estimating radar cross-section of canonical targets in ... · 1. electromagnetic reverberation...
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Estimating RadarCross-Section of
Canonical Targets inReverberation
Chamber
P. Besnier, J. Sol, S. Méric
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Outline
1. Electromagnetic Reverberation Chambers
2. RC and RCS. A State of the Art
3. Theory of Monostatic RCS Measurement in a RC
4. Test with a reference target
5. Measurement in a Classical (Anechoic Chamber) Test Set-up
6. Tests with smaller metal plates
7. Summary
2 EMC-EUROPE Angers 2017. P. Besnier et. al
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1. Electromagnetic Reverberation Chambers
Production of a statistically homogeneous and isotropic �eld inmulti-mode cavity [1]
• If the number of signi�cantly excited modes is high enough(modal overlapping) :
I The �eld may be described by simple statisticsI It follows the in�nite plane wave spectrum theory (D. Hill)I The electromagnetic �eld is gaussian (perfect di�use �eld or
random �eld)
[1] : P. Besnier, B. Demoulin, Electromagnetic reverberation chambers, ISTE Wiley & Sons, 2011.
3 EMC-EUROPE Angers 2017. P. Besnier et. al
![Page 4: Estimating Radar Cross-Section of Canonical Targets in ... · 1. Electromagnetic Reverberation Chambers Production of a statistically homogeneous and isotropic eld in multi-mode cavity](https://reader030.vdocuments.mx/reader030/viewer/2022041000/5ea0b3c6a8454b1e231201eb/html5/thumbnails/4.jpg)
1. Electromagnetic Reverberation Chambers
Production of a statistically homogeneous and isotropic �eld inmulti-mode cavity [1]
• If the number of signi�cantly excited modes is high enough(modal overlapping) :
I The �eld may be described by simple statisticsI It follows the in�nite plane wave spectrum theory (D. Hill)I The electromagnetic �eld is gaussian (perfect di�use �eld or
random �eld)
[1] : P. Besnier, B. Demoulin, Electromagnetic reverberation chambers, ISTE Wiley & Sons, 2011.
3 EMC-EUROPE Angers 2017. P. Besnier et. al
![Page 5: Estimating Radar Cross-Section of Canonical Targets in ... · 1. Electromagnetic Reverberation Chambers Production of a statistically homogeneous and isotropic eld in multi-mode cavity](https://reader030.vdocuments.mx/reader030/viewer/2022041000/5ea0b3c6a8454b1e231201eb/html5/thumbnails/5.jpg)
1. Electromagnetic Reverberation Chambers
Production of a statistically homogeneous and isotropic �eld inmulti-mode cavity [1]
• If the number of signi�cantly excited modes is high enough(modal overlapping) :
I The �eld may be described by simple statisticsI It follows the in�nite plane wave spectrum theory (D. Hill)I The electromagnetic �eld is gaussian (perfect di�use �eld or
random �eld)
[1] : P. Besnier, B. Demoulin, Electromagnetic reverberation chambers, ISTE Wiley & Sons, 2011.
3 EMC-EUROPE Angers 2017. P. Besnier et. al
![Page 6: Estimating Radar Cross-Section of Canonical Targets in ... · 1. Electromagnetic Reverberation Chambers Production of a statistically homogeneous and isotropic eld in multi-mode cavity](https://reader030.vdocuments.mx/reader030/viewer/2022041000/5ea0b3c6a8454b1e231201eb/html5/thumbnails/6.jpg)
1. Electromagnetic Reverberation Chambers
Production of a statistically homogeneous and isotropic �eld inmulti-mode cavity [1]
• If the number of signi�cantly excited modes is high enough(modal overlapping) :
I The �eld may be described by simple statisticsI It follows the in�nite plane wave spectrum theory (D. Hill)I The electromagnetic �eld is gaussian (perfect di�use �eld or
random �eld)
[1] : P. Besnier, B. Demoulin, Electromagnetic reverberation chambers, ISTE Wiley & Sons, 2011.
