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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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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