Introduction to Hybrid Beamforming
Techniques
James Chen
Advisor : Andy Wu
Graduate Institute of Electronics Engineering
National Taiwan University
Taipei, Taiwan
Mar. 31, 2015
Outline
Introduction of Precoding
Why Hybrid beamforming?
Problem Formulation
Existing Hybrid Beamforming Technique
Summary
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Introduction of
Precoding MIMO System
Precoding mitigates channel interference
SVD is the optimal method but require higher
bandwidth
Transmit
.
.
.
.
.
.
Transmit
Antennas
Precoding
Receive
Antennas
Transmit
Antennas
Channel
x
V
VH
σ4
Feedback link
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Receive
Antennas
.
.
.
.
.
.
Transmit
Antennas
Receive
Antennas
RX
Noise
σ1
Equivalence
Channel
Reduce the interference among antennas
SVD:H=UΣVH
Precoder
Receive
.
Beamforming .
.
(Combiner) .
.
.
.
.
.
. Beamforming
. (Precoder)
.
Decoder
v1 H
σ1
U
UH
y
H = u1 u2 u3
σ2
v2 H
σ3
SVD
H (from RX)
U
Σ
v3 H
VH
3
Why Hybrid beamforming?(1/2)
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
BS
MS
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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]
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Two-staged transmitting (FRF,FBB) structure
5
Problem Formulation(1/3)
Step 1: The optimal solution of the precoding matrix,
Fopt ,is given by:
Fopt  V1
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)
( FBB , FRF ) 
arg min
FRF , FBB
Fopt  FRF FBB
Tx Precoding for Hybrid Beamformer
AoD
F
SL- SVD
V1
RF-Chain
RF-Chain
……
RF-Chain
FRF
WRF
RF-Chain
RF-Chain
Baseband Equalizer
H
……
……
……
……
……
……
MIMO
Channel
……
RF Beamformer
RF-Chain
RF-Chain
FBB
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H
FRF
FBB
Baseband Precoder
Number of RF chains
can be reduced
CSI
Acquisition
Spatially Sparse Precoding
RF-Chain
WBB
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Problem Formulation(2/3)
Step 1: Get the optimal FOPT
N BS N MS
L
L
 a
The channel matrix H[3]:
aBS(ɵ𝐵𝑆
𝑙 ) is the AOD of active path :
H

aBS ( l )  [1, e
BS
j
2

d sin( lBS )
,..., e
j ( N BS 1)
2

l
l 1
d sin( lBS )
MS
(l MS )aBS (l BS )*  U V 
]T
Fopt=V1 can be formed by linear combinations of aBS(ɵl)
Tx Precoding for Hybrid Beamformer
AoD
BS
BS
1
a BS (θ
)
CSI
Acquisition
Spatially Sparse Precoding
SL- SVD
V1
H
FRF
FBB
a BS (θ 2 BS )
RF-Chain
RF-Chain
……
WRF
RF-Chain
Baseband Equalizer
FRF
RF-Chain
……
RF Beamformer
H
……
MIMO
Channel
RF-Chain
RF-Chain
FBB
……
……
……
……
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MS
RF-Chain
……
1


2
j
d sin( 3BS )


e 





 j ( N BS 1) 2 d sin(3BS ) 

e

Baseband Precoder
a BS (θ3BS )
RF-Chain
WBB
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Problem Formulation(3/3)
Step 2: Separate Fopt into(FBB ,FRF)
FRF , FBB
Fopt  FRF FBB
Tx Precoding for Hybrid Beamformer
AoD
SL- SVD
V1
RF-Chain
RF-Chain
RF-Chain
WRF
FRF
FBB
RF-Chain
Baseband Equalizer
H
RF-Chain
……
……
……
……
……
……
MIMO
Channel
RF-Chain
FBB
1
[a BS (1BS ) T , a BS ( 2BS ) T , a BS (LBS1 ) T ,..., a BS (LBS ) T ]
Nt
RF Beamformer
RF-Chain
……
Baseband Precoder
Acan 
H
FRF
FBB
Due to spatial sparsity, this is
equivalent to solve an
optimization problem
CSI
Acquisition
Spatially Sparse Precoding
F
……
( FBB , FRF ) 
arg min
RF-Chain
WBB
FRF
Choose best Nrf columns to form FRF ,
and then Find FBB
B
S
V1  C N t  N s
a BS (θ1BS )
Acan  C N t  L
~
FBB  C L N s
a BS (θ 2 BS )
1


