1 analysis for adaptive doa estimation with robust beamforming in smart antenna system...
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Analysis for Adaptive DOA Estimation with Robust Analysis for Adaptive DOA Estimation with Robust Beamforming in Smart Antenna SystemBeamforming in Smart Antenna System
指導教授：黃文傑 W.J. Huang研究生 ：蔡漢成 H.C. Tsai
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OutlineOutline
• Conception of Smart Antenna• Beamforming Method• DOA Estimation• θ- LMS Algorithm (My Point)• Local Minimum problems• θ- LMS Algorithm with Robust Beamforming• Conclusion
3
Conception of Smart AntennaConception of Smart Antenna
• There are constructed by some specially geometric antenna array.
• It changes the beam-pattern with some different methods.
• It increases the CINR and Capacity
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Category -1Category -1
• Switched Beam System
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Category -2Category -2
• Adaptive Beam System
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OutlineOutline
• Conception of Smart Antenna• Beamforming Method• DOA Estimation• θ- LMS Algorithm• Local Minimum problems• θ- LMS Algorithm with Robust Beamforming• Conclusion
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Beamforming MethodBeamforming Method
Summation
Beamforming Weighting
DO
A E
stim
atio
n
*
1
( ) ( ) ( )L
Hl l
l
y t w x t t
w x
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Beamforming Tech.Beamforming Tech.
Array Response y(t)*
1
( ) ( ) ( )L
Hl l
l
y t w x t t
w x
Output power P(w) 2
1
1
1( ) ( )
1( ) ( )
N
l
NH
l
H
P y tN
t tN
w
w x x w
w R w
1. Conventional Beam-former
2. Capon’s Beam-former
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Conv. Conv. BeamformingBeamforming & Steering Vector & 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(M-1)d
X
Y
)()(
)(
aa
aw
H
BF
)()(
)()()(
aa
aRaH
H
BFP
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ULA
d = 0.5 λ
M = 4 、 8 、 12
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MVDR Beamforming(Capon’s)MVDR Beamforming(Capon’s)
1)( awH
)()(
)(1
1
aRa
aRw
H
CAP
)()(
1)( 1
aRa
H
CAPP
2 22 2
min{ ( )}
min ( ) ( )H
P
E s t w
w
w a w
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OutlineOutline
• Conception of Smart Antenna• Beamforming Method• DOA Estimation• θ- LMS Algorithm• Local Minimum problems• θ- LMS Algorithm with Robust Beamforming• Conclusion
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DOA EstimationDOA Estimation
• Conventional • Capon’s• Subspace
– MUSIC
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Conventional DOA EstimationConventional DOA Estimation
w(0~180)Conventional
u(n)Receiving signal
Pattern(0~180)
DOAEst.
w(n)
BeamformingWeighting
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Capon’s DOA EstimationCapon’s DOA Estimation
w(0~180)Capon’s
u(n)Receiving signal
Pattern(0~180)
DOAEst.
w(n)
BeamformingWeighting
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MUSICMUSIC((MUMUltiple ltiple SISIgnal gnal CClassificationlassification ) )
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
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Compare the three methodsCompare the three methods
ULA
M = 4
d = 0.5λ
User’s DOA =
90°、 120 °
SNR=10dB
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OutlineOutline
• Conception of Smart Antenna• Beamforming Method• DOA Estimation• θ- LMS Algorithm (My point)• Local Minimum problems• θ- LMS Algorithm with Robust Beamforming• Conclusion
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LMS (Least Mean Square ) LMS (Least Mean Square )
1
0
( ) ( ) ( ) ( ) ( )M
Hi i
i
y n n n w n u n
w u
( 1) ( ) { ( )}n n w w J w
( ) ( ) ( ) ( )He n d n n n w u
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ww – LMS Algorithm – LMS Algorithm
d(n)
w - LMS
u(n)
w(n)
w(n+1)
y(n)
e(n)+
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θθ- LMS Algorithm- LMS Algorithm
+
d(n)
ө- LMS
u(n)
w(n)
w(n+1) y(n)
e(n)
ө(n+1)ө(n)
4 x1
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θθ- LMS Algorithm - LMS Algorithm
u(n) w(n) wH(n) u(n)-d(n)
Cost functionJ(θ)
find DOA θ0 Beamforming
Weighting by DOA θ0
w(n)Weighting
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Weighting is Instead of Weighting is Instead of θθ
( 1) ( ) { ( )}n n w w J w
2
( 1) ( ) { ( )}
( )( )
n n
e nn
J
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2
* cos ( 1) cos0
( , )( )
12 sin 0 1 ( 1) ( , )ikd i M kd
e nn
e ikd e M e nM
u
( 1) ( ) ( )n n n
• Adaptive θ(n) is defined
DefinitionDefinition
=
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ULA
M = 4
d = 0.5λ
DOA= 120 °
Initial DOA = 90 °
Step size = 0.01
SNR =20
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ULA
M = 4
d = 0.5λ
DOA= 0 ° ~180 °
Initial DOA = 90 °
Step size = 0.01
SNR =20
DOA=90*sin(0:0.01:80*pi) + 90;
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Steering Vector TrackingSteering Vector Tracking
ULA
M = 4
d = 0.5λ
DOA= 0 ° ~180 °
Initial DOA = 90 °
Step size = 0.01
“*” steering vector
“o” tracking vector
DOA=90*sin(0:0.05:80*pi) + 90;
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Beampattern TrackingBeampattern Tracking
ULA
M = 4
d = 0.5λ
DOA= 0 ° ~360 °
Initial DOA = 90 °
Step size = 0.01
“o” DOA
DOA=180*sin(0:0.05:80*pi) + 180;
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OutlineOutline
• Conception of Smart Antenna• Beamforming Method• DOA Estimation• θ- LMS Algorithm• Local Minimum problems• θ- LMS Algorithm with Robust Beamforming• Conclusion
