## Recherche

###### Article de conférence

## On the Network Characterization of Nano-Satellite Swarms09

**In Proc. 28th IEEE Symposium on Computers and Communications (ISCC 2023), Tunis, Tunisia, 9-12 July, 2023.**

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.

Réseaux / Systèmes spatiaux de communication

###### Séminaire

## Massive MIMO Radar for Target Detection

**Seminar of TeSA, Toulouse, June 28, 2023.**

Traitement du signal et des images / Systèmes de communication aéronautiques, Localisation et navigation et Systèmes spatiaux de communication

###### Article de conférence

## Fair Network Division of Nano-satellite Swarms

**In Proc. IEEE 97th Vehicular Technology Conference (VTC Spring), Florence, Italy, June 2023.**

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.

Réseaux / Systèmes spatiaux de communication

## Lightweight synchronization to NB-IoT enabled LEO Satellites through Doppler prediction

**In Proc. The 19th International Conference on Wireless and Mobile Computing, Networking and Communications (IEEE WiMob 2023), Montreal, Canada, Canada, 21-23 June 2023.**

In the last decade, it has been quickly recognized that backhauling Low Power Wide Area Networks (LPWAN) through Low Earth Orbit (LEO) satellites paves the way to the development of novel applications for a truly ubiquitous Internet of Things (IoT). Among LPWAN communications technologies, Narrowband IoT (NB-IoT) does not suffer from interference by other concurrent technologies since it works on a licensed frequency spectrum. At the same time, thanks to its medium access scheme based on contention resolution and resource allocation, NB-IoT is a key enabler for the specific market slice of IoT applications requiring a good level of reliability. In the architectural configuration analyzed throughout this contribution, an NB-IoT low power User Equipment (UE) can communicate with a LEO satellite equipped with an Evolved Node B (eNB) for a time limited to the visibility window of that satellite from the UE position on the Earth. However, the Doppler effect inherent to the time-varying relative speed of the eNB needs to be dealt with additional resources. The solutions proposed until now are non-trivial, thus making the use of NB- IoT for ground-to-satellite communications still expensive and energetically inefficient. Timely, this contribution proposes a procedure for a UE to infer the future values of the Doppler shift from the beacon signals so that frequency pre-compensation can be easily applied in the following interactions during the visibility time. The presented simulation results show that a UE needs to listen to about 10 beacon signals in 1 second to accurately and robustly predict the Doppler curve, thus enabling a lightweight (and eventually truly energy-efficient) implementation of NB-IoT over ground-to-satellite links.

Communications numériques / Systèmes spatiaux de communication

###### Séminaire

## Hidden Markov Models and Bayesian Inference

**Seminar of TeSA, Toulouse, June 12, 2023.**

Traitement du signal et des images / Autre

###### Article de conférence

## Theoretical Performance Analysis of GNSS Tracking Loops

**In Proc. IEEE/Institute of Navigation (ION) Positioning, Location, and Navigation Symposium (PLANS), Monterey, California-USA. April 24-28, 2023.**

This paper aims to characterize the estimation precision at the output of the GNSS receiver tracking stage. We define an original statistical modelling of the GNSS tracking loop, which can then be exploited by an optimal linear Kalman Filter (KF) in order to obtain an analytical expression of the steady-state regime. The latter is designed to encompass dynamic information of the GNSS receiver. Two observation models are of interest: the first one considers the propagation delay and Doppler parameters, and the second one also including the Doppler rate, i.e., the acceleration, which is known to be relevant for high dynamics scenarios and can easily be included into the acquisition step. Within this context, the steady-state asymptotic performance of the tracking stage is obtained by solving an algebraic discrete Riccati equation. In both cases, simulation results are provided to show the validity of the proposed approach and the resulting steady-state performance.

