Estimating RadarCross-Section of

Canonical Targets inReverberation

Chamber

P. Besnier, J. Sol, S. Méric

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

4. Test with a reference target

Measurement parameters :I Frequency step : δfs =50 kHz.I Frequency span : ∆f =500 MHz

10 EMC-EUROPE Angers 2017. P. Besnier et. al

4. Test with a reference target

Reference target : A rectangular plate (148 mm × 151 mm)

11 EMC-EUROPE Angers 2017. P. Besnier et. al

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

)]

12 EMC-EUROPE Angers 2017. P. Besnier et. al

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

13 EMC-EUROPE Angers 2017. P. Besnier et. al

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

14 EMC-EUROPE Angers 2017. P. Besnier et. al

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.

15 EMC-EUROPE Angers 2017. P. Besnier et. al

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.

16 EMC-EUROPE Angers 2017. P. Besnier et. al

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

17 EMC-EUROPE Angers 2017. P. Besnier et. al

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

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

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

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

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

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