criteria for symbol detection are fully met (Optimal) or partially met (Sub-optimal)

34. © Imperial College LondonPage 34 Optimum ST-CDMA Receivers ST - RAKE Receiver: Optimum Single-User Receiver ST - MLSE Receiver: Optimum Multi-User Receiver which must take into account the PN-codes of all other CDMA users in the system. Non-linear and computationally far too complex >Huge gap in performance and complexity between an optimum single-user and an optimum multi-user receiver >Decorrelating MU Receiver:This is a typical sub-optimal MU Rx (but much simpler that the optimum MU Rx):

35. © Imperial College LondonPage 35 Space-Time Channels

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37. © Imperial College LondonPage 37 cont. Space-Time Channels

38. © Imperial College LondonPage 38 cont. Space-Time Channels

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40. © Imperial College LondonPage 40

41. © Imperial College LondonPage 41 Example – ULA of 3 elements

42. © Imperial College LondonPage 42 Example - Channel Estimator >Surface and contour plots shows that all 5 path delays and directions are correctly estimated

43. © Imperial College LondonPage 43 Example - Decision Variables

44. © Imperial College LondonPage 44 Example - SNIR Comparisons

45. © Imperial College LondonPage 45 Example – “Near-Far” Resistance

46. © Imperial College LondonPage 46 Example – Subspace Tracking

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49. © Imperial College LondonPage 49 Conclusions: ST Comms based on Subspace-Techniques: –blind –near-far resistant, –superresolution capabilities –The number of multipaths that can be resolved is not constrained by the number of array elements (antennas).

50. © Imperial College LondonPage 50