This paper presents some theoretical results and measurements of passive intermodulation (PIM) products made on a waveguide flange contact nonlinearity with 2 and 3 carriers at different power levels. The dependence of the passive intermodulation (PIM) products power on the carrier power is the main difference between active and passive intermodulation (IM) products. For easy computation, memoryless active nonlinearities are generally modelled by polynomials or by analytical mathematical functions (e.g. hyperbolic tangent) [1, 2]. These functions are continuous, have continuous derivatives of all orders and can be approximated by their Taylor series developments, at least in “small signal” conditions where the IM power is much less than the fundamental carrier power, mathematically in a domain around the origin. In these conditions, the power of each active IM products depends on the carrier power elevated to an exponent equal to the order of the IM product, e.g. exponent 3 for order 3, exponent 5 for order 5 [1, 2]. On a dB/dB graph, the slopes of IM levels versus carrier level are equal to their order 3, 5, … This is not the case for passive IM products where the level of IM products depends on the carrier level with a slope that is different from the order, generally a non-integer value between 2 and 3 and about the same for all orders on a dB/dB graph [3 - 8]. A model based on a non-analytical power function has been proposed [9]. It has been used to predict the behavior of the passive IM products such as the level of high order of products, the nearly equal slope for all IM orders, and the decrease of a 2-carrier IM product power when a third carrier is added [9, 10]. The experiment is carried out on a nonlinear graphite material introduced between two waveguide flanges in a PIM test bench in Ku band using two low PIM triplexers. Two carriers with power up to 40 watts per carrier or three carriers with power up to 40 watts per carrier can be transmitted on the test bench. The main theoretical and experimental results are presented in this paper and validate the theoretical results: a slope of 2.4 dB/dB is measured on the third order PIM product and the levels of higher order PIM products are correctly obtained in different configurations of carriers and power by using the non-analytical model based on a power law nonlinearity with an exponent of 2.4 for order 3. Measurement with 3 carriers (with the same or different power) are compared with the theory. A particular combination of 3 carrier powers shows that some third order PIM can be nearly eliminated in concordance with the theory.

CNES, the French Space Agency, has been studying space high power radio frequency (RF) effects -Multipactor, Corona and Passive Intermodulationfor many decades, starting from J. Sombrin Multipactor theory and models [1] to ongoing activities covering TRL 1 from 1 to 7 with our collaborators from academia, agencies, and industries. This paper intends to discuss recent advances related to Multipactor analysis, and present our way towards our main objective in this field: to improve modelling and experimental Multipactor predictions and the synergy between the two. We are studying electron emission physics to enhance our models and measurement methods on dielectric materials, their TEEY 2 , charge dynamics, treatment of secondary and backscattered electrons and the impact on Multipactor predictions. We are developing SPIS 3 to create a robust Multipactor modelling tools, dealing with dielectric materials and electron sources, while considering couplings with current reference software such as CST Studio, Spark3D and ANSYS Multipaction. We are also studying multipactor mitigation techniques based on surface treatments for both conductor and dielectric materials, and RF components design innovations to deal with current trends such as miniaturisation and high performances leading to high power density hence Multipactor risks. These studies align with the European roadmap on Multipactor theme [2] and complement ESA funded activities. We share the main goal as to give our community experimental and numerical tools to get better Multipactor predictions to, in fine, improve the reliability and performances of our high power RF systems. As a national agency we also engage on community awareness, explaining to various space communities that high power effects should be a common concern, and robust analyses should be better integrated in development plans and not wait for an anomaly and/or a major satellite loss to happen.

A novel Digital-Twin technology platform is introduced for enabling system-level IC-Package-PCB-Antenna co-design, co-simulation and co-verification. The platform, based on noise and correlation-aware physics-informed behavioral modeling, integrating VISION (IVCAD) software developed by Dassault Systèmes, hosts an innovative SPICE compatible broadband RLC representation of antenna elements. The ability of the platform to account for dynamic impedance loading of antennas by multi-harmonic (MH) nonlinear RF electronics is demonstrated using energy-efficient hybrid 3D heterogeneous front-end-module technologies integrating adaptive biasing and antenna tuners (load-aware matching). The Digital-Twin technology will enable new generations of tooling (unified EDA & OTA) where classical Electromagnetic (EM) metrics (radiation pattern, noise, auto and cross-correlation functions, power-spectral density) are extended with wireless-circuit metrics (e.g., EVM, SNR, ACPR, NMSE). Unification of EDA and OTA, based on holistic Multiphysics (EM, Thermal, Mechanical) approaches, will foster new standards for joint communication and sensing at any time and from anywhere (remote ubiquitous connectivity).

This paper presents some measurements made on samples of raw materials used for antenna reflectors on communication satellites. Two theoretical results have been experimented: the first one is the power dependence of the passive intermodulation products versus the power of the carriers; the second one is the direction along which intermodulation products are radiated when the incident carriers come from different directions.

This paper addresses the propagation of acoustics or ultrasonics waves through atmosphere and the causality property. The physicists community seems to agree with the following sentence: "... empirical observation indicates that such systems are indeed causal even though the transfer function may not be a causal transform." We explain that the complex gain is not causal when not properly chosen, and that this issue can be addressed.

