A New Approach to Beamformer Design for Massive MIMO Systems Based on k-regularity

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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
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Massive MIMO Systems
MIMO
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?

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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.
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System Model
Single user
massive MIMO
BS
MS
Assumptions
(1)
The size of antenna array at the MS is limited
(2)
(3)
due to hardware constraint.
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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?
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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.
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The Proposed Scheme k-regular Beamformer
At transmitter
RF chain
RF chain
k-regular beamformer
RF chain
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The Proposed Scheme k-regular Beamformer
Specifically
Each of the M data streams is multiplied by k
complex gains
k-regular beamformer
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.
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The Proposed Scheme k-regular Beamformer
For example,
Each column of V has k2 nonzero elements.
? k-regularity
or k-sparse constraint
But, how to design the matrix V?
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Problem Formulation
Data streams
k-regular 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
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Observations
In combinatorial approach, (brute search)
Impossible to implement
should be required to find optimum V
Need an algorithm to reduce complexity!
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Observations
Without k-regular constraint,
the optimal transmit beamforming matrix V is
given by
(SVD)
where
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.
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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
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The Relaxed Problem
Original Problem
-norm relaxation of k-regular constraint
?
where
How can we solve the relaxed problem?
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Iterative Shrinkage Thresholding Algorithm
For a convex function
?
lt Iterative Shrinkage Thresholding Algorithm
(ISTA) gt
Shrinkage operator
Gradient method
where
Here,
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Iterative Shrinkage Thresholding Algorithm
?
If we directly apply ISTA to our problem
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Iterative Shrinkage Thresholding Algorithm
?
without the power constraint,
If we directly apply ISTA to our problem
Shrinkage operator for i-th column vector
where
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Projected ISTA (PISTA)
With the power constraint,
Projected ISTA (PISTA)
Metric projection of vector i-th column onto B
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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
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Simulation Results
Antenna selection scheme
Parameters
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Simulation Results
k-regular beamformer scheme
Parameters
k-regular gain
Antenna Selection gain
200
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Simulation Results
k-regular beamformer scheme with varying k
Parameters
eigen BF gain
Antenna Selection gain
with small k
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Simulation Results
Distribution of antennas over numbers of
connections
Parameters
89
69
44
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A large portion of antennas are not connected to
signals for small k
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Simulation Results
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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