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A Physical Interpretation of Beamforming, BLAST and SVD Algorithms

A Physical Interpretation of Beamforming, BLAST and SVD Algorithms. Ada Poon, Bob Brodersen. Physical Interpretation?. Under “certain” channel conditions, in a wireless system with N users,

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A Physical Interpretation of Beamforming, BLAST and SVD Algorithms

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  1. A Physical Interpretation ofBeamforming, BLAST and SVD Algorithms Ada Poon, Bob Brodersen

  2. Physical Interpretation? Under “certain” channel conditions, in a wireless system with N users, a base-station with M = N + K receive antennas can separate the N transmitted signals as well as achieve K + 1 degrees of diversity for each transmitted signal. (Jack Winters et al, 1994)

  3. Physical Interpretation SU M = 3 N = 2 users K = 1 Array Processing SU BS

  4. Physical Interpretation SU M = 3 N = 2 K = 1 Array Processing SU BS

  5. Physical Interpretation … means the radiation patterns at the transmitter and receiver resulting from the array processing algorithms SU M = 3 N = 2 K = 1 Array Processing SU BS

  6. Beamforming & Antenna Diversity • Beamforming focuses the energy from the antenna • Enables a high gain steerable antenna • Increases SNR • Diversity provides redundancy • Enabled by spatial interleaving of signals • Decreases the fluctuations in SNR

  7. Line-of-sight Channel Array Processing where i is the mean angle of arrival from user i to base-station.

  8. Single-user, Single-receive Antenna where A is the path gain( orloss) and  is the path delay. Narrowband baseband equivalent: where .

  9. Single-user, Multiple-receive Antennas d where  is the mean angle of arrival and . Vector form: where a() is the normalized array response vector.

  10. Multiple-user, Multiple-receive Antennas Array Processing Summing over all the users, the received signal vector is

  11. Continued … Matrix form:

  12. Beamforming Beamforming solution: In N users, a base-station with M = N + K receive antennas can separate the N transmitted signals as well as achieve K + 1 degrees of diversity for each transmitted signal Example:

  13. Array Processing Beamforming: Radiation Pattern

  14. Array Processing Beamforming: Radiation Pattern

  15. Multi-transmit, Multi-receive Antennas Array Processing

  16. Multi-transmit, Multi-receive Antennas Array Processing Array Processing

  17. Adding Reflector Array Processing Array Processing

  18. Adding Reflector Array Processing Array Processing Vector form: where ar() and at() is the normalized array response vector at the receiver and the transmitter , respectively.

  19. More Reflectors 1st path 2nd path Array Processing Array Processing 3rd path Summing over all the multipaths, the received signal vector is

  20. Continued … Matrix form: Multipath is not enemy but friend for capacity enhancement

  21. Example

  22. Array Processing Array Processing Radiation Pattern: Beamforming 1st path, a1 = 1 2nd path, a2 = 0.6

  23. Array Processing Array Processing Radiation Pattern: Beamforming 1st path, a1 = 1 2nd path, a2 = 0.6

  24. QR Decomposition (BLAST) QR decomposition of H:

  25. Continued … Therefore, Successive Decoding and Cancellation:

  26. Array Processing Array Processing Radiation Pattern: QR Decomposition 1st path, a1 = 1 2nd path, a2 = 0.6

  27. Array Processing Array Processing Radiation Pattern: QR Decomposition 1st path, a1 = 1 2nd path, a2 = 0.6

  28. Singular Value Decomposition (SVD) Singular value decomposition of H: MIMO technology !!!

  29. Array Processing Array Processing Radiation Pattern: SVD 1st path, a1 = 1 2nd path, a2 = 0.6 Multipath is not enemy but friend for capacity enhancement

  30. Array Processing Array Processing Radiation Pattern: SVD 1st path, a1 = 1 2nd path, a2 = 0.6 Multipath is not enemy but friend for capacity enhancement

  31. Summary • Beamforming at receiver • 1 transmit antenna and M receive antennas • BLAST (layered space-time coding) • N transmit and M receive antennas • Beamforming and diversity gain at receiver • SVD (Singular value decomposition) • N transmit and M receive antennas • Beamforming and diversity gain at both receiver and transmitter

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