a new approach to beamformer design for massive mimo systems based on k-regularity gilwon lee dept....
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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
GLOBECOM 2012 Workshop LTE-B4G, Dec. 3, 2012
Joint work with Juho Park, Youngchul Sung and Junyeong Seo
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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.
MIMO
Massive MIMO
• Rate↑
• Transmission reliability↑
• Energy efficiency↑Internet Internet
120°
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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
Assumptions
(1)
(3)
(2)
The size of antenna array at the MS is limited
RF chain
RF chain
due to hardware constraint.
BS MS
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The Conventional Method: Antenna Selection
RF chain
RF chain
RF chain
At transmitter
Antenna selection: M RF chains select M different antennas out of the NT available transmit antennas.
HardwareComplexity↓
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The Conventional Method: Antenna Selection
RF chain
RF chain
RF chain
At transmitter
However, the performance of antenna selection should be far interiorto that of a method using all of transmit antennas.
Especially, the gap of performance will be increasing as NT increases.
AntennaSelection
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The Proposed Scheme: k-regular Beamformer
RF chain
At transmitter
RF chain
RF chain
RF chain
RF chain
RF chain
AntennaSelection
k-regularbeamformer
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Specifically
RF chain
RF chain
RF chain
k-regularbeamformer
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 antennasand signals assigned to the same transmit antenna will be added to be transmitted.
The Proposed Scheme: k-regular Beamformer
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For example,
Each column of V has k=2 nonzero elements.
But, how to design the matrix V?
⇒ k-regularity
or k-sparse constraint
The Proposed Scheme: k-regular Beamformer
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Problem Formulation
Data streams
k-regularbeamformer Channel
M independent data stream transmissionwith equal power for each stream
Assumptions
There is no power amp in k-regularbeamformer
k-regular constraint
power constraint
k-regularity
Problem)
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Observations
In combinatorial approach, (brute search)
should be required to find optimum VImpossible to implement
Need an algorithm to reduce complexity!
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Observations
Without k-regular constraint,
the optimal transmit beamforming matrix V is given by
where
The matrix is called eigen beamforming matrix
(SVD)
is i-th column of
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:
Maximum correlation method (MCM)
to approximate the eigen beamforming matrix of Hunder k-regular constraint
⇒ 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
where
-norm relaxation of k-regular constraint
How can we solve the relaxed problem?
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Iterative Shrinkage Thresholding Algorithm
For a convex function
⇔
< Iterative Shrinkage Thresholding Algorithm (ISTA) >
Gradient methodShrinkage operator
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
⇔
If we directly apply ISTA to our problem
Shrinkage operator for i-th column vector
without the power constraint,
where
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Projected ISTA (PISTA)
With the power constraint,
Metric projection of vector i-th column onto B
Projected ISTA (PISTA)
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Projected ISTA (PISTA)
The Projected ISTA for k-regular Beamformer Design
0. (Initialization) Generate randomly
2. (Stop criterion) If
3. (Hard-thresholding) For update,
4. (Power adjusting) For update,
1. (PISTA) Update
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Simulation Results
Antenna selection scheme:
Parameters:
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Simulation Results
k-regular beamformer scheme:
Parameters:
AntennaSelection gain
k-regulargain
200%
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Simulation Results
k-regular beamformer scheme with varying k
Parameters:
with small k
AntennaSelection gain
eigen BFgain
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Simulation Results
Distribution of antennas over numbers of connections
Parameters:
A large portion of antennas are not connected to signals for small k
89%
69%
44%
28%
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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