3 EMC-EUROPE Angers 2017. P. Besnier et. al
![Page 7: Estimating Radar Cross-Section of Canonical Targets in ... · 1. Electromagnetic Reverberation Chambers Production of a statistically homogeneous and isotropic eld in multi-mode cavity](https://reader030.vdocuments.mx/reader030/viewer/2022041000/5ea0b3c6a8454b1e231201eb/html5/thumbnails/7.jpg)
1. Electromagnetic Reverberation Chambers
Production of a statistically homogeneous and isotropic �eld inmulti-mode cavity [1]
• If the number of signi�cantly excited modes is high enough(modal overlapping) :
I The �eld may be described by simple statisticsI It follows the in�nite plane wave spectrum theory (D. Hill)I The electromagnetic �eld is gaussian (perfect di�use �eld or
random �eld)
[1] : P. Besnier, B. Demoulin, Electromagnetic reverberation chambers, ISTE Wiley & Sons, 2011.
3 EMC-EUROPE Angers 2017. P. Besnier et. al
![Page 8: Estimating Radar Cross-Section of Canonical Targets in ... · 1. Electromagnetic Reverberation Chambers Production of a statistically homogeneous and isotropic eld in multi-mode cavity](https://reader030.vdocuments.mx/reader030/viewer/2022041000/5ea0b3c6a8454b1e231201eb/html5/thumbnails/8.jpg)
1. Electromagnetic Reverberation Chambers
Nowadays : numerous applications of RC (EMC, antennas,...)
• Illumination under a di�use �eld (radiated immunity)
• Measurement of power balance (total radiated �eld, antennae�ciency, absorption properties, ...)
• Simulation of propagation channel
• Time reversal
• .../...
Why try to measure the RCS of targets in a reverberation chamber ?
• There is a simple way to detect the target
• The means required are modest
• A true monostatic measurement is possible
4 EMC-EUROPE Angers 2017. P. Besnier et. al
![Page 9: Estimating Radar Cross-Section of Canonical Targets in ... · 1. Electromagnetic Reverberation Chambers Production of a statistically homogeneous and isotropic eld in multi-mode cavity](https://reader030.vdocuments.mx/reader030/viewer/2022041000/5ea0b3c6a8454b1e231201eb/html5/thumbnails/9.jpg)
1. Electromagnetic Reverberation Chambers
Nowadays : numerous applications of RC (EMC, antennas,...)
• Illumination under a di�use �eld (radiated immunity)
• Measurement of power balance (total radiated �eld, antennae�ciency, absorption properties, ...)
• Simulation of propagation channel
• Time reversal
• .../...
Why try to measure the RCS of targets in a reverberation chamber ?
• There is a simple way to detect the target
• The means required are modest
• A true monostatic measurement is possible
4 EMC-EUROPE Angers 2017. P. Besnier et. al
![Page 10: Estimating Radar Cross-Section of Canonical Targets in ... · 1. Electromagnetic Reverberation Chambers Production of a statistically homogeneous and isotropic eld in multi-mode cavity](https://reader030.vdocuments.mx/reader030/viewer/2022041000/5ea0b3c6a8454b1e231201eb/html5/thumbnails/10.jpg)
1. Electromagnetic Reverberation Chambers
Nowadays : numerous applications of RC (EMC, antennas,...)
• Illumination under a di�use �eld (radiated immunity)
• Measurement of power balance (total radiated �eld, antennae�ciency, absorption properties, ...)
• Simulation of propagation channel
• Time reversal
• .../...
Why try to measure the RCS of targets in a reverberation chamber ?
• There is a simple way to detect the target
• The means required are modest
• A true monostatic measurement is possible
4 EMC-EUROPE Angers 2017. P. Besnier et. al
![Page 11: Estimating Radar Cross-Section of Canonical Targets in ... · 1. Electromagnetic Reverberation Chambers Production of a statistically homogeneous and isotropic eld in multi-mode cavity](https://reader030.vdocuments.mx/reader030/viewer/2022041000/5ea0b3c6a8454b1e231201eb/html5/thumbnails/11.jpg)
1. Electromagnetic Reverberation Chambers
Nowadays : numerous applications of RC (EMC, antennas,...)