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Converse to Error DirectionConverse to Error Direction
ULA
M = 4
d = 0.5λ
DOA= 90 °
Initial DOA = 120 °
Step size = 0.01
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Error patternError pattern
d(n )
x(n)4 x1
d(n )
x(n)
w(0~180)
e(0~180)4 x1 +
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Cost functionCost functionULA
M = 4
d = 0.5λ
DOA= 90 °
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ULA
M = 4
d = 0.5λ
DOA= 0 ° ~180 °
DOA=90 °
Error Surface (DOA )Error Surface (DOA )
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Error Surface (d )Error Surface (d )ULA
M = 4
d = 0 ~1λ
DOA= 90 °
d=0.5 λ
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Error Surface (M )Error Surface (M )ULA
M = 2 ~8
d = 0.5λ
DOA= 90 °
M=4
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2 Ants2 Antsθθ- LMS Algorithm- LMS Algorithm
d(n)
ө- LMS
u(n)
w(n)
w(n+1) y(n)
e(n)
ө(n+1)ө(n)
2 x1 +
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Error Surface Error Surface (M=2 d=0.5 )(M=2 d=0.5 )
ULA
M = 2
d = 0.5λ
DOA= 90 °
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Error Surface Error Surface (M=2 d=0.25 )(M=2 d=0.25 )
ULA
M = 2
d = 0.25λ
DOA= 90 °
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Simulation (1)Simulation (1)
ULA
M = 2
d = 0.25λ
DOA= 5 °
Initial DOA = 175 °
SNR = 30 dB
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ULA
M = 2
d = 0.25λ
DOA= 170 °
Initial DOA = 5 °
SNR = 30dB
Simulation (2)Simulation (2)
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2 – 4 “2 – 4 “θθ-LMS” -LMS”
2 antennas “θ-LMS”
4 antennas “θ-LMS”
Initial θ
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OutlineOutline
• Conception of Smart Antenna• Beamforming Method• DOA Estimation• θ- LMS Algorithm• Local Minimum problems• θ- LMS Algorithm with Robust Beamforming• Conclusion
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Noise problemNoise problem
• θ- LMS Algorithm needs high SNR level.
• High noise level brings the DOA estimation result worse.
• The DOA estimation error will cause the terrible performance
• We use the Robust Beamforming Method to conquer the estimation error problem.
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The flow chart of Robust BeamformingThe 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
0max
max max
( )( )r H
d
kk
w e
e R e
Ref : Riba J., Goldberg J., Vazquez G., “Robust Beamforming for Interference Rejection in Mobile Communications”, Signal Processing, IEEE Transactions on
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Robust BeamformingRobust Beamforming
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BER AnalysisBER Analysis
BPSK
ULA
M = 4
d = 0.5 λ
DOA = 90°
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OutlineOutline
• Conception of Smart Antenna• Beamforming Method• DOA Estimation• θ- LMS Algorithm• Local Minimum problems• θ- LMS Algorithm with Robust Beamforming• Conclusion
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ConclusionConclusion
• DOA is an important parameter for beamforming system.
• But, the MUSIC algorithm is complex.• The new method “ө - LMS” is simpler to realized• Robust Beamforming can repair the fault of “ө - L
MS”
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Future WorkFuture Work
• Noise and channel problem • Multi-user problems• SINR Analysis• Multi-path & DOA distribution• Moving Source analysis• Performance Analysis
(User # 、 DOA 、 SNR 、 Beamforming method 、 Antenna # …etc.)
• Adaptive Analysis (Step-size Moving DOA 、 SNR 、 other adaptive structure)
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Capon’s BeamformingCapon’s Beamforming
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Step SizeStep Size
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Cost functionCost function
22( ) ( ) HE e n E d
J w w u
2
*
*
*
2
( ) ( ) ( )2
( ) ( )
2 ( )
H
e ee
d n n ne
n n
e n
w w
w u
w w
u
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New cost functionNew cost function
{J()} is defined partial J() by
2
*
*
( ) ( )2
( ) ( ) ( )2
H
e n e ne
d n n ne
w u
0 0( , ) ( ) ( )n s n u a
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cos ( )
( 1) cos ( )
1
( , ( )) 1( , ( ))
ikd n
i M kd n
en nn n
M M
e
aw
2
*0
*0
* cos ( 1) cos0
( , ) ( , )2 ( , )
1 ( , )2 ( , )
12 sin 0 1 ( 1) ( , )
H
H
ikd i M kd
e n ne n
ne n
M
e ikd e M e nM
wu
au
u
The Formula Derives The Formula Derives
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Initial = 90 ° DOA = 0 °
ULA
M = 2
d = 0.25λ
DOA= 0 °
Initial DOA = 90 °
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Initial = 90 ° DOA = 180 °
ULA
M = 2
d = 0.25λ
DOA= 180 °
Initial DOA = 90 °
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Noise problemNoise problem
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Degree spreadingDegree spreading
k = 0
2 2( ), ( (0), ( )), (0) 0m m m mk N k 2| (0), ( )m m mp k
,( ) ( ) ( )y d i nk yk E k k R R R R
Ref : Riba J., Goldberg J., Vazquez G., “Robust Beamforming for Interference Rejection in Mobile Communications”, Signal Processing, IEEE Transactions on
59
Robust BeamformingRobust Beamforming
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
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
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Complex SurfaceComplex Surface
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