Clear-air Turbulence Effects Modeling on Terrestrial and Satellite Free-Space Optical Channels F.S. Marzano 1 , D. Carrozzo 1 , S. Mori 1 , F. Moll 2 1 Dept. of Information Engineering, Electronics and Telecommunications (DIET) Sapienza University of Rome, Rome, Italy marzano@diet.uniroma1.it, mori@diet.uniroma1.it, dnt.carrozzo@gmail.com 2 Institute of Communications and Navigation, German Aerospace Center (DLR) Oberpfaffenhofen, D-82234 Wessling, Germany Florian.Moll@dlr.de Abstract—Wireless communications using free space optics (FSO) are sensitive to atmospheric conditions. Clear-air turbulence can introduce severe impairments reducing FSO channel availability. Radiosounding profiles, available near Rome (Italy) and Munich (Germany), are used to estimate the power scintillation index through a new physical refractive index structure constant model and to estimate scintillation fade statistics for near-infrared FSO. Preliminary qualitative validation is performed using FSO campaign near Munich for both terrestrial and slant links. Keywords—free space optics, atmospheric turbulence, optical modelling, meteorological data, scintillation fade. I. INTRODUCTION Free Space Optics (FSO) represent a promising technology and, at the same time, a complementary choice to radio frequency (RF) peer-to-peer links and wide area networks (WANs) [1]-[3]. FSO can allow line-of-sight links of several kilometers in optimal conditions, but an acceptable quality of service (QoS) can be guaranteed only for shorter ranges. In fact, atmospheric effects are perhaps the biggest challenge in FSO because they can limit operating avaliability [4], [5]. FSO links are very sensitive to the presence of atmospheric droplets within the beam such as fog and hydrometeors [4], [6]- [10]. Tropospheric turbulence, due to small temperature variations of atmopsheric masses, can be responsible of beam power losses due to the beam spot spreading and of space-time fluctuations of the laser beam intensity, better known as scintillation [6]. In this paper we will briefly summarize a physical model of refractive index structure constant and scintillation (Sect. II). We will then apply it to radiosounding profiles (Sect. III) and compare with FSO channel data (sect. IV), in order to perform a preliminary validation using available measurements. Conclusions will be drawn in Sect. V. II. FSO SCINTILLATION MODEL Atmospheric turbulence is often represented as a cascade of air eddies with different temperature, humidity and density thus inducing a random space-time varibility of the refractive index [3]. This effect causes electro-magnetic scintillation: the fluctuation of amplitude and phase of the optical beam transmitted through atmospheric turbulence [5]. The structure constant of the atmospheric refractive index for optical applications can be expressed as [6]: ܥ ௡ ଶ ሺݖǢ ሻ ൌ ቆ ͺͲͳͲ ଺ ݌  ଶ ቇ ଶ ܥ  ଶ ሺݖሻ ൌ  ଶ ሺ ܭ ு ܭ ெ Τ ሻ ܮ ଴ ସଷ Τ ൬   ݖ ൰ ଶ (1) where a 2 =2.8 is an empirical constant, K H /K M = 1.35 (the ratio is the exchange coefficients for heat and