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Department of Research in Electromagnetics. SUPELEC - Plateau de Moulon 91192 Gif sur Yvette - France Walid Tabbara - tabbara@lss.supelec.fr. Department of Research in Electromagnetics. Academics PhD students 1 anechoïc chamber 2 reverberating chambers 2 near-field measurement setups
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Department of Research in Electromagnetics SUPELEC - Plateau de Moulon 91192 Gif sur Yvette - France Walid Tabbara - tabbara@lss.supelec.fr COST 286 _ Wroclaw
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
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
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
Randomness, when ? (1) COST 286 _ Wroclaw
Randomness, when ? (2) COST 286 _ Wroclaw
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
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
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
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
A TL in a room vs TL over ground plane COST 286 _ Wroclaw
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
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
Regression model Realization of a gaussian process with zero mean and known covariance function Cov (x1),x2)) = cx1,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
Statistical Analysis (5) Kriging of the 95 % quantile I95 Cubic covariance function COST 286 _ Wroclaw
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