Context

Radiometers are consistently increasing in size and complexity to detect always weaker signals with high accuracy. This implies costly antenna characterizations. New SAR imagery systems rely on leakywave antennas, which scan various regions of space when moving the input frequency. Although this allows for fixed positioned antennas, this scan property is hard to measure accurately. Solutions are also required for testing antennas on large LEO constellations. All these needs translate into antenna measurement challenges. Measurement times must be short while reliability must be high, with minimal and quantified uncertainties.

To assess the far-field pattern of an antenna, measurements are typically performed in an anechoic chamber: a controlled environment inside which free-space is emulated. Measured data correspond to S-parameters between the antenna under test (AUT) and one or several probes. Both the antenna and probes are placed on mobile positioners to capture the radiation in diverse directions and polarizations.

A physical model is required to relate the raw S-parameters to the AUT response. This model must include the probes [1]. Spurious echoes due to scatterings in the measurement environment are also sometimes included [2, 3]. Finally, from data captured on regular frequency and position grids, the AUT response is estimated through the inversion of the physical model. This provides usual far-field characteristics, e.g. gain patterns in co and cross polarizations.

A commonly-used physical model to remove echoes is time gating that makes use of the additional propagation distances of the multipath via Fourier transforms. The resolution in terms of delay of this approach is however limited by the frequency band, which renders it unsuitable for narrow-band antennas and for small anechoic chambers. 

With other models, the measured S-parameters are formulated as a space or angular convolution between two functions: one related to the probe and environment, and another one related to the AUT. Obtaining the antenna response from raw measured data thus amounts to a deconvolution. As recently proposed by ENAC in collaboration with CNES, the deconvolution for spherical measurements can be expressed in terms of spin-spherical and Wigner harmonics, i.e. the spectral representations of signals on the sphere and rotation group, respectively. This has led to a two-step method for obtaining the AUT pattern. The first step is a calibration to estimate the term in the convolution related to the probe and environment. The second step allows to recover the AUT response.

Despite the post-processing of the measured data, uncorrectable uncertainties will always remain. They are notably related to various sources of noise, mechanical defects (misalignment and deflection of the positioners), or uncertainties in the probe radiation. Descriptive and deterministic methods exist to relate how they impact the measurement results [1]. 

Objective

The objective of this PhD is to increase the reliability of antenna measurements by:

    • improving the methods to assess the far-field pattern from raw measurement data;

    • quantifying the uncertainties that cannot be corrected by means of a fully stochastic approach.

The developed tools will have to meet computation-time and accuracy requirements. They will be tested on means of measurements at ENAC and CNES. 

A first line of research will concern new narrow-band delay-based models to mitigate the impact of spurious scatterings. A solution will be based on the method proposed in [4] for atmospheric channels. Another idea will rely on the Wigner-Smith operator, where modes with well-defined delays can be defined from S-parameters and their derivatives at a single frequency [5]. For a dedicated probe configuration, these modes could minimize the impact of echoes even for single frequency measurements.

A second line of research is the introduction of wavelets as a basis to perform the deconvolution and access to the AUT response. Wavelets provide directionality and localization properties that could be harnessed to mitigate spurious signals.

The last line of research will consist in determining how randomness in the environment yields stochastic uncertainties in the estimated AUT pattern. As in [6], the combination of spin spherical harmonics with polynomial chaos will provide closed-form stochastic descriptors of the radiated field in all directions, from which key statistical quantities, e.g. the probability density functions, can be obtained.

[1] C. Parini et al.,  Theory and practice of modern antenna range measurements,  IET, 2014.

[2] J. T. Toivanen et al., IEEE Trans. on Antenn. and Propag. vol. 58, no. 11, 2010.

[3] A. Quennelle et al., ICEAA, Italy, 2023.

[4] H. Zhou et al.,  IEEE Trans. on Aero. and Elec. Sys., vol. 61, no. 5, 2025.

[5] U. R. Patel et al., IEEE Trans. on Antenn. and Propag , vol. 69, no. 2, 2021.

[6] E. M. Djelloul et al.,  ICEAA, Italy, 2025.

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For more Information about the topics and the co-financial partner (found by the lab!); contact Directeur de thèse - alexandre.chabory@recherche.enac.fr

Then, prepare a resume, a recent transcript and a reference letter from your M2 supervisor/ engineering school director and you will be ready to apply online  before March 13th, 2026 Midnight Paris time!