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The Simulation of Beamforming Techniques 指指指指 指指指 指 指 指指指

The Simulation of Beamforming Techniques

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The Simulation of Beamforming Techniques. 指導教授:黃文傑 學  生:蔡漢成. Outline. Review of all common Beamforming tech. Compare with different elements Compare with different antenna space Tracks the moving source Conclusion. Review of all common Beamforming tech. Conventional Beamforming - PowerPoint PPT Presentation

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Page 1: The Simulation of Beamforming Techniques

The Simulation of Beamforming Techniques指導教授:黃文傑學  生:蔡漢成

Page 2: The Simulation of Beamforming Techniques

Outline

Review of all common Beamforming tech. Compare with different elements Compare with different antenna space Tracks the moving source Conclusion

Page 3: The Simulation of Beamforming Techniques

Review of all common Beamforming tech. Conventional Beamforming MVDR Beamforming (Capon’s) Robust Beamforming

Page 4: The Simulation of Beamforming Techniques

Conv. Beamforming & Steering Vector

( ) ( ) ( ) ( )

( ) ( )

n s n n

n n

u a n

x n

TkdLjjkd ee ]1[)( cos)1(cos a

22

c

fk

d d

θ(L-1)d

X

Y

)()(

)(

aa

aw

H

BF

)()(

)()()(

aa

aRaH

H

BFP

Page 5: The Simulation of Beamforming Techniques

ULA M = 4 8 12

Page 6: The Simulation of Beamforming Techniques

ULA SNR = 0 ~30

Page 7: The Simulation of Beamforming Techniques

ULA with different λ

Page 8: The Simulation of Beamforming Techniques

UCA

22 sin( )

2d R

M

R

θ= 2π/L

l = 0

l = L-1

l = 1

TLjj ee ]1[)( )1( a

2 ( 1) 2 ( 1)( , ) cos cos sin sin

l ll kR

L L

2 2cfkc

Page 9: The Simulation of Beamforming Techniques

UCA 0.5 λ

Page 10: The Simulation of Beamforming Techniques

UCA 1.0 λ

Page 11: The Simulation of Beamforming Techniques

UCA 1.5λ

Page 12: The Simulation of Beamforming Techniques

UCA 2λ

Page 13: The Simulation of Beamforming Techniques

MVDR Beamforming

1)( awH

)()(

)(1

1

aRa

aRw

H

CAP

)(min wP

)()(

1)(

1

aRa

H

CAPP

Page 14: The Simulation of Beamforming Techniques

Capon’s Beam-pattern

)()(

1)( 1

aRa

H

CAPP

Page 15: The Simulation of Beamforming Techniques

ULA 0.5 λ

Geometry d M SNR SOI SNOI User

ULA 0.5λ 4 8 12 30 90 50、 130 3

Page 16: The Simulation of Beamforming Techniques

ULA 1λ

Geometry d M SNR SOI SNOI User

ULA 1λ 4 8 12 30 90 50、 130 3

Page 17: The Simulation of Beamforming Techniques

UCA 0.5 λ

Geometry d M SNR SOI SNOI User

UCA 0.5λ 4 8 12 30 90 50、 130 3

Page 18: The Simulation of Beamforming Techniques

UCA 1 λ

Geometry d M SNR SOI SNOI User

UCA 1λ 4 8 12 30 90 50、 130 3

Page 19: The Simulation of Beamforming Techniques

UCA 1.5 λ

Geometry d M SNR SOI SNOI User

UCA 1.5λ 4 8 12 30 90 50、 130 3

Page 20: The Simulation of Beamforming Techniques

Robust Beamforming

k = 0

2 2( ), ( (0), ( )), (0) 0m m m mk N k

,( ) ( ) ( )y d i nk yk E k k R R R R 20 0 0 0 0 0 0( ) | (0), ( ) ( ) ( )H

d k p k d R a a

1

2 2

1

( ) | (0), ( ) ( ) ( )N

Hi n m m m m m m m

m

k p k d

R a a I

2| (0), ( )m m mp k

1

2 2(0) (0)

0

( ) (0), ( )N

Hy m m mm m

m

k k

R a a Q I

2 2 2(0)2 2 ( ) cos

(0), ( )( ) m m

m

d p qkm pq

e

Q

Page 21: The Simulation of Beamforming Techniques

Degree spreading

0max

max max

( )( )r H

d

kk

w e

e R e

( ) arg min ( )Hyr k k

ww w R w

0( )Hd k w R w

,( ) ( ) ( )y d i nk yk E k k R R R R

20 0 0 0 0 0 0( ) | (0), ( ) ( ) ( )H

d k p k d R a a

1

2 2(0) (0)

0

( ) (0), ( )N

Hy m m mm m

m

k k

R a a Q I

2 2 2(0)2 2 ( ) cos

(0), ( )( ) m m

m

d p qkm pq

e

Q

1

2 2

1

( ) | (0), ( ) ( ) ( )N

Hi n m m m m m m m

m

k p k d

R a a I

Page 22: The Simulation of Beamforming Techniques

The flow chart of Robust Beamforming

SOI DOATracker

Sample correlation matrix

Parametric desired correlation matrix

From average correction matrices

{y(k)}

DOA spreading matrix

Compute robustBeamformer

0(0) (0)dR

(0)yR

( )d KR

( )y KR

2max ( )K

( )r Kw

Page 23: The Simulation of Beamforming Techniques

ULA 0.5 λ

Geometry d angle spread SNR SOI

ULA 0.5λ 0 10 20 30 30 90

Page 24: The Simulation of Beamforming Techniques

ULA 1 λ

Geometry d angle spread SNR SOI

ULA λ 0 10 20 30 30 90

Page 25: The Simulation of Beamforming Techniques

ULA 1.5 λ

Geometry d angle spread SNR SOI

ULA 1.5λ 0 10 20 30 30 90

Page 26: The Simulation of Beamforming Techniques

UCA

Page 27: The Simulation of Beamforming Techniques

UCA 1.5 λ

Geometry d angle spread SNR SOI

UCA 1.5λ 0 10 20 30 30 90

Page 28: The Simulation of Beamforming Techniques

DOA Estimation

Conventional Capon’s MUSIC

Page 29: The Simulation of Beamforming Techniques

Conventional

w(0~180)Conventional

u(n)Receiving signal

PatternDOAEst.

w(n)

Weighting Vector

Page 30: The Simulation of Beamforming Techniques

Capon’s

w(0~180)Capon’s

u(n)Receiving signal

PatternDOAEst.

w(n)

Weighting Vector

Page 31: The Simulation of Beamforming Techniques

MUSIC

PMUSIC Pattern

u(n)Receiving signal

Eigen decompositionNoise Space

Vn

1( )

( ) ( )MUSIC H H Hn n

P

a V V a

a(0~180)

DOAEst.

w(n)Weighting Vector

Page 32: The Simulation of Beamforming Techniques

Compare the three methods

Page 33: The Simulation of Beamforming Techniques

Compare the three methods

Page 34: The Simulation of Beamforming Techniques

Conclusion