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

.

.

.

.

.

.

Transmit Antennas

ReceiveAntennas

.

.

.

.

.

.

.

.

.

.

.

.

TransmitBeamforming(Precoder)

ReceiveBeamforming(Combiner)

Transmit Antennas

ReceiveAntennas

EquivalenceChannel

.

.

.

.

.

.

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

ACCESS

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%

ACCESS

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.

17