1 Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication NGUYEN DINH QUY, Prof. GAN WOON SENG The Second International Conference on Digital Communication (ICDT’07) July 1-6, 2007 - Sillicon Valley, USA
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Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
NGUYEN DINH QUY, Prof. GAN WOON SENG
The Second International Conference on Digital Communication (ICDT’07)July 1-6, 2007 - Sillicon Valley, USA
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Scope
Basic communication problemTime Reversal Signal Processing (TRSP)Time Reversal (TR) communicationGreen’s function estimationDiscussionsApplicationsConclusionsFuture works
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Basic Communication Problem
Multipath corrupts information (fading)
Multipath reduces the effectiveness of channel capacity by increasing inter-symbol interference (ISI)
Channel equalization requires very high complexity Multipath environment
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
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Time Reversal Signal Processing (TRSP)
TRSP is lower complexity than channel equalization
TRSP mitigates the effects of multipaths
TRSP increases channel bandwidth
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
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TR communication (1)
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
Green’s function estimation on transmission
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Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
TR communication (2)
Green’s function estimation on reception
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Green’s function estimation Medium:
HomogeneousMultiple scattering (multipath environment)
Green’s function estimation: Depend on total length between transmitter and receiver through multiple
scatterers because ofTime shiftAmplitude reduction
→ Objective: How to estimate total length propagation Li
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
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1( ; ) ( )
Ni
i i
Lg r t t
L vδ
=
= −∑
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Total length estimation in arbitrary Cartesian 2D,3D
2 2 2 2 2( ) ( ) ( ) ( )Di i t i t i r i rL x x y y x x y y= − + − + − + −
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
3 2 2 2 2 2 2( ) ( ) ( ) ( ) ( ) ( )Di i t i t i t i r i r i rL x x y y z z x x y y z z= − + − + − + − + − + −
(1)
(2)
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Total length estimation in 2D,3D in theory
2 2 2 2 2( )Di i i i iL x y x a y= + + − +
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
3 2 2 2 2 2 2( )Di i i i i i iL x y z x a y z= + + + − + +
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Total length estimation in 2D,3D in theory
2 2 2 2 2ˆ ( )Dit i i i iL x y x a y= + + − + 3 2 2 2 2 2 2ˆ ( )D
it i i i i i iL x y z x a y z= + + + − + +
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ˆ1ˆ ( ; ) ( )
ˆ
DND it
t Di it
Lg r t t
vLδ
=
= −∑
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
Total length estimation in 2D in practice:
Green’s function estimation in 2D in practice:
v: propagation speed
Total length estimation in 3D in practice:
Green’s function estimation in 3D in practice:
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ˆ1ˆ ( ; ) ( )
ˆ
DND it
t Di it
Lg r t t
vLδ
=
= −∑
(3) (4)
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• In practical condition:Total length propagation is longer because of reflection and scattering Li is Big Oh function of previous function
Apply Cauchy–Bunyakovski–Schwarz inequality
Total length estimation in 2D in practical condition
2 2 2 2 2 2 2( ) ( ) 2i i i i i ix b y x b y x b y+ + + − + ≤ + +
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
2 2 2 2 2 2 2 2 2 2( ) ( ) 2i i i i i i i i ix b y z x b y z x y z b+ + + + − + + ≤ + + +
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Total length estimation in 2D,3D in practice
2 2 2 2ˆ ( , ) 2Dir i i i iL x y x y b= + + 3 2 2 2 2ˆ ( , , ) 2D
ir i i i i i iL x y z x y z b= + + +
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
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ˆˆ ( ; ) ( )
ˆ
DND i ir
r Di ir
C Lg r t t
vLδ
=
= −∑
Total length estimation in 2D in practice:
Green’s function estimation in 2D in practice:
Ci: Reflectivity coefficient.
Total length estimation in 3D in practice:
Green’s function estimation in 3D in practice:
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ˆˆ ( ; ) ( )
ˆ
DND i ir
r Di ir
C Lg r t t
vLδ
=
= −∑
(5) (6)
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Complexity comparison
Total length propagation estimation 3D
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
1 22Square root
3 44Multiplication
3 47Additions
Proposed reality Proposed theory Previous theory
1 2 2Square root
5 6 6Multiplication
3 6 11Additions
Proposed reality Proposed theory Previous theory
Total length propagation estimation 2D
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Discussion (1)
Advantage:Reduces from 27.27% to 52.94% of computational complexity (addition and multiplication) compared to previousThe proposed Green’s function in practical condition 3D is minimal computational complexity and more accurateThe proposed Green’s function estimation is more robust and accurate in DSP implementationThe proposed Green’s function estimation contributes to a feasibility study of time reversal signal processing in communication
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
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Discussion (2)
Disadvantage:Applicable in specific environment (homogeneous and scattering phenomenon)In complicated environment, proposed Green’s functions are more errors than that in Wienner method (but drawbacks are intensive computation and large memory requirement)
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
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Applications
Communication in highly reverberation Enhance higher data rates
Medical ultrasound treatmentIntruder detection
Focus measurement Location of scatterers estimation
Maximum Likelihood Estimation (MLE)
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
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Conclusions
Proposed Green’s function estimations have less computational complexity and more accuracy in homogeneous and scattering environment
Green’s function estimation can be applied in TRSP communication that is efficient method in highly reverberation
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
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Future works
Develop Green’s function estimation in heterogeneous medium
Apply Green’s function estimation in Time Reversal Signal Processing for focusing sound
Improve TRSP in communication
Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
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Green’s function estimation in homogeneous and scattering medium for Time Reversal Signal Processing (TRSP) communication
THANK YOU!Any information, feel free contact:Nguyen Dinh [email protected]
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