Department of Research in Electromagnetics

1. Department of Research in Electromagnetics SUPELEC - Plateau de Moulon 91192 Gif sur Yvette - France Walid Tabbara - tabbara@lss.supelec.fr COST 286 _ Wroclaw

2. Department of Research in Electromagnetics • Academics • PhD students • 1 anechoïc chamber • 2 reverberating chambers • 2 near-field measurement setups • 1 SAR measurement setup COST 286 _ Wroclaw

3. SAR measurement and analysis: handsets and base stations Propagation in forests Research projects EMC and wireless communication Statistical analysis of coupling to cables and PCBs in an enclosure Communication in underground transportation COST 286 _ Wroclaw

4. Statistical Analysis • Determine the main factors governing the coupling. • ANOVA, Experiment design, Regression • Build a methodology of prediction of coupling based on a statistical approach. • Experiment design, Monte Carlo, Kriging COST 286 _ Wroclaw

5. Randomness, when ? (1) COST 286 _ Wroclaw

6. Randomness, when ? (2) COST 286 _ Wroclaw

7. Emitter: position, orientation TL: Length, location Room: filling factor Dipole: position, orientation TL: length, wire separation Impedances Transmission line in a room Collaboration with Ph. De Doncker (ULB) and M. Hélier (UPMC) COST 286 _ Wroclaw

8. Dimensions: 4 m x 6 m x 2.5 m Bay-window: 0.5 cm thick, r = 1.5 Wall thickness: 10 cm, r = 4-j0.18 Ceiling thickness: 20 cm, r = 4-j0.18 Length: 4.5 Width (2h): 5mm to 25mm ZL = 0  to 200  : 1 GHz Power: 2 W 50  ZL A TL in a room - Model - COST 286 _ Wroclaw

9. Analytical solution for the field inside an empty room: method of images. Computation for several random positions and orientations of the dipole. (8000) Plot the histogram of the field values  probability density function (p.d.f.) A TL in a room - Probabilistic analysis (1) - Histogram Rice pdf COST 286 _ Wroclaw

10. For each position and orientation of the dipole  end voltage and current at ZL . Computation based on Taylor’s model. Plot the histogram of the current values  Quantile Iq P( I < Iq ) = q % Stable with respect to sample size Histogram of the field on the line Histogram of the current A TL in a room - Probabilistic analysis (2) - COST 286 _ Wroclaw

11. A TL in a room vs TL over ground plane COST 286 _ Wroclaw

12. Statistical Analysis (1) Characteristic parameter of the coupling Quantile Iq P( I < Iq ) = q %  Observable Control parameters 2h, L, ZL  Factors Levels of the factors (2h1, 2h2, 2h3) (L1, L2, L3) (ZL1, ZL2, ZL3) COST 286 _ Wroclaw

13. For (2h’,L’,ZL’)  Iq from the values in the experiment design Statistical Analysis (2) One dimensional experiment design Consider each factor separately Compute the observable for each value of the factor Iqj = Iq (Lj) j=1,2,3  (Iq1, Iq2, Iq3) 3 experiments Multi-dimensional experiment design Consider all factors simultaneously Compute the observable for each triplet of values of the factors Iqijk = Iq (2hi, Lj, ZLk) i,j,k=1,2,3  27 experiments COST 286 _ Wroclaw

14. Regression model Realization of a gaussian process with zero mean and known covariance function Cov (x1),x2)) = cx1,x2) Statistical Analysis (3) Kriging interpolator Predict Iq from a reduced set of valuesIqijk (i.e. experiment design) ModelIq(2h,L,ZL) = rt(2h,L,ZL)p* + (2h,L,ZL) B.L.U. PredictorÎq (2h,L,ZL) = ijk Iq (2hi, Lj, ZLk) COST 286 _ Wroclaw

15. Statistical Analysis (5) Kriging of the 95 % quantile I95 Cubic covariance function COST 286 _ Wroclaw

16. Statistical Analysis (4) Kriging main features • Prediction from a reduced set of data: 2 to 4 levels per factor. •  Data: numerical simulation, experimental or a combination of both. •  Cost efficiency increases with the number of factors. •  A standard deviation is computed for each predicted value: • defines a confidence interval.  Interpolator goes through data points.  Handle uncertainties in the data.  Covariance function plays a pivotal role. COST 286 _ Wroclaw