Most nonlinear behavioural models of amplifiers are based on functions that are analytic at the origin and thus can be replaced by their Taylor series development around this point, e.g. polynomials of the input signal. Chebyshev Transforms can be used to compute the harmonic response of the model to a sine input signal. These responses are polynomials of the input signal amplitude. A second application of the Chebyshev transform to the first harmonic response or RF characteristic will lend the carriers and intermodulation (IM) products for a 2-carrier input signal, again polynomials. An important class of non-analytic nonlinear behaviour encountered in practice, such as hard limiters and detectors are either empirically treated or only approximated by an analytic function such as the hyperbolic tangent. This work proposes to generalize the polynomial nonlinearity theory by adding non-analytic at the origin functions that, like polynomials, are invariant elements of the Chebyshev Transform. Devices modelled with these non-analytic at the origin functions exhibit intermodulation behaviour significantly different from that of classical polynomial models, giving theoretical foundation to a number of important unexplained practical measurement observations.

This paper describes existing and new criteria for comparison and optimization of non-linear power amplifiers such as RF or microwave transmitters. In addition to intermodulation, receiver noise, and losses in the transmission system, the proposed new criteria take into account efficiency or consumed power. This results in the global optimization of a combined signal-to-noise-plus-intermodulation ratio as a function of saturated or nominal power but also consumed or dissipated power. Saturated power is limited by available technology. Consumed power and dissipated power are some of the main constraints in telecommunication satellite payloads, mobile phone handsets, and RFID (Radio Frequency IDentification). Another constraint comes from the limited size of antennas, which limits the system equivalent isotropic radiated power and gain-to-temperature ratio. With the proposed criteria the designer will be able to compare different amplifier technologies and to optimize the design and operating point of each stage of a multistage amplifier or a linearizer for a given amplifier. Interference from same or other systems is also introduced in the optimization through the use of signal-to-noise-plus-IM-plus-interference ratio criteria.

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.

Nous proposons de partitionner l’architecture d’un réseau ad-hoc mobile en plusieurs groupes, afin de re-distribuer équitablement la charge entre les membres du réseau. Notre étude porte sur un essaim de nanosatellites fonctionnant commue un télélescope spatial distribué, placé en orbite lunaire. Chaque nanosatellite de l’essaim collecte des données d’observation de l’espace, puis les échange avec les autres membres de l’essaim. Les données recueillies sont ensuite combinées localement afin de produire l’image globale observée par l’essaim. Cependant, un système fondé sur ce mode opératoire est particulièrement sensible aux pertes de paquets et aux pannes d’énergie. En effet, la transmission simultanée d’un important volume de données peut entraîner des problèmes de communication, notamment en surchargeant le canal radio ou en augmentant le risque de collisions, menant dans les deux cas à des pertes de paquets. La consommation énergétique totale de l’essaim est également proportionnelle au nombre de paquets transmis : il faut alors trouver une solution pour limiter le nombre de transmissions afin d’économiser l’énergie des nanosatellites. La principale contribution de ce papier est de proposer une approche basée sur la division équitable du réseau en plusieurs groupes de nanosatellites. Nous comparons les performances de trois algorithmes de division de graphe : Random Node Division (RND), Multiple Independent Random Walks (MIRW), et Forest Fire Division (FFD). Nos résultats montrent que MIRW obtient les meilleurs scores en termes d’équité, peu importe le nombre de groupes produit.

EVM (Error Vector Measurement) is used to measure the end-to-end quality of digital communication links. It comes from noise, linear and non-linear distortion, and interference if any. I propose a method to discriminate between random noise that is independent of the signal and distortion that depends on the signal. Interference is more complex to discriminate as it is not random but can be either synchronous with the signal or not. Echoes such as multipath cause linear distortion if they are static. However, variable echoes, such as those created in a reverberation chamber must be treated specifically.

Low-frequency radio interferometry is crucial to understanding the universe and its very early days. Unfortunately, most of the current instruments are ground-based and thus impacted by the interferences massively produced by the Earth. To alleviate this issue, scientific missions aim at using Moonorbiting nano-satellite swarms as distributed radio-telescopes in outer space, keeping them out of Earth interference range. However, swarms of nano-satellites are systems with complex dynamics and need to be appropriately characterized to achieve their scientific mission. This paper presents a methodology based on graph theory for characterizing the swarm network system by computing graph theory metrics around three properties: the node density, network connectivity and ISL availability. We show that these properties are well-suited for highlighting a possible heterogeneity in a network and adapt a routing strategy accordingly. This work is the first milestone in defining the best-suited routing strategy within the swarm from the derived network properties.

We address the problem of partitioning a network of nano-satellites to distribute fairly the network load under energy consumption constraints. The study takes place in a context where this swarm of nano-satellites orbits the Moon and works as, but not limited to, a distributed radio-telescope for low-frequency radio interferometry. During an interferometry mission, each nano-satellite collects observation data, then shares them with the other swarm members to compute a global image of space. However, the simultaneous transmission of large volumes of data can cause communication issues by overloading the radio channel, leading to potential packet loss. In this context, we investigate three division algorithms based on graph sampling techniques. We prove that random walk-based algorithms overall perform the best in terms of conservation of graph properties and fairness for group sizes down to 10% of the original graph.

The exponential increase in the number of satellites along with the hazards of the space environment they encounter endangers the sustainability of low earth orbit (LEO). The consequences of events such as collisions, fragmentations and fatal failures are then becoming more than ever a threat to any kind of space activity. Therefore, the space situational awareness is of utter importance in all its aspects, i.e., assessing and predicting the risks from space weather and SST (Space Surveillance and Tracking), in addition to implementing mitigation measures. In this context, this paper covers the benefits of in-orbit inspection combined with the aggregation and processing of existing space data, proposed by the French company SpaceAble for low earth orbit sustainability. Collision risk awareness for a LEO constellation is raised in this paper through the analysis of the conjunction risks of the Starlink constellation. An inspection plan is also derived in terms of the number of inspections for different scenarios, and with respect to different LEO altitudes.

Non-linear amplifiers distort signal constellations through their amplitude (AM/AM) and phase (AM/PM) curves versus input amplitude. This causes an increase in the average Error Vector Magnitude (EVM) of the amplified signal. Most commercial EVM simulation software and measurement devices display the ideal and distorted constellations. When computing separate EVMs for each value of ideal symbol power, it is possible to obtain a representation of the effect of AM/AM and AM/PM curves on the constellation. A new type of display, with the distorted constellation folded up on the real axis, is proposed to get a direct representation of the amplifier non-linearity. This can also be used for nonlinear equalization of the signal to improve the EVM.