• Illumination under a di�use �eld (radiated immunity)
• Measurement of power balance (total radiated �eld, antennae�ciency, absorption properties, ...)
• Simulation of propagation channel
• Time reversal
• .../...
Why try to measure the RCS of targets in a reverberation chamber ?
• There is a simple way to detect the target
• The means required are modest
• A true monostatic measurement is possible
4 EMC-EUROPE Angers 2017. P. Besnier et. al
![Page 12: Estimating Radar Cross-Section of Canonical Targets in ... · 1. Electromagnetic Reverberation Chambers Production of a statistically homogeneous and isotropic eld in multi-mode cavity](https://reader030.vdocuments.mx/reader030/viewer/2022041000/5ea0b3c6a8454b1e231201eb/html5/thumbnails/12.jpg)
1. Electromagnetic Reverberation Chambers
Nowadays : numerous applications of RC (EMC, antennas,...)
• Illumination under a di�use �eld (radiated immunity)
• Measurement of power balance (total radiated �eld, antennae�ciency, absorption properties, ...)
• Simulation of propagation channel
• Time reversal
• .../...
Why try to measure the RCS of targets in a reverberation chamber ?
• There is a simple way to detect the target
• The means required are modest
• A true monostatic measurement is possible
4 EMC-EUROPE Angers 2017. P. Besnier et. al
![Page 13: Estimating Radar Cross-Section of Canonical Targets in ... · 1. Electromagnetic Reverberation Chambers Production of a statistically homogeneous and isotropic eld in multi-mode cavity](https://reader030.vdocuments.mx/reader030/viewer/2022041000/5ea0b3c6a8454b1e231201eb/html5/thumbnails/13.jpg)
2. RC and RCS. A State of the Art
Analysis of the total RCS from a device (equivalent absorption areaor scattering area) [2]
I Evaluation of the total absorption area, the target being in a�xed position (in contrast with the empty RC)
I Evaluation of the total di�raction area, the target beingarbitrarily moved around in the RC
Detection of ballistic waves (antenna radiation patternmeasurement)
I Linear movement of an antenna in the direction of another one(Pseudo-Doppler e�ect) [3]
I Estimation of the K -factor of a Ricean propagation channel [4]
[2] G. Lerosey, J. de Rosny, Scattering cross section measurement in reverberation chamber, IEEE Trans.Electromagn. Compat. vol. 49, no. 2, pp. 280-284, May 2007. [3] M. Garcia-Fernandez, D. Carsenat,C. Decroze, Antenna gain and radiation pattern measurements in reverberation chamber using Dopplere�ect, IEEE Trans. Antennas Propagat. vol. 62, no.10, pp 5389-5394, Oct. 2014. [4] G. Lemoine,E. Amador, P. Besnier, J.M. Floc'h, Antenna directivity measurement in reverberation chamber fromRician K-factor estimation, IEEE Trans. Antennas Propagat. vol. 61, no.10, pp 5307-5310, Oct. 2013.
