Secrecy Capacity Analysis Over κ–μ Fading Channels: Theory and Applications

In this paper, we consider the transmission of confidential information over a κ-μ fading channel in the presence of an eavesdropper who also experiences κ-μ fading. In particular, we obtain novel analytical solutions for the probability of strictly positive secrecy capacity (SPSC) and a lower bound of secure outage probability (SOPL) for independent and non-identically distributed channel coefficients without parameter constraints. We also provide a closed-form expression for the probability of SPSC when the μ parameter is assumed to take positive integer values. Monte-Carlo simulations are performed to verify the derived results. The versatility of the κ-μ fading model means that the results presented in this paper can be used to determine the probability of SPSC and SOPL for a large number of other fading scenarios, such as Rayleigh, Rice (Nakagamin), Nakagami-m, One-Sided Gaussian, and mixtures of these common fading models. In addition, due to the duality of the analysis of secrecy capacity and co-channel interference (CCI), the results presented here will have immediate applicability in the analysis of outage probability in wireless systems affected by CCI and background noise (BN). To demonstrate the efficacy of the novel formulations proposed here, we use the derived equations to provide a useful insight into the probability of SPSC and SOPL for a range of emerging wireless applications, such as cellular device-to-device, peer-to-peer, vehicle-to-vehicle, and body centric communications using data obtained from real channel measurements.

Kelvin-Helmholtz instability in solar chromospheric jets: theory and observation

Using data obtained by the high-resolution CRisp Imaging SpectroPolarimeter instrument on the Swedish 1 m Solar Telescope, we investigate the dynamics and stability of quiet-Sun chromospheric jets observed at the disk center. Small-scale features, such as rapid redshifted and blueshifted excursions, appearing as high-peed jets in the wings of the Hα line, are characterized by short lifetimes and rapid fading without any descending behavior. To study the theoretical aspects of their stability without considering their formation mechanism, we model chromospheric jets as twisted magnetic flux tubes moving along their axis, and use the ideal linear incompressible magnetohydrodynamic approximation to derive the governing dispersion equation. Analytical solutions of the dispersion equation indicate that this type of jet is unstable to Kelvin–Helmholtz instability (KHI), with a very short (few seconds) instability growth time at high upflow speeds. The generated vortices and unresolved turbulent flows associated with the KHI could be observed as a broadening of chromospheric spectral lines. Analysis of the Hα line profiles shows that the detected structures have enhanced line widths with respect to the background. We also investigate the stability of a larger-scale Hα jet that was ejected along the line of sight. Vortex-like features, rapidly developing around the jet’s boundary, are considered as evidence of the KHI. The analysis of the energy equation in the partially ionized plasma shows that ion–neutral collisions may lead to fast heating of the KH vortices over timescales comparable to the lifetime of chromospheric jets.