Research Article

Ionospheric scintillation modeling II. Theoretical study of power spectral densities of ionospheric scintillation

¹ DEMR, ONERA, Université de Toulouse, 31000 Toulouse, France
² DEMR, ONERA, 13330 Salon-de-Provence, France

^* Corresponding author: gregory.morel@onera.fr

Received: 23 April 2025
Accepted: 16 October 2025

Abstract

An electromagnetic signal that has passed through a layer of ionospheric irregularities can undergo significant modifications. The Power Spectral Density (PSD) of such a signal can then be rich in information about the medium through which it has passed. Thus, this paper is dedicated to the theoretical study of the PSD of the log-amplitude and phase of a signal received by a ground receiver, for a satellite-Earth link that encounters ionospheric irregularities. Incident plane wave (PW), incident spherical wave (SW) and corrected plane wave (CPW) formalisms are considered. For each approach, an analytic integral formulation of the log-amplitude and phase PSD of the received signal are established and compared under the assumptions of weak scattering and a thin layer of irregularities relative to the length of the satellite-Earth link. The SW analytic formalism is validated trough comparison with a numerical approach solving the Parabolic Wave Equation (PWE) in spherical coordinates combined with Multiple Curved Phase Screens (MCPS). Asymptotic derivations of the PSD analytic formulations for low and high frequencies are proposed, and in addition, particular attention is given to the frequency corresponding to the maximum of the log-amplitude PSD. These formulations are analysed, and their sensitivity to the characteristics of the medium is discussed to address the inversion problem, consisting of deriving parameters that describe the irregularities of the medium through its log-amplitude and phase PSD.