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

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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

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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