The Simulation of Beamforming Techniques

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 MVDR Beamforming (Capon’s) Robust Beamforming

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

ULA M = 4 8 12

ULA SNR = 0 ~30

ULA with different λ

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

UCA 0.5 λ

UCA 1.0 λ

UCA 1.5λ

UCA 2λ

MVDR Beamforming

1)( awH

)()(

)(1

1

aRa

aRw

H

CAP

)(min wP

)()(

1)(

1

aRa

H

CAPP

Capon’s Beam-pattern

)()(

1)( 1

aRa

H

CAPP

ULA 0.5 λ

Geometry d M SNR SOI SNOI User

ULA 0.5λ 4 8 12 30 90 50、 130 3

ULA 1λ

Geometry d M SNR SOI SNOI User

ULA 1λ 4 8 12 30 90 50、 130 3

UCA 0.5 λ

Geometry d M SNR SOI SNOI User

UCA 0.5λ 4 8 12 30 90 50、 130 3

UCA 1 λ

Geometry d M SNR SOI SNOI User

UCA 1λ 4 8 12 30 90 50、 130 3

UCA 1.5 λ

Geometry d M SNR SOI SNOI User

UCA 1.5λ 4 8 12 30 90 50、 130 3

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

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

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

ULA 0.5 λ

Geometry d angle spread SNR SOI

ULA 0.5λ 0 10 20 30 30 90

ULA 1 λ

Geometry d angle spread SNR SOI

ULA λ 0 10 20 30 30 90

ULA 1.5 λ

Geometry d angle spread SNR SOI

ULA 1.5λ 0 10 20 30 30 90

UCA

UCA 1.5 λ

Geometry d angle spread SNR SOI

UCA 1.5λ 0 10 20 30 30 90

DOA Estimation

Conventional Capon’s MUSIC

Conventional

w(0~180)Conventional

u(n)Receiving signal

PatternDOAEst.

w(n)

Weighting Vector

Capon’s

w(0~180)Capon’s

u(n)Receiving signal

PatternDOAEst.

w(n)

Weighting Vector

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

Compare the three methods

Compare the three methods

Conclusion