5 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
Backscattered �eld in an empty RCI The measurement antenna radiates a sine wave signal at the
frequency f0 = ω0/2π.I The hypothesis of a perfect random �eld is applied throughout
the paper
S(f0) = SFS(f0) + (1− |SFS(f0)|2)H(f0)ηant (1)
Backscattered �eld from the target located in the line of sight fromthe measurement antenna
I An additional term appears that is proportional to the squareroot of the target RCS, σT (f0)
ST (f0) = SFS(f0) + C (f0)√σT (f0)
+ (1− |SFS(f0)|2)HT (f0)ηant (2)
6 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
Backscattered �eld in an empty RCI The measurement antenna radiates a sine wave signal at the
frequency f0 = ω0/2π.I The hypothesis of a perfect random �eld is applied throughout
the paper
S(f0) = SFS(f0) + (1− |SFS(f0)|2)H(f0)ηant (1)
Backscattered �eld from the target located in the line of sight fromthe measurement antenna
I An additional term appears that is proportional to the squareroot of the target RCS, σT (f0)
ST (f0) = SFS(f0) + C (f0)√σT (f0)
+ (1− |SFS(f0)|2)HT (f0)ηant (2)
6 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
Backscattered �eld in an empty RCI The measurement antenna radiates a sine wave signal at the
frequency f0 = ω0/2π.I The hypothesis of a perfect random �eld is applied throughout
the paper
S(f0) = SFS(f0) + (1− |SFS(f0)|2)H(f0)ηant (1)
Backscattered �eld from the target located in the line of sight fromthe measurement antenna
I An additional term appears that is proportional to the squareroot of the target RCS, σT (f0)
ST (f0) = SFS(f0) + C (f0)√σT (f0)
+ (1− |SFS(f0)|2)HT (f0)ηant (2)
6 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
Backscattered �eld in an empty RCI The measurement antenna radiates a sine wave signal at the
frequency f0 = ω0/2π.I The hypothesis of a perfect random �eld is applied throughout
the paper
S(f0) = SFS(f0) + (1− |SFS(f0)|2)H(f0)ηant (1)
Backscattered �eld from the target located in the line of sight fromthe measurement antenna
I An additional term appears that is proportional to the squareroot of the target RCS, σT (f0)
ST (f0) = SFS(f0) + C (f0)√σT (f0)
+ (1− |SFS(f0)|2)HT (f0)ηant (2)
6 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
ST (f0) = SFS(f0) + C (f0)√σT (f0)
+ (1− |SFS(f0)|2)HT (f0)ηant (3)
The target is supposed to be at a far-�eld distance from themeasurement antenna, we have for C (f0) (from the radar
equation) :
|C (f0)| =Gant(f0)λ0(4π)3/2R2
(1− |SFS(f0)|2) (4)
If the target size is much smaller than the distance R (pointsource), the phase of C (f0) is known relatively to a constant
φ0 :
C (f0) = |C (f0)| exp −j2πf02Rc
exp(jφ0) (5)
where c is the celerity.7 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
The di�erence between the two previous measurement enable to obtain an expressionfor the RCS, σT :
ST (f0)− S(f0) =
(1− |SFS (f0)|2)(HT (f0)− H(f0))ηant
+√σT (f0)
Gant(f0)λ0
(4π)3/2R2(1− |SFS (f0)|2)
× exp−j2πf02R
cexp(jφ0) (6)
Interference signal ∝ to the di�erence of two centered Gaussian random variables withsame variance.Represents the radar echo
I Evolves as a function of the frequency according to a sine waveform with aperiodicity δf = c
2R
I σT (f0) : May be extracted from a sinusoidal curve �tting of periodicity δf andmagnitude A, centered around f0.
I This is achieved with a frequency sweep with a step frequency δfs .
I The frequency span ∆f is selected such that δf ≤ ∆f � f0.
8 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
The di�erence between the two previous measurement enable to obtain an expressionfor the RCS, σT :
ST (f0)− S(f0) =
(1− |SFS (f0)|2)(HT (f0)− H(f0))ηant
+√σT (f0)
Gant(f0)λ0
(4π)3/2R2(1− |SFS (f0)|2)
× exp−j2πf02R
cexp(jφ0) (6)
Interference signal ∝ to the di�erence of two centered Gaussian random variables withsame variance.Represents the radar echo
I Evolves as a function of the frequency according to a sine waveform with aperiodicity δf = c
2R
I σT (f0) : May be extracted from a sinusoidal curve �tting of periodicity δf andmagnitude A, centered around f0.
I This is achieved with a frequency sweep with a step frequency δfs .
I The frequency span ∆f is selected such that δf ≤ ∆f � f0.
