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Frame Based Beam Launching for 3D FieldSimulations in Urban Environments
Christine LETROU
Lab. SAMOVAR (UMR CNRS 5157) - TELECOM SudParis - FRANCE
ACC Antennas Mini-Symposium - Tel-Aviv University -November 21, 2013
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Gaussian beams as an alternative to rays ?
Good localization proper-ties selection of beamsand partial account fordiffraction
0 10 20 30 40 50 60−10
−5
0
5
10
15
20
25
30
z/λ
x/λ
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Each beam tracked like aray (axis path). Paraxialoperators computed only
along the beam axes.
“Big rays” but withoutdiscontinuity effects(smooth decrease).
Paraxial propagatorsNo far field approximation, no caustics.
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Source field representation
The decomposition into paraxial GBs can be performed rigorouslythrough frame based algorithms.
Discrete sum of GB fieldsGaussian beam launching - or
shooting (GBS)Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Outline
1 Frame-based Gaussian beam shooting (FB-GBS)Frame basicsParaxial beams launched from frame windows
2 FB-GBS applied to indoor propagation simulation in themillimetric range
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
3 FB-GBS for propagation simulations in urban environmentsGBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
4 Conclusion
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
Outline
1 Frame-based Gaussian beam shooting (FB-GBS)Frame basicsParaxial beams launched from frame windows
2 FB-GBS applied to indoor propagation simulation in themillimetric range
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
3 FB-GBS for propagation simulations in urban environmentsGBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
4 Conclusion
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
E0(x, y): a planar source distribution of electric field in plane xOy, radiatinginto the half space z > 0.
Eα0 (x, y), α = x, y: one of the two components of E0.
We want to express the field radiated E0(x, y) as a GB summation:
E(r) =∑
α∈x,y
∑j∈J
ajBαj (r)
with Bαj a Gaussian beam field radiated by an α-polarized source.
Hence, we wish to write Eα0 (x, y), α = x, y, as:
Eα0 (x, y) =∑j∈J
ajΨj(kx, ky)
where the set Ψj, j ∈ J is a set of Gaussian functions in L2(R2).
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
The set Ψj, j ∈ J must be a set of Gaussian functions with the followingproperties:
be a complete set of functions, providing stable analysis and synthesisof any function in L2(R2),
span the whole phase-space domain the Gaussian functions Ψj aretranslated in the spatial and spectral domains.
=⇒ Ψj, j ∈ J is a Gabor frame of Gaussian functions.
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
Gabor frames in L2(R)
Sets of translated and modulated functions:
ψmn(x) = ψ(x− mx)einkxx , (m, n) ∈ Z2
with x and kx : spatial and spectral translation steps.
Such a set is a Gabor frame⇔ x kx ≤ 2π
The set ψmn is a frame of Gaussian functions⇔ x kx ≤ 2πOversampling factor: ν = x k/2π < 1
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
Phase-space coverage by a frame of Gaussian functions
SpatialLx
νx
x = νxLx
SpectralΩx
νk = ν/νx
k = νkΩx
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
Gaussian “mother” window ψ
ψ(x) =
√√2
Le−π
x2
L2 =
(kπb
)1/4
e−kx2/2b =1√σ√π
e−x2
2σ2
L: Gaussian window “width” (half-width at 1/e)b: collimation distance; b = L2/λ σ: variance
Gabor frames of Gaussian functions in L2(R2)
Defined as product frames:
Ψµ(x, y) = ψx|mn(x)ψy|pq(y) with µ = (m, n, p, q) ∈ Z4
ψx|mn, ψy|mn: Gabor frames of Gaussian functions in L2(R).
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
Frame analysis/synthesis
f =∑
(m,n)∈Z2
amnψmn ⇔ f =∑
(n,m)∈Z2
amneimnkx xψnm
Frame coefficients calculationProjection of f on the dual frame functions ψmn:
amn = 〈f , ψmn〉 =
∫ ∞−∞
f (x)ψ∗mn(x)dx =
∫ ∞−∞
f (x)ψ∗(x− mx)e−inkxxdx
... or projection of f on the dual frame functions ˆψnm:
amn = e−imnxkx 〈f , ˆψmn〉 =
e−imnxkx
2π
∫ ∞−∞
f (kx)ˆψ∗(kx − nkx)eimxkx dkx
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
For high enough oversampling (ν ≤ 0.33): ψ ≈ ν
‖ψ‖2ψ.