CNES is involved in the protection of Radio Astronomy near the far side of the Moon, in a zone defined by ITU as the Shielded Zone of the Moon (SZM). The 2483.5-2500 MHz band has been chosen for lunar in-situ PNT notably since it is the only band recommended by SFCG (Space Frequency Coordination Group) for lunar in situ PNT. This band is also the only GNSS band recommended by SFCG for radiocommunications from Martian orbit to Martian surface. CNES proposed this band for lunar and Martian frequencies to SFCG. Regarding the protection of Radio Astronomy in Shielded Zone of the Moon (SZM), which is more or less the far side of the Moon and above, this 2483.5-2500 MHz band is well adapted, while it is not the case for any part of the other GNSS bands used on Earth: both RNSS L and C bands constitute each an important threat for Radio Astronomy in the SZM. SFCG issued two recommendations concerning the protection of lunar in-situ PNT in its 2483.5-2500 MHz band: Recommendation SFCG 32-2R6, so called “Freqs for lunar region”, and Recommendation SFCG 43-1, so called “Protection of lunar S-band PNT”. Obeying both SFCG RECs 32-2R6 and 43-1simultaneously is mandatory to ensure protection of lunar in-situ PNT from wireless WIFI and 3GPP (like 4G, 5G, …) lunar surface links. Adjacent to the 2483.5-2500 MHz in-situ lunar PNT band recommended by SFCG 32-2R6, the bands 2400-2480 MHz and 2503.5-2655 MHz are among the bands recommended for lunar surface wireless systems. This means that there is a minimum of 3.5 MHz mandatory guard bands on each side of the 2483.5-2500 MHz PNT band in SFCG 32-2R6 for the protection of lunar in-situ PNT. The SFCG REC 43-1 recommends the PNT devices to implement filtering, and that each lunar surface wireless system should not generate an aggregated PFD exceeding -121dBW/m²/MHz at the input of the PNT receiving antenna. The SFCG REC 32-2R6 recommends the Wireless device to implement filtering when necessary to avoid Out Of Band harmfull interference to PNT. The paper details these 2 SFCG recommendations which are fundamental for protection of in-situ lunar PNT. It provides some rules to the implementers to respect both SFCG recommendations. A model of PNT receiver response to interference has been developed by TéSA. Different cases are considered, such as astronauts on the lunar surface in a suit equipped with wireless and PNT devices and related antennas on their backpack, with the wireless transmitters (WIFI and 5G) interfering with the PNT reception. Technical justifications of the PFD limit of SFCG REC 43-1 are also provided. These explanations and rules are valid for in-situ lunar PNT, like the AFS (Augmented Forward Service) of LunaNet, but also for the baseline of the future Chinese insitu lunar PNT service. This paper presents the Wireless to PNT interference simulator developed by TéSA. The interference results from this simulator were used by CNES to participate to the elaboration of REC 32-2R6 and REC 43-1 in order to contribute protecting lunar in-situ PNT and, consequently, Radio Astronomy in the SZM. The SFCG recommendation applicable in the Mars region is REC 22-1R4, “Frequency assignment guidelines for communications in the Mars region” , so called “Freqs for Mars region”. In addition to the 2483.5-2500 MHz orbit to surface band, REC 22-1R4 recommends several surface wireless bands, including 2400-2480 MHz and 2503.5-2620 MHz (likely to be extended up to 2655 MHz in a next version). CNES showed that there would also be Radio Astronomy issues with GNSS L and C bands if one of them were broadcast by a Martian radiocom constellation, since Mars is regularly visible from the Shielded Zone of the Moon. The protection measures for a Martian in-situ PNT in 2483.5-2500 MHz would then be similar to the ones described for lunar in-situ PNT systems. This paper introduces the CCSDS Standard for lunar and Martian 3GPP and WIFI wireless links. This CCSDS Standard specifies to comply with the described SFCG recommendations. The paper finally concludes the systematic need to conduct system studies for each lunar wireless network, combining wireless and PNT, and involving wireless to PNT interference computations.

This work provides a comparative study of the complexity and performance for a range of different types of robust estimators. The interest of this analysis is to find the preferred robust estimator that can define the system time for a swarm of satellites. The Student’s t-distribution is used as a model for the noise corrupting the measurements. The ideal performance of an unbiased estimator for a fixed number of degrees of freedom is known in the form of the Cram´er-Rao Bound (CRB). In this article, two examples of a robust Mestimator and an approximation of the Maximum Likelihood Estimator (MLE) resulting from an Expectation-Maximization algorithm are each tested with respect to the performance bounds. Each estimator is also compared with the Gaussian MLE under Gaussian noise, to identify any losses in efficiency under Gaussian conditions. The complexity of the algorithms is also studied by comparing the time until convergence in the iterative update of the robust estimators.

Global Navigation Satellite Systems rely on estimating the signal propagation delay and Doppler shift to a set of visible satellites, which in turn allows to determine the receiver position, velocity and timing. However, the presence of interfering signals degrades the estimation of such synchronization parameters, reason why robust solutions must be accounted for. One specific kind of interference are jamming, where a powerful signal is emitted in the same bandwidth as the signal of interest. One possible way to mitigate jamming is to resort to an antenna array. Doing so, spatial diversity can help to estimate the most powerful signal, allegedly the interference, and perform detection, localization and mitigation. In our solution, we propose two methods: the first one is an offline one, which uses snapshots where the interference is the most powerful to allow for precise detection and localization of the interferer. The other one is an online one, allowing to perform detection, localization and mitigation in real time of the interfering signal.