2
j
d sin( 3BS )


e 





 j ( N BS 1) 2 d sin(3BS ) 

e

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a BS (θ3BS )
M
S
Nt: Number of Tx antennas
Nrf: Number of RF chains
L: Number of Active Path
Ns: Number of Tx data streams
FRF
FBB
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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
V1  C N t  N s
Acan  C N t  L
Nt: Number of Tx antennas
Nrf: Number of RF chains
L: Number of Active Path
Ns: Number of Tx data streams
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~
FBB  C L N s
FRF
FBB
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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: R  log 2 (| I N  R 1WBB* WRF* HFRF FBB FBB* FRF* H *WRFWBB |)
s
Ns
n
[3]
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Problem 1: Impractical
Candidate Matrix
Impossible to get all AOD’s information
Acan1 
1
[a BS (1BS ) T , a BS ( 2BS ) T , a BS (LBS1 ) T ,..., a BS (LBS ) T ]
Nt
Require large bandwidth to return all AOD’s information from Rx
Need a candidate matrix without the information of All AOD
BS
V1  C N t  N s
a BS (θ1BS )
Acan  C Nt L
~
FBB  C L N s
a BS (θ 2 BS )
a BS (θ3BS )
1


2
j
d
sin( 3BS )


e 





 j ( N BS 1) 2 d sin(3BS ) 

e

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MS
Nt: Number of Tx antennas
Nrf: Number of RF chains
L: Number of Active Path
Ns: Number of Tx data streams
FRF
FBB
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Problem 2: High Complexity
Optimization 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
V1  C N t  N s
Acan  C N t  L
Nt: Number of Tx antennas
Nrf: Number of RF chains
L: Number of Active Path
Ns: Number of Tx data streams
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~
FBB  C L N s
FRF
FBB
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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
B
S
V1  C N t  N s
a BS (θ1BS )
Acan  C N t  N t
~
FBB  C N t  N s
a BS (θ 2 BS )
a BS (θ3BS )
1


 j 2 d sin(3BS ) 
e

 


 j ( N BS 1) 2 d sin(3BS ) 

e

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FRF
M
S
Acan: DFT codebook
Nt: Number of Tx antennas
Nrf: Number of RF chains
Ns: Number of Tx data streams
FBB
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Existing Hybrid Beamforming
Technique (II) (2/3)
For problem 2, OBMP with DFT codebook is used instead
of OMP with Acan1
~
A C
V C
F C
Nt Nt
Nt N s
Constraints: Acan must be orthogonal
Using 1 iteration to find (FBB ,FRF)
No pseudo-inverse
1
can
Nt N s
BB
FRF
FBB
Algorithm : Othogonality-Based Matching Pursuit
Require : Fopt
1: F res = FOPT
2: Ψ = A*can Fres
3: k = {n | n is the largest N RF index of ( * )l ,l }
4: FRF = A (k) can
5: FBB = F*RF Fopt
FBB
6: FBB = N s
Fopt -FRF FBB
7: return FRF , FBB
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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
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
( FBB , FRF ) 
arg min
FRF , FBB
Fopt  FRF FBB
F
Method for finding (FBB ,FRF)
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OMP[3]
OBMP
Number of iteration
Nrf
1
Complexity
High
Low
Constraints
None
Orthogonal
Acan
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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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