−4 −3 −2 −1 0 1 2 3 40
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
x/Lx
FONCTION DUALE
ν = 0.25
−4 −3 −2 −1 0 1 2 3 4−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
x/Lx
FONCTION DUALE
ν = 0.5
−4 −3 −2 −1 0 1 2 3 4−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
x/Lx
FONCTION DUALE
ν = 0.95
Dual functions for different ν (x =√νL)
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
Eα0 (x, y) =∑µ
aαµΨµ(x, y) , α ∈ x, y , µ = (m, n, p, q) ∈ Z4
Eα0 (kx, ky) =∑µ∈Z4
aαµΨµ(kx, ky)
E(r) =∑
α∈x,y
∑µ∈Z4
aαµei(mnxkx+pqyky)Bαµ(r)
Bαµ(r) =
√2LxLy
4π2
∫∫ ∞−∞
fα(kx, ky)eiφ(kx,ky)dkxdky
φ(kx, ky) = kx(x−mx)+ky(y−py)+kzz +iπΩ2
x(kx−nkx)
2 +iπΩ2
y(ky−qky)
2
f x(kx, ky) = x− kxkz
z and f y(kx, ky) = y− ky
kzz
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
Paraxial approximation (for spectrally narrow windows)
Beams radiated by frame windows withq = 0. Cut in the xOz plane.
Beam coordinate system:
(Omp, xµ, yµ, zµ)
with:zµ along the “beam axis”:
zµ · x = nkx/k , zµ · y = qky/k
ξµ = (xµ, yµ)
the transverse position vectorof the observation point
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Frame basicsParaxial beams launched from frame windows
Paraxial beam expression
Bαµ(r) ∼ B0 fα(nkx, qky)
(det Γ(zµ)
det Γ(0)
)1/2
eikzµeik2 ξ
TµΓ(zµ)ξµ
B0 =(
2LxLy
)1/2
and Γ is the “complex curvature matrix” of Bαµ.
Complex curvature matrix of Bαµ
Γ(zµ) =
[zµ − ib11 ib12
ib12 zµ − ib22
]−1
Γ−1(zµ) = Γ−1(0) + zµId
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
Outline
1 Frame-based Gaussian beam shooting (FB-GBS)Frame basicsParaxial beams launched from frame windows
2 FB-GBS applied to indoor propagation simulation in themillimetric range
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
3 FB-GBS for propagation simulations in urban environmentsGBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
4 Conclusion
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
Description of the problem
MVNA
Laboratory Tables
Windows
Metallic Door
Wood Closet
Tx .
.
.
.
Rx3
3.5m
6.5
m
wood
metallic structure
plasterboard
O x
z
Rx1
Rx2
Rx4
Emitting and receivingantennas:open waveguides
Frequency: 60GHz
Frame: ν = 0.25, L = 6λ
625 frame windows:M=P=0, N=Q=12
Number of interactions:7 reflexions
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
* Tx
* Rx
z
xO
3.5m
6.5m
Beam launchingsimilar to ray launching:
paths along beam axes
image principle (imagebeams)
reflexion/transmissionoperators along beam axes
signal coupled to receiver viareceived antenna
time-delays easily derivedfrom path lengths andobservation point coordinates
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
x
z
zi
beam axis
equiphase
surfaces
oM
oP
t =Re (zµ + 1
2~ξ Tµ Q(zµ)~ξµ)
c
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
Amplitude-delay profiles: LOS
RX2
0 10 20 30 40 50 60 70 80 90 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1x 10
−5
retard [ns]
am
plit
ud
e
mesures
simulations
Measurements:
Simulations:
τm
=30.8780
τrms
=19.8964
τm
=28.5086
τrms
=11.2615
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
Amplitude-delay profiles: LOS
RX3
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
−6
retard [ns]
am
plit
ud
e
mesures
simulations
Measurements:
Simulations:
τm
=41.8237
τrms
=16.7361
τm
=34.2219
τrms
=7.7589
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
Frame to frame channel transfer matrix HC
100
200
300
400
500
10
20
30
40
0.2
0.4
0.6
0.8
1
Tx frame index (23*23)Rx frame index (7*7)
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
Azimuth DoD-DoA channel transfer matrix
Directions of Departure (φ in deg.)
Dir
ecti
on
s o
f A
rriv
al (φ
in
deg
.)
−60 −40 −20 0 20 40 60
−100
−80
−60
−40
−20
0
20
40
60
80
100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Outline
1 Frame-based Gaussian beam shooting (FB-GBS)Frame basicsParaxial beams launched from frame windows
2 FB-GBS applied to indoor propagation simulation in themillimetric range
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
3 FB-GBS for propagation simulations in urban environmentsGBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
4 Conclusion
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Limitation of the region of validity of FB-GBS from oneplane
Half-wavelength dipole far field modulus at r = 50λ.
