A Physical Interpretation of Beamforming, BLAST and SVD Algorithms

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 K 2
Array Processing
SU
BS
4
Physical Interpretation
SU
M 3 N 2 K 2
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 2
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 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
Example
13
Beamforming Radiation Pattern
14
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
21
Example
22
Radiation Pattern Beamforming
1st path, a1 1
2nd path, a2 0.6
23
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
Radiation Pattern QR Decomposition
1st path, a1 1
2nd path, a2 0.6
27
Radiation Pattern QR Decomposition
1st path, a1 1
2nd path, a2 0.6
28
Singular Value Decomposition (SVD)
Singular value decomposition of H
29
Radiation Pattern SVD
1st path, a1 1
2nd path, a2 0.6
30
Radiation Pattern SVD
1st path, a1 1
2nd path, a2 0.6
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