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Introduction to Hybrid Beamforming Techniques James s Chen Advisor : Andy Wu Graduate Institute of Electronics Engineering National Taiwan University Taipei, Taiwan Mar. 31, 2015 Outline Introduction of Precoding Why Hybrid beamforming?

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Introduction to Hybrid Beamforming Techniques

Graduate Institute of Electronics Engineering National Taiwan University Taipei, Taiwan

James s Chen

  • Mar. 31, 2015

Advisor : Andy Wu

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Outline

Introduction of Precoding Why Hybrid beamforming? Problem Formulation Existing Hybrid Beamforming Technique Summary 2

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Precoding mitigates channel interference SVD is the optimal method but require higher bandwidth

Precoding Reduce the interference among antennas

. . . . . .

Transmit Antennas Receive Antennas

. . . . . . . . . . . . Transmit Beamforming (Precoder) Receive Beamforming (Combiner)

Transmit Antennas Receive Antennas

Equivalence Channel

. . . . . .

Transmit Antennas Receive Antennas

Introduction of Precoding MIMO System

3

V x y U VH UH σ1 σ4

Channel Precoder SVD Feedback link H (from RX) Noise Decoder RX

SVD:H=UΣVH

u1 u2 u3 v1

H

v2

H

v3

H

σ1 σ2 σ3

H =

U Σ VH

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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

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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]

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

1

  • pt

F V 

…… Baseband Precoder Baseband Equalizer

……

RF Beamformer

RF-Chain RF-Chain RF-Chain RF-Chain

……

RF-Chain RF-Chain RF-Chain RF-Chain

CSI Acquisition Spatially Sparse Precoding SL- SVD Tx Precoding for Hybrid Beamformer

RF

F

MIMO Channel

H

1

V

BB

F

RF

W

BB

W AoD

H

…… …… …… …… ……

BB

F

RF

F

F BB RF

  • pt

BB RF RF BB

F F F F F F F   , min arg ) , (

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Problem Formulation(2/3)

Step 1: Get the optimal FOPT

The channel matrix H[3]: aBS(ɵ𝑚

𝐶𝑇) is the AOD of active path :

Fopt=V1 can be formed by linear combinations of aBS(ɵl)

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* 1

( ) ( )

L MS BS BS MS l MS l BS l l

N N H a a U V L    

 

  

…… Baseband Precoder Baseband Equalizer

……

RF Beamformer

RF-Chain RF-Chain RF-Chain RF-Chain

……

RF-Chain RF-Chain RF-Chain RF-Chain

CSI Acquisition Spatially Sparse Precoding SL- SVD Tx Precoding for Hybrid Beamformer

RF

F

MIMO Channel

H

1

V

BB

F

RF

W

BB

W AoD

H

…… …… …… …… ……

BB

F

RF

F

BS

BS BS 1

a (θ )

BS BS 2

a (θ )

BS BS 3

a (θ )

MS

T d N j d j BS BS

BS l BS BS l l

e e a ] ,..., , 1 [ ) (

) sin( 2 ) 1 ( ) sin( 2      

              

 ) sin( 2 ) 1 ( ) sin( 2

3 3

1

BS BS BS

d N j d j

e e

     

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Problem Formulation(3/3)

Step 2: Separate Fopt into(FBB ,FRF) Due to spatial sparsity, this is equivalent to solve an

  • ptimization problem

Choose best Nrf columns to form FRF , and then Find FBB

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B S

BS BS 1

a (θ )

BS BS 2

a (θ )

BS BS 3

a (θ )

M S

              

 ) sin( 2 ) 1 ( ) sin( 2

3 3

1

BS BS BS

d N j d j

e e

     

s t N

N

C V

1 L N can

t

C A

s

N L BB

C F

 ~

FBB

Nt: Number of Tx antennas Nrf: Number of RF chains L: Number of Active Path Ns: Number of Tx data streams FRF

…… Baseband Precoder Baseband Equalizer

……

RF Beamformer

RF-Chain RF-Chain RF-Chain RF-Chain

……

RF-Chain RF-Chain RF-Chain RF-Chain

CSI Acquisition Spatially Sparse Precoding SL- SVD Tx Precoding for Hybrid Beamformer

RF

F

MIMO Channel

H

1

V

BB

F

RF

W

BB

W AoD

H

…… …… …… …… ……

BB

F

RF

F

FRF FBB

] ) ( a ,..., ) ( a , ) ( a , ) ( a [ 1

T BS T 1 BS T 2 BS T 1 BS BS L BS L BS BS t

N Acan    

F BB RF

  • pt

BB RF RF BB

F F F F F F F   , min arg ) , (

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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

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s t N

N

C V

1 L N can

t

C A

s

N L BB

C F

 ~

FBB

Nt: Number of Tx antennas Nrf: Number of RF chains L: Number of Active Path Ns: Number of Tx data streams

FRF

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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:

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[3]

|) (| log

* * * * * 1 2 BB RF RF BB BB RF RF BB s N

W W H F F F HF W W R N I R

n s

  

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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

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s t N

N

C V

1 L N can

t

C A

s

N L BB

C F

 ~

FBB

Nt: Number of Tx antennas Nrf: Number of RF chains L: Number of Active Path Ns: Number of Tx data streams

FRF

] ) ( a ,..., ) ( a , ) ( a , ) ( a [ 1 1

T BS T 1 BS T 2 BS T 1 BS BS L BS L BS BS t

N Acan    

BS

BS BS 1

a (θ )

BS BS 2

a (θ )

BS BS 3

a (θ )

MS

              

 ) sin( 2 ) 1 ( ) sin( 2

3 3

1

BS BS BS

d N j d j

e e

     

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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:𝑃(𝑜3) Need an algorithm without pseudo-inverse

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s t N

N

C V

1 L N can

t

C A

s

N L BB

C F

 ~

FBB

Nt: Number of Tx antennas Nrf: Number of RF chains L: Number of Active Path Ns: Number of Tx data streams

FRF

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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

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s t N

N

C V

1

t t N

N can

C A

s t N

N BB

C F

 ~

Nt: Number of Tx antennas Nrf: Number of RF chains Ns: Number of Tx data streams

FRF FBB

Acan: DFT codebook

B S

BS BS 1

a (θ )

BS BS 2

a (θ )

BS BS 3

a (θ )

M S

              

 ) sin( 2 ) 1 ( ) sin( 2

3 3

1

BS BS BS

d N j d j

e e

     

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Existing Hybrid Beamforming Technique (II) (2/3)

For problem 2, OBMP with DFT codebook is used instead

  • f OMP with Acan1

Constraints: Acan must be orthogonal Using 1 iteration to find (FBB ,FRF) No pseudo-inverse

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s t

N N

C V

1

t t

N N can

C A

s t

N N BB

C F

 ~

FRF FBB

Algorithm : Othogonality-Based Matching Pursuit

  • pt

Require : F

OPT

1: F = F

res * can res

2: Ψ = A F

* ,

3: k = {n | n is the largest N index of ( ) }

RF l l



(k) RF can

4: F = A

* BB RF opt

5: F = F F

BB BB s

  • pt

RF BB

F 6: F = N F -F F

RF BB

7: return F , F

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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 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)

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OMP[3] OBMP Number of iteration Nrf 1 Complexity High Low Constraints None Orthogonal Acan

F BB RF

  • pt

BB RF RF BB

F F F F F F F   , min arg ) , (

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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

  • n , 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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