Reference
Synthetized by FB-GBS from oneplane
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Proposed approach
Define 6 overlappingPWS in the 6 planesPj (deduced from farfields in 6half-spaces)
Multiply these PWSby partitioningfunctions χj
Shoot beams from allplanes, and sum allthe radiated fields.
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Partitioning functions
Partitioning function χ5 Partitioning function χ1
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Partitioned PWS in plane P1: x1-component
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Partitioned PWS in plane P1: y1-component
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Partitioned PWS in plane P1: z1-component
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Radiated field synthesized by GBS from the 6 Pj planes
Synthesized field normNormalized absolute error ofsynthetized complex vector
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
A challenge for GBS !
Proposed scheme:
re-shooting of paraxial GBsfrom the surface of the obstacle,using frame discretizationand narrow/wide Gaussian windowspatial/spectral localization.
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Spectrum of the incident beam field in the plane P′:
ψP′
µ (kx′) = ψµ(kx)kz
k′zeik·−−→OO′
Projection integral of this spectrum on the approximated dualfunctions of the Fourier transforms of the spatially narrow windows:
a′µ′ =
(1
2π
)2 ∫∫ ∞−∞
ψP′
µ (kx′)ν ′xν′y
‖ψ′‖2ψ′×µ′(kx′) d2kx′
Paraxial approximation ... leads to closed form expression for theframe coefficients a′µ′ for the incident field
Transformation at the interface: applied to narrow windowscoefficients (truncation), or later on wide windows coefficients andfields.
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Frame change
u(x′) =∑µ∈Z4
A′µ′ψ′µ′(x′) =
∑µ∈Z4
Aµψµ(x′)
Aµ =
∫ ∞−∞
u(x′) ϕ×µ(x′) d2x′
=∑µ′
A′µ′
∫ ∞−∞
ψ′µ′(x′) ϕ×µ(x′) d2x′
=∑µ′
Cµ′
µ A′µ′ with Cµ′
µ =
∫ ∞−∞
ψ′µ′(x′) ϕ×µ(x′) d2x′
Approximate ϕµ closed form expression of Cµ′
µ
A = CA′
where the matrix C can be precomputed in closed form.Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Scenario
Test caseTilt in the horizontal plane:L = 10λ, ν = 0.09, n=25, q=0 θµ = 48.6 deg tilt
Obstacle description
Perfectly conductingIn the vertical lateral planedefined by x0 = 50λCenter: y0 = 0, z0 = 41.5λSquare with side length = 3λ
Narrow window frameν′ = 0.09 and L′ = 0.075λ
Observation region
In the vertical plane x0 = 30λCenter: y0 = 0, z0 = 60λSquare with side length = 80λ
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Truncated field on the obstacle surface
Ey incident field component magnitude onthe obstacle surface.
Comparison of frame summationsand PWS integral referencealong the horizontal axis.
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Coefficients de re-decomposition
Fenetres etroites
A′µ′(m′, p′)pour n′ = q′ = 0
Fenetres larges
Aµ(n, q)pour m = p = 0sans “selection”
spectrale
Fenetres larges
Aµ(n, q)pour m = p = 0avec “selection”
spectrale
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Reflected-diffracted field in the observation region
Ey component magnitude obtained by GBS after re-expansion
Comparison with reference PWS integralalong the horizontal axis in the
observation region
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
GBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
Reflected-diffracted field in the observation region
Normalized error of GB summation (in dB).Reference: PWS integral.
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Outline
1 Frame-based Gaussian beam shooting (FB-GBS)Frame basicsParaxial beams launched from frame windows
2 FB-GBS applied to indoor propagation simulation in themillimetric range
Description of the problemAmplitude-delay profilesFrame to frame channel transfer matrix
3 FB-GBS for propagation simulations in urban environmentsGBS from non directive sources: spectral partitioning solutionDiffraction: playing with frame “resolution”
4 Conclusion
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments
IntroductionFrame-based Gaussian beam shooting (FB-GBS)
FB-GBS applied to indoor propagation simulation in the millimetric rangeFB-GBS for propagation simulations in urban environments
Conclusion
Gaussian beams:well-suited for intensive multipath propagation, including non farfield interactions.
Use of frame decomposition:- guarantees the “completeness” and stability of initial and successivediscretisations,- offers flexibility to cope with non uniform surfaces (rough or withmoderately small details).
Numerical efficiency to be evaluated.
Christine LETROU Frame Based Beam Launching for 3D Field Simulations in Urban Environments