8 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
The di�erence between the two previous measurement enable to obtain an expressionfor the RCS, σT :
ST (f0)− S(f0) =
(1− |SFS (f0)|2)(HT (f0)− H(f0))ηant
+√σT (f0)
Gant(f0)λ0
(4π)3/2R2(1− |SFS (f0)|2)
× exp−j2πf02R
cexp(jφ0) (6)
Interference signal ∝ to the di�erence of two centered Gaussian random variables withsame variance.Represents the radar echo
I Evolves as a function of the frequency according to a sine waveform with aperiodicity δf = c
2R
I σT (f0) : May be extracted from a sinusoidal curve �tting of periodicity δf andmagnitude A, centered around f0.
I This is achieved with a frequency sweep with a step frequency δfs .
I The frequency span ∆f is selected such that δf ≤ ∆f � f0.
8 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
The di�erence between the two previous measurement enable to obtain an expressionfor the RCS, σT :
ST (f0)− S(f0) =
(1− |SFS (f0)|2)(HT (f0)− H(f0))ηant
+√σT (f0)
Gant(f0)λ0
(4π)3/2R2(1− |SFS (f0)|2)
× exp−j2πf02R
cexp(jφ0) (6)
Interference signal ∝ to the di�erence of two centered Gaussian random variables withsame variance.Represents the radar echo
I Evolves as a function of the frequency according to a sine waveform with aperiodicity δf = c
2R
I σT (f0) : May be extracted from a sinusoidal curve �tting of periodicity δf andmagnitude A, centered around f0.
I This is achieved with a frequency sweep with a step frequency δfs .
I The frequency span ∆f is selected such that δf ≤ ∆f � f0.
8 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
The di�erence between the two previous measurement enable to obtain an expressionfor the RCS, σT :
ST (f0)− S(f0) =
(1− |SFS (f0)|2)(HT (f0)− H(f0))ηant
+√σT (f0)
Gant(f0)λ0
(4π)3/2R2(1− |SFS (f0)|2)
× exp−j2πf02R
cexp(jφ0) (6)
Interference signal ∝ to the di�erence of two centered Gaussian random variables withsame variance.Represents the radar echo
I Evolves as a function of the frequency according to a sine waveform with aperiodicity δf = c
2R
I σT (f0) : May be extracted from a sinusoidal curve �tting of periodicity δf andmagnitude A, centered around f0.
I This is achieved with a frequency sweep with a step frequency δfs .
I The frequency span ∆f is selected such that δf ≤ ∆f � f0.
8 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
The RCS is �nally estimated from :∣∣∣σT (f0)∣∣∣ ≈ |A(f0)|2 (4π)3R4
((1− |SFS(f0)|2)2G 2ant(f0)λ20
(7)
Where |A(f0)|2 is the square of a peak magnitude of the periodicsine wave signal obtained from the di�erence of the real part or ofthe imaginary part of ST (f )− S(f ).For the real part :
argminA(f0)|A(f0) cos(2π(f0 + fi )2R
c)
−<(ST (f0 + fi )− S(f0 + fi ))| (8)
avec fi = i .δfs pour i = −N,−N + 1, ..., 0, ...,N − 1,N.
9 EMC-EUROPE Angers 2017. P. Besnier et. al
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3. Theory of Monostatic RCS Measurement in a RC
The RCS is �nally estimated from :∣∣∣σT (f0)∣∣∣ ≈ |A(f0)|2 (4π)3R4
((1− |SFS(f0)|2)2G 2ant(f0)λ20
(7)
Where |A(f0)|2 is the square of a peak magnitude of the periodicsine wave signal obtained from the di�erence of the real part or ofthe imaginary part of ST (f )− S(f ).For the real part :
argminA(f0)|A(f0) cos(2π(f0 + fi )2R
c)
−<(ST (f0 + fi )− S(f0 + fi ))| (8)
avec fi = i .δfs pour i = −N,−N + 1, ..., 0, ...,N − 1,N.
9 EMC-EUROPE Angers 2017. P. Besnier et. al
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4. Test with a reference target
Measurement parameters :I Frequency step : δfs =50 kHz.I Frequency span : ∆f =500 MHz
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4. Test with a reference target
Reference target : A rectangular plate (148 mm × 151 mm)
11 EMC-EUROPE Angers 2017. P. Besnier et. al
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4. Test with a reference target
Reference target : A rectangular plate (148 mm × 151 mm).
