arXiv subjects

Pierre Popineau

Publications and source records attributed to Pierre Popineau.

3 recordsLinked to original sources

arXiv2025

Timing advance and Doppler shift estimation in LEO satellite networks: A recursive Bayesian study

Low earth orbit (LEO) satellite based non-terrestrial networks are a key theme of the upcoming 6G networks. These space networks are proposed to be used for high-mobility use-cases like airplanes and vehicles. The initial access process between a base station (BS) and a user equipment (UE) involves timing advance (TA) value computation at the BS, requiring precise BS location information at the UE. It becomes more challenging in LEO satellite networks due to the fast moving LEO satellites and large pathloss, in addition to the mobile UE. This paper aims to compute the TA and Doppler shift experienced at the UE by modeling the joint system dynamics in a LEO satellite-mobile UE network through an extended Kalman filter (EKF) based recursive Bayesian framework. The framework accurately models the joint system dynamics by considering the LEO satellite acceleration. It constructs the Jacobian to linearize the inherent non-linearities present in the motion. Probabilistic insights regarding the state-update and propagation are also provided. The analytical framework factors in the limited satellite visibility at the UE and the satellite-UE geometry w.r.t. the earth center. The proposed framework is also useful when the satellite and UE clocks are not in sync, with the corresponding clock drift a function of the measured time difference of arrivals. Our results showcase the efficacy and robustness of the proposed EKF framework to estimate the TA and Doppler shift, even at very high UE speeds. The work is expected to be extremely useful in realizing LEO satellite based non-terrestrial networks.

eess.SP↗

arXiv2023

An instability condition for queuing systems with state-dependent departure rates

In this paper, we present a condition to obtain instability for a class of queueing networks where the arrival rates in each server are constant and the departure rate in each server is a decreasing function of the queue lengths of other servers. Under a stronger assumption, that the departure rates are proportional to the queue length in each server, we obtain a characterization of the stability region through a system of equations. We start by defining the mathematical model and the queueing discipline we will study. We then obtain irreducibility and monotonicity for the dynamics, which allow us to state our two main results. We then use this result to obtain instability conditions for two queueing networks for which stability is known: a medium access algorithm and an interference queueing network.

math.PR↗

arXiv2023

On multiclass spatial birth-and-death processes with wireless-type interactions

This paper studies a multiclass spatial birth-and-death (SBD) processes on a compact region of the Euclidean plane modeling wireless interactions. In this model, users arrive at a constant rate and leave at a rate function of the interference created by other users in the network. The novelty of this work lies in the addition of service differentiation, inspired by bandwidth partitioning present in 5G networks: users are allocated a fixed number of frequency bands and only interfere with transmissions on these bands. The first result of the paper is the determination of the critical user arrival rate below which the system is stochastically stable, and above which it is unstable. The analysis requires symmetry assumptions which are defined in the paper. The proof for this result uses stochastic monotonicity and fluid limit models. The monotonicity allows one to bound the dynamics from above and below by two adequate discrete-state Markov jump processes, for which we obtain stability and instability results using fluid limits. This leads to a closed form expression for the critical arrival rate. The second contribution consists in two heuristics to estimate the steady-state densities of all classes of users in the network: the first one relies on a Poisson approximation of the steady-state processes. The second one uses a cavity approximation leveraging second-order moment measures, which leads to more accurate estimates of the steady-state user densities. The Poisson heuristic also gives a good estimate for the critical arrival rate.

math.PR↗