1. A Physical Interpretation of Beamforming, 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 InterpretationSU
M = 3
N = 2 users
K = 1
Array
Processing SU BS

4. Physical InterpretationSU
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( or loss) and  is the path delay.
Narrowband baseband equivalent:
where

9. Single-user, Multiple-receive Antennasd
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: Example:
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. Beamforming: Radiation Pattern
Array
Processing

14. Beamforming: Radiation Pattern
Array
Processing

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

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

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

25. Continued …
Therefore,
Successive Decoding and Cancellation:

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

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

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

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

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

31. Summary Beamforming at receiver BLAST (layered space-time coding)
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)
Beamforming and diversity gain at both receiver and transmitter