Waveform of <(ST (f )− S(f )) with f0 = 10 GHz, δfs =50 kHz and∆f =500 MHz
9.75 9.85 9.95 10.05 10.15 10.25−0.03
−0.02
−0.01
0
0.01
0.02
0.03
Frequence [GHz]
Re[S
T(f
)−S(f
)]
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4. Test with a reference target
Reference plate (148 mm × 151 mm).
RCS pattern in azimuth plane at 10 GHz
−30 −20 −10 0 10 20 30−25
−20
−15
−10
−5
0
5
10
θ [◦]
σ[dBm
2]
MesureTheorie
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4. Test with a reference target
Reference plate (148 mm × 151 mm).
RCS pattern in azimuth plane at 8.25 GHz and 11.75 GHz
−30 −20 −10 0 10 20 30−25
−20
−15
−10
−5
0
5
10
θ [◦]
σ[dBm
2]
Mesure : 8.25 GHz
Theorie : 8.25 GHzMesure : 11.75 GHz
Theorie : 11.75 GHz
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5. Measurement in a Classical (Anechoic Chamber) Test Set-up
Measurement principle of RCS in an anechoic chamber :I Two X-band horn-antennas.I Measurement over the 8-12 GHz bandwidth (VNA).I Targer over a mast. Calibrating with reference to Max of RCS.I Inserse Fourier transform. Time gating. Fourier transform.
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5. Comparaison avec une mesure en chambre anéchoïque
Comparison for the reference target (148 mm × 151 mm) at 10GHz
−30 −20 −10 0 10 20 30−25
−20
−15
−10
−5
0
5
10
θ [◦]
σ[dBm
2]
Mesure C.A.Mesure C.R.
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6. Tests with smaller metal plates
Metal plate targets of size 99 mm×102 mm and 74 mm×76 mm at10 GHz
−30 −20 −10 0 10 20 30−25
−20
−15
−10
−5
0
5
θ [◦]
σ[dBm
2]
C.A. pl. 99 X 102
C.R. pl. 99 X 102
C.A. pl. 74 X 76
C.R. pl. 74 X 76
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7. Summary
Main conclusions
I Detection of RCS pattern of simple targets in RC
I Uses only a set of S11 measurement with an singlemeasurement antenna w/o the target
I Results are consistent with standard (anechoic chamber)measurements for not too small RCS values
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7. Summary
Main conclusions
I Detection of RCS pattern of simple targets in RC
I Uses only a set of S11 measurement with an singlemeasurement antenna w/o the target
I Results are consistent with standard (anechoic chamber)measurements for not too small RCS values
18 EMC-EUROPE Angers 2017. P. Besnier et. al
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7. Summary
Main conclusions
I Detection of RCS pattern of simple targets in RC
I Uses only a set of S11 measurement with an singlemeasurement antenna w/o the target
I Results are consistent with standard (anechoic chamber)measurements for not too small RCS values
18 EMC-EUROPE Angers 2017. P. Besnier et. al
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7. Summary
Future work
I Ways of increasing performance : averaging (thermal noise) &mechanical stirring (stirrer was �xed into an arbitrary positionfor all tests)
I Multi-target detection (in progress).
I Alternative signal processing
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7. Summary
Future work
I Ways of increasing performance : averaging (thermal noise) &mechanical stirring (stirrer was �xed into an arbitrary positionfor all tests)
I Multi-target detection (in progress).
I Alternative signal processing
19 EMC-EUROPE Angers 2017. P. Besnier et. al
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7. Summary
Future work
I Ways of increasing performance : averaging (thermal noise) &mechanical stirring (stirrer was �xed into an arbitrary positionfor all tests)
I Multi-target detection (in progress).
I Alternative signal processing
19 EMC-EUROPE Angers 2017. P. Besnier et. al