1. Multipe-Symbol Sphere Decoding for Space- Time Modulation Vincent Hag March 7 th 2005

2. Why MIMO? Limited radio resources Need for higher data rate (3G services and beyond)  Make the best possible use of the spectrum in order to further increase throughput as well as user-capacity MIMO antennas is a key technology

3. Why Multiple-Symbol Detection? N received symbols are jointly processed to estimate N-1 symbols  Better evaluation of the channel statistics yields improved performances

4. Why Non-coherent Detection? Phase estimation difficult or costly  Develop (de)modulation techniques that do not require CSI Extend DPSK to MIMO systems

5. Problem Formulation Performance (exploit space and time dimensions) Complexity (exponential in space and time dimensions)  Need for fast-algorithm based detection

6. Talk Outline  Transmission  Channel Model  Reception: Sphere Decoder  Simulation Results  Conclusions and Further Works

7. Transmission Non-coherent Detection  Differential Transmission Diagonal codes (= extension of DPSK signals to STC)

8. Differential Encoding Code matrices are differentially encoded such as

9. Diagonal Codes

10. Channel Model AWGN Rayleigh fading Multi-channel action:

11. Communication link

12. Catch-up slide

13. Talk Outline  Transmission  Channel Model  Reception: Sphere Decoder  Simulation Results  Conclusions and further Works

14. Reception: Metric Metric: ML decision rule:

15. Sphere Decoding: Concept Fix and examine signals such that  Search of signals lying inside a sphere of radius instead of the whole space

16. Sphere Decoding with U upper triangular  can be determined component-wise, starting from and tracking up to

17. Sphere Decoding

18. choose that minimizes to keep it as small as possible: Partial distance criterion:

19. Sphere Decoding radius updated to Then, restart the sphere decoding algorithm with the new radius value

20. Sphere Decoding Phase ambiguities : fix and start sphere decoding at Search strategy : Zigzag procedure: hypothetical symbols (examined for the ith component) are ordered according monotically increasing distance

21. Zigzag for 8-PSK constellation

22. Representation in a tree

23. DFDD Attractive low-complexity algorithm performing differential detection Linear predictor making decision on based on and

24. Talk Outline  Transmission  Channel Model  Reception: Sphere Decoder  Simulation Results  Conclusions and further Works

25. Simulation Results Simulation setup BER performances Computational Complexity BER vs. Complexity

26. Simulation Setup bit/channel use, Spatially independent Rayleigh continuous fading channels Detect at least 1000 bit errors to assess the BER at any SNR Number of multiplications as a measure of the complexity

27. BER performances Error floor removed Single Antenna System

28. BER performances MSDSD vs DFDD

29. BER performances Mismacth of the Doppler rate 4dB shift Robust?

30. Computational Complexity Average Number of Real Multiplications done to estimate a 10-length sequence

31. Computational Complexity

32. BER vs Complexity Restrict the number of multiplications for practical reasons

33. BER vs Complexity

34. Conclusion SD outperforms DFDD, a good low- complexity algorithms Excellent performance versus complexity trade-off: ML performances But orders of magnitudes below that of brute-force search (ML detection) Gains in power efficiency almost for free

35. Further Works Investigate other STC, possibly with other search strategy for PDP Take interference into account

36. Questions?