0. A New Approach to Beamformer Design for Massive MIMO Systems Based on k-regularity
Gilwon Lee
Dept. of Electrical Engineering
KAIST
Joint work with Juho Park, Youngchul Sung and Junyeong Seo
GLOBECOM 2012 Workshop LTE-B4G, Dec. 3, 2012

1. Massive MIMO Systems Massive MIMO is an emerging technology,
which scales up MIMO by an order of magnitude.
Antenna arrays with a few hundred elements.
Massive MIMO
Rate↑
Transmission reliability↑
Energy efficiency↑

2. Practical Issues on Massive MIMO
Antenna elements: cheap.
But, the multiple RF chains associated with multiple antennas are costly in terms of
size, power and hardware.
The number of RF chains is restricted in massive MIMO systems.

3. System Model Single user massive MIMO BS MS Assumptions (1) (2) (3)
RF chain
RF chain
Assumptions
(1)
The size of antenna array at the MS is limited
(2)
(3)
due to hardware constraint.

4. The Conventional Method: Antenna Selection
At transmitter
RF chain
RF chain
RF chain
Antenna selection:
M RF chains select M different antennas
out of the NT available transmit antennas.
Hardware
Complexity↓

5. The Conventional Method: Antenna Selection
At transmitter
RF chain
RF chain
Antenna
Selection
RF chain
However,
the performance of antenna selection should be far interior
to that of a method using all of transmit antennas.
Especially, the gap of performance will be increasing
as NT increases.

6. The Proposed Scheme: k-regular Beamformer
At transmitter
RF chain
RF chain
Antenna
Selection
RF chain
k-regular
beamformer
RF chain

7. The Proposed Scheme: k-regular Beamformer
Specifically
RF chain
k-regular
beamformer
k-regular beamformer:
Each of the M data streams is multiplied by k complex gains
and assigned to k out of the available NT transmit antennas
and signals assigned to the same transmit antenna will be added to be transmitted.

8. The Proposed Scheme: k-regular Beamformer
For example,
Each column of V has k=2 nonzero elements.
⇒ k-regularity
or k-sparse constraint
But, how to design the matrix V?

9. Problem Formulation Data k-regular streams beamformer Channel
k-regularity
Problem)
k-regular constraint
power constraint
Assumptions
M independent data stream transmission
with equal power for each stream
There is no power amp in k-regular
beamformer

10. Observations In combinatorial approach, (brute search)
Impossible to implement
should be required to find optimum V
Need an algorithm to reduce complexity!

11. Observations Without k-regular constraint,
the optimal transmit beamforming matrix V is given by
where
(SVD)
is i-th column of
The matrix is called eigen beamforming matrix
Based on this fact, we can propose a method to design k-regular beamformer.

12. The Maximum Correlation Method
A simple way to design k-regular BF matrix:
to approximate the eigen beamforming matrix of H
under k-regular constraint
Maximum correlation method (MCM) ⇒
Pick k largest absolute values in v
and let other values be zeroes.
After then, normalize it
Very simple,
Systematic ⇒
Possible to analyze
Heuristic ⇒
Performance loss

13. The Relaxed Problem Original Problem
-norm relaxation of k-regular constraint ⇒
where
How can we solve the relaxed problem?

14. Iterative Shrinkage Thresholding Algorithm
For a convex function ⇔
< Iterative Shrinkage Thresholding Algorithm (ISTA) >
Shrinkage operator
Gradient method
where
Here,

15. Iterative Shrinkage Thresholding Algorithm⇔
If we directly apply ISTA to our problem

16. Iterative Shrinkage Thresholding Algorithm⇔
If we directly apply ISTA to our problem
without the power constraint,
Shrinkage operator
for i-th column vector
where

17. Projected ISTA (PISTA)
With the power constraint,
Projected ISTA (PISTA)
Metric projection
of vector i-th column onto B

18. Projected ISTA (PISTA)
The Projected ISTA for k-regular Beamformer Design
0. (Initialization) Generate randomly
1. (PISTA) Update
2. (Stop criterion) If
3. (Hard-thresholding) For
update,
update,
4. (Power adjusting) For

19. Simulation Results
Antenna selection scheme:
Parameters:

20. Simulation Results k-regular beamformer scheme: Parameters: 200%
gain
Antenna
Selection gain
200%

21. Simulation Results k-regular beamformer scheme with varying k
Parameters:
eigen BF
gain
Antenna
Selection gain
with small k

22. Simulation Results
Distribution of antennas over numbers of connections
Parameters:
89%
69%
44%
28%
A large portion of antennas are not connected to signals for small k

23. Simulation Results

24. Conclusion Proposed k-regular beamformer architecture
Proposed PISTA and MCM to design k-regular beamforming
Enable system designers to choose optimal trade-off their hardware constraint and required rate performance
showed that the proposed k-regular BF significantly improves the rate gain over simple antenna selection