Introduction to Hybrid Beamforming Techniquesaccess.ee.ntu.edu.tw/course/under_project_1032/... · Introduction to Hybrid Beamforming Techniques Graduate Institute of Electronics
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Introduction to Hybrid Beamforming Techniques
Graduate Institute of Electronics Engineering
National Taiwan University
Taipei, Taiwan
James Chen
Mar. 31, 2015
Advisor : Andy Wu
ACCESS
Outline
Introduction of Precoding
Why Hybrid beamforming?
Problem Formulation
Existing Hybrid Beamforming Technique
Summary
2
ACCESS
Precoding mitigates channel interference
SVD is the optimal method but require higher bandwidth
Precoding
Reduce the interference among antennas
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Transmit Antennas
ReceiveAntennas
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TransmitBeamforming(Precoder)
ReceiveBeamforming(Combiner)
Transmit Antennas
ReceiveAntennas
EquivalenceChannel
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Transmit Antennas
ReceiveAntennas
Introduction of Precoding MIMO System
3
Vx yUVH
UH
σ1
σ4
ChannelPrecoder
SVDFeedback link
H (from RX)
Noise Decoder
RXSVD:H=UΣVH
u1 u2 u3
v1H
v2H
v3H
σ1
σ2
σ3
H =
U Σ VH
ACCESS
Why Hybrid beamforming?(1/2)
BS
MS
In mmWave scenario, the pathloss is extremely high[3]
30 GHz shows additional about 20 dB loss compared to 3 GHz.
High pathloss can be compensated by:
Large antenna array to increase the array gain
Beamforming via precoding
Channel is rank deficient
Maximum supportable streams are less then the number of Tx antennas
4
ACCESS
Why Hybrid beamforming?(2/2)
Traditional Beamforming is done at BB
Requiring one RF chain per transmitting antenna
A RF chain consists of a mixer, PA/LNA and DAC/ADC
Hybrid Beamforming relies on RF precoding to reduce the number of RF chains[2]
Two-staged transmitting (FRF,FBB) structure
5
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Problem Formulation(1/3)
Step 1: The optimal solution of the precoding matrix, Fopt ,is given by:
V1 is eigenvectors corresponding to Ns largest eigenvalues of H
V1 can be acquired from performing SVD on H
Step 2: We further realize Fopt by hybrid precoder (FRF,FBB)
Number of RF chains
can be reduced
1optF V
……
Ba
se
ba
nd
Pre
co
de
r
Ba
se
ba
nd
Eq
ua
lize
r
……
RF
Be
am
form
erRF-Chain
RF-Chain
RF-Chain
RF-Chain
……
RF-Chain
RF-Chain
RF-Chain
RF-Chain
CSI
AcquisitionSpatially Sparse Precoding
SL- SVD
Tx Precoding for Hybrid Beamformer
RFF
MIMO
Channel
H
1V
BBF
RFW
BBW
AoD
H
…… ……
……
……
……
BBF
RFF
FBBRFopt
BBRF
RFBB FFFFF
FF ,
minarg),(
6
ACCESS
Problem Formulation(2/3)
Step 1: Get the optimal FOPT
The channel matrix H[3]:
aBS(ɵ𝑙𝐵𝑆) is the AOD of active path :
Fopt=V1 can be formed by linear combinations of aBS(ɵl)
7
*
1
( ) ( )L
MS BSBS MSl MS l BS l
l
N NH a a U V
L
……
Ba
se
ba
nd
Pre
co
de
r
Ba
se
ba
nd
Eq
ua
lize
r
……
RF
Be
am
form
erRF-Chain
RF-Chain
RF-Chain
RF-Chain
……
RF-Chain
RF-Chain
RF-Chain
RF-Chain
CSI
AcquisitionSpatially Sparse Precoding
SL- SVD
Tx Precoding for Hybrid Beamformer
RFF
MIMO
Channel
H
1V
BBF
RFW
BBW
AoD
H
…… ……
……
……
……
BBF
RFF
BSBS
BS 1a (θ )
BS
BS 2a (θ )
BS
BS 3a (θ )
MS
TdNjdj
BS
BS
BSlBS
BSl
leea ],...,,1[)(
)sin(2
)1()sin(2
)sin(2
)1(
)sin(2
3
3
1
BSBS
BS
dNj
dj
e
e
ACCESS
Problem Formulation(3/3)
Step 2: Separate Fopt into(FBB ,FRF)
Due to spatial sparsity, this is
equivalent to solve an
optimization problem
Choose best Nrf columns to form FRF ,
and then Find FBB
8
BS
BS
BS 1a (θ )
BS
BS 2a (θ )
BS
BS 3a (θ )
MS
)sin(2
)1(
)sin(2
3
3
1
BSBS
BS
dNj
dj
e
e
st NNCV
1
LN
cantCA
sNL
BB CF
~
FBB
Nt: Number of Tx antennasNrf: Number of RF chainsL: Number of Active PathNs: Number of Tx data streams
FRF
……
Ba
se
ba
nd
Pre
co
de
r
Ba
se
ba
nd
Eq
ua
lize
r
……
RF
Be
am
form
erRF-Chain
RF-Chain
RF-Chain
RF-Chain
……
RF-Chain
RF-Chain
RF-Chain
RF-Chain
CSI
AcquisitionSpatially Sparse Precoding
SL- SVD
Tx Precoding for Hybrid Beamformer
RFF
MIMO
Channel
H
1V
BBF
RFW
BBW
AoD
H
…… ……
……
……
……
BBF
RFF
FRFFBB] )(a ,..., )(a , )(a , )(a[
1 T
BS
T
1BS
T
2BS
T
1BS
BS
L
BS
L
BSBS
tNAcan
FBBRFopt
BBRF
RFBB FFFFF
FF ,
minarg),(
ACCESS
Existing Hybrid Beamforming Technique (I) (1/2)
[3] Use Orthogonal Matching Pursuit(OMP) to calculate (FBB ,FRF)
Perform Nrf iterations of correlation to find FRF
Perform pseudo-inverse to fine FBB
9
st NNCV
1
LN
cantCA
sNL
BB CF
~
FBB
Nt: Number of Tx antennasNrf: Number of RF chainsL: Number of Active PathNs: Number of Tx data streams
FRF
ACCESS
Existing Hybrid Beamforming Technique (I) (2/2)
Hybrid precoding shows near optimal spatial efficiency
while compared with traditional baseband precoding
Spatial efficiency: the data rate that can be transmitted over a given bandwidth (units: bit/s/Hz)
Formula:
10
[3]
|)(|log *****1
2 BBRFRFBBBBRFRFBB
s
N WWHFFFHFWWRN
IRns
ACCESS
Problem 1: Impractical Candidate Matrix
Impossible to get all AOD’s information
Require large bandwidth to return all AOD’s information from Rx
Need a candidate matrix without the information of All AOD
11
st NNCV
1
LN
cantCA
sNL
BB CF
~
FBB
Nt: Number of Tx antennasNrf: Number of RF chainsL: Number of Active PathNs: Number of Tx data streams
FRF
] )(a ,..., )(a , )(a , )(a[1
1 T
BS
T
1BS
T
2BS
T
1BS
BS
L
BS
L
BSBS
tNAcan
BSBS
BS 1a (θ )
BS
BS 2a (θ )
BS
BS 3a (θ )
MS
)sin(2
)1(
)sin(2
3
3
1
BSBS
BS
dNj
dj
e
e
ACCESS
Problem 2: High ComplexityOptimization Algorithm
Long computation time for finding (FBB ,FRF)
OMP need Nrf iterations
Need an faster algorithm with less iterations
Pseudo-inverse is not suitable for HW implementation
Computational complexity:𝑂(𝑛3)
Need an algorithm without
pseudo-inverse
12
st NNCV
1
LN
cantCA
sNL
BB CF
~
FBB
Nt: Number of Tx antennasNrf: Number of RF chainsL: Number of Active PathNs: Number of Tx data streams
FRF
ACCESS
Existing Hybrid Beamforming Technique (II) (1/3)
For problem 1, a DFT codebook is used
Predefined set: Consist of orthogonal column vectors
Don’t require all AOD’s information
Possibly find all Nrf columns using only 1 iteration
Equally space 360 degree with Nt angles to form
a full rank matrix
Hence Acan has Nt columns
13
st NNCV
1
tt NN
can CA
st NN
BB CF
~
Nt: Number of Tx antennasNrf: Number of RF chainsNs: Number of Tx data streams
FRF
FBB
Acan: DFT codebook
BS
BS
BS 1a (θ )
BS
BS 2a (θ )
BS
BS 3a (θ )
MS
)sin(2
)1(
)sin(2
3
3
1
BSBS
BS
dNj
dj
e
e
ACCESS
Existing Hybrid Beamforming Technique (II) (2/3)
For problem 2, OBMP with DFT codebook is used instead of OMP with Acan1
Constraints: Acan must be orthogonal
Using 1 iteration to find (FBB ,FRF)
No pseudo-inverse
14
st NNCV
1
tt NN
can CA
st NN
BB CF
~
FRF
FBB
Algorithm : Othogonality-Based Matching Pursuit
optRequire : F
OPT1: F = Fres*
can res2: Ψ = A F*
,3: k = {n | n is the largest N index of ( ) }RF l l(k)
RF can4: F = A*
BB RF opt5: F = F FBB
BB s
opt RF BB
F6: F = N
F -F F
RF BB7: return F , F
ACCESS
Existing Hybrid Beamforming Technique (II) (3/3)
OBMP’s computation time for finding (FBB ,FRF)
is less then that of OMP by 89.6% when Nrf equals 8
15
89.6%
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Summary
Advantage of hybrid beamforming
Reduce the number of RF chains but remain
near optimal performance
Design goal of hybrid beamforming
Method for finding (FBB ,FRF)
16
OMP[3] OBMP
Number of iteration Nrf 1
Complexity High Low
Constraints None OrthogonalAcan
FBBRFopt
BBRF
RFBB FFFFF
FF ,
minarg),(
ACCESS
Reference
[1] M. Vu and A. Paulraj, “MIMO wireless linear precoding,” IEEE Signal Process. Mag., vol. 24, no. 5, pp. 86–105, Sept. 2007.
[2] Roh, W.; Ji-Yun Seol; Jeongho Park; Byunghwan Lee; Jaekon Lee; Yungsoo Kim; Jaeweon Cho; Kyungwhoon Cheun; Aryanfar, F., "Millimeter-wave beamforming as an enabling technology for 5G cellular communications: theoretical feasibility and prototype results," Communications Magazine, IEEE , vol.52, no.2, pp.106,113, February 2014
[3] El Ayach, O.; Rajagopal, S.; Abu-Surra, S.; Zhouyue Pi; Heath, R.W., "Spatially Sparse Precoding in Millimeter Wave MIMO Systems," Wireless Communications, IEEE Transactions on , vol.13, no.3, pp.1499,1513, March 2014
[4] D. P. Palomar, J. M. Cioffi, and M. A. Lagunas, “Joint Tx-Rx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization,” IEEE Trans. Signal Process., vol. 51, no. 9, pp. 2381–2401, 2003.
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