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First-Principles Modeling and Statistical Analyses Wave Propagation in Complex Environments
Evelyn Dohme, Shen Lin, Brian MacKie Mason, Shu Wang,
Zhen Peng
Applied Electromagnetics Group
University of New Mexico
24 July 2018
Communication through Diffuse Multipath Environments
Part I: Introduction & Overview
Confined systems:Indoor communication and
navigation
Naval ship compartments
Open environments:Wireless channels in urban environments
Radar systems and SAR imaging
http://www.uclight.ucr.edu
Communication through Diffuse Multipath Environments
Part I: Introduction & Overview
http://wamoresearch.org Chaos: Classical and Quantum
Chaotic ray dynamics:• Extreme multiple path• Exponential sensitivity• Ergodicity• Broadband spectra of
dynamics in phase space
Advanced applications:• MIMO communications• Time-reversal systems• Wavefront shaping and
focusing• Sensing and targeting
Overview of Proposed Work
Part I: Introduction & Overview
Objective: first-principles mathematical model which statistically replicates the multipath, ray-chaotic interactions between transmitters and receivers
Stochastic Green’s Function
The fundamental solution of wave
equations in wave-chaotic media
Stochastic Integral Equation
The statistical characterization of complex multipath
environments
Hybrid Formulation
Incorporation of the component-specific
information
Methodology and contributions:• Physics-oriented statistical representations of complex multipath environments• Quantitative statistical analysis of EM systems exhibiting chaotic dynamics• Encoding the governing physics into the mathematical information theory
Motivation for Stochastic Green’s Function
Part II: Theoretical & mathematical foundationsMotivation for Stochastic Green’s Function (SGF)
Multi-antenna information theory:
I = log2 det I + G+ G/ N
Free-space environment
Free-space Green’s Function
Ray-chaotic environment
Chaotic Green’s Function
G0 =e− j k|r 0− r |
4⇡ |r 0− r |GS?
5
Stochastic Green’s Function for Wave Chaotic Media
Part II: Theoretical & mathematical foundations
Stochastic Green’s Function (SGF)
Two theoretical tools:
Random Plane Wave Hypothesis and Random Matrix Theory (RMT)
GS r , r0
=1
⇡
X
i
! 2i
k2 − k2i
k∆
ki
sin ki |~r 0− ~r |
4⇡ |~r 0− ~r || { z }
cor r el at ed G c o
+X
i
! i !0i
k2 − k2i
k∆
4⇡ 2
sin ki ~r 0− ~r 00
ki ~r 0− ~r 00
sin ki |~r − ~r 0 |
ki |~r − ~r 0 || { z }
uncor r elat ed G u c
! i and ! 0i : two independent
Gaussian random variables
ki : eigenvalues dist ributed based on
random matrix theory (RMT)
∆ : mean-spacing between adjacent
eigenvalues (Weyl Formula)
6
Stochastic Green’s Function for Wave Chaotic Media
Part II: Theoretical & mathematical foundations
3D SGF
G r, r0
=1
⇡
X
i
! 2i
k2 − k2i
k∆
ki
sin ki |~r 0− ~r |
4⇡ |~r 0− ~r || {z }
cor r el at ed G c o
+X
i
! i !0i
k2 − k2i
k∆
4⇡ 2
sin ki ~r 0− ~r 00
ki ~r 0− ~r 00
sin ki |~r − ~r 0 |
ki |~r − ~r 0 || { z }
uncor r elat ed G u c
Correlated Gco :
spatial correlat ion function
decay as the distance|r 0− r |
increases
coherent propagat ion
Uncorrelated Gu c :
independent of the spatial
distance|r 0− r |
ergodicity
Gaussian di↵use energy propagator
|r 0− r | % =) correlated:sin k i |~r 0− ~r |
|~r 0− ~r |& =) uncorrelated
10
Stochastic Integral Equation
Part II: Theoretical & mathematical foundations
Experimental Validation
Mode stirrer
Receiving
Transmitting
(a) Internal view of the 3D box (b) Computational setup
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
|S|
0
2
4
6
8
10
12
P(|
S|)
PDF of S-parameters
S11
Measurement
S12
Measurement
S11
Computation
S12
Computation
(c) Probability density function
(a) WG & aperture are modeled in first-principle using finite element method
(b) Plate is big enough to capture the near-field effects (deterministic)
(c) Incorporate the universal statistical chaotic effects in ABI at aperture
(d) Solve the stochastic matrix equation with random parameter g
Part III: Experiment Validation & Verification
Experimental ValidationExperimental Validation-Open system
two decoupled monopoles
Rayleigh fading
(without line-of-sight signal)
P (R;σ) = R
σ 2 e− R 2 / 2σ 2
two coupled monopoles
Rician fading
(with strong line-of-sight signal)
P (R;σ,⌫) = Rσ 2 e− (R 2 + ⌫2 ) / 2σ 2
I 0R⌫σ 2
15
SGF on the outer surface of antennas representing multipath interaction
Part III: Experiment Validation & Verification
Experimental Verification
Part III: Experiment Validation & Verification
Experimental Verification
Part III: Experiment Validation & Verification
Remarks and Conclusion
Part IV: Summary & Overview