Traitement du signal et des images / Localisation et navigation et Systèmes spatiaux de communication

## GNSS L5/E5 Maximum Likelihood Synchronization Performance Degradation under DME Interferences

**In Proc. IEEE/Institute of Navigation (ION) Positioning, Location, and Navigation Symposium (PLANS), Monterey, California-USA. April 24-28, 2023.**

Global Navigation Satellite Systems (GNSS) are a key player in a plethora of applications. For navigation purposes, interference scenarios are among the most challenging operation conditions, which clearly impact the maximum likelihood estimates (MLE) of the signal synchronization parameters. While several interference mitigation techniques exist, a theoretical analysis on the GNSS MLE performance degradation under interference, being fundamental for system/receiver design, is a missing tool. The main goal of this contribution is to introduce a mathematical tool to evalute the effect of any type of interference on any GNSS signal. Regarding such tool, we provide closedform expressions of the misspecified Cram´er-Rao (MCRB) bound and estimation bias, for a generic GNSS signal corrupted by an interference. The proposed expressions are used to analyze the GNSS performance degradation induced by the distance measuring equipment (DME) system.

Traitement du signal et des images / Localisation et navigation et Systèmes spatiaux de communication

## A simple and robust K-factor computation method for GNSS integrity needs

**In Proc. 2023 IEEE/ION Position, Location and Navigation Symposium (PLANS), pp. 399-407, Monterey, CA, USA, 24-27 April 2023.**

The aviation Minimum Operational Performance Standard defines the SBAS protection levels as the product of the estimated standard deviation of the positioning error and a scaling factor called K-factor. The K-factor depends on the time window of interest and on the correlation between errors in the time window. The K-factors defined in aviation are difficult to generalize to other specifications in other domains, such as rail and maritime applications. This article presents a simple formula to calculate the K-factor for any value of integrity risk and time interval. The resulting K-factor is shown to be mathematically rigorous under the hypothesis of Gaussian error distribution but without any assumption on the correlation structure of the successive position estimates. The Gaussian assumption can be relaxed and replaced by overbounding with a Gaussian distribution with a very good approximation. This formula can be used in any GNSS application where integrity is needed.

Traitement du signal et des images / Localisation et navigation

###### Article de journal

## On the accuracy limits of misspecified delay-Doppler estimation

**Signal Processing, article 108872, vol. 205, April, 2023.**

This work derives compact closed-form expressions of the misspecified Cramér–Rao bound and pseudo-true parameters of time-delay and Doppler for a high dynamics signal model. Those expressions are validated by analyzing the mean square error (MSE) of the misspecified maximum likelihood estimator. A noteworthy outcome of these MSE results is that, for some magnitudes of acceleration and signal-to-noise ratios, neglecting the acceleration is beneficial in the MSE sense. The variance performance improvement is obtained at the cost of a systematic error in the true parameter estimation. This can be seen as a specific case of the trade-off between bias and variance. Neglecting the acceleration can improve the Doppler estimation when the error induced on the misspecified model is less than the variance increase due to including an extra parameter to estimate. Then, for some non-zero acceleration magnitudes and short integration times, the Doppler estimation using a misspecified model outperforms a correctly specified model in the MSE sense.

Traitement du signal et des images / Localisation et navigation et Systèmes spatiaux de communication

## Untangling first and second order statistics contributions in multipath scenarios

**Signal Processing, vol. 205, Art. no 108868, April, 2023.**

In ranging-based applications, ignoring the presence of multipath often leads to a bias upon the estimated range, which actually originates from misspecified estimation problem because the assumed data signal model, here without multipath, is not equal to the true one. Such misspecification also results in an error covariance matrix around the biased estimates, so-called pseudotrue parameters, that differs from the Cramér–Rao bound applied to the true model. This error covariance matrix can be lower bounded by a misspecified Cramér–Rao bound (MCRB). In this work, a closed-form expression of the MCRB under multipath conditions is proposed, which only depends on the baseband signal samples and both delay, Doppler and complex amplitude pseudotrue parameters. These MCRB expressions are fundamental (i) to understand and characterize the impact of multipath conditions when not taken into account, (ii) for system/signal design, and (iii) to derive new robust estimators. The proposed MCRBs are validated for a representative navigation signal, comparing the resulting bounds with the mean square error obtained by the misspecified maximum likelihood estimator with respect to the pseudotrue parameters.

Traitement du signal et des images / Localisation et navigation

#### ADRESSE

7 boulevard de la Gare

31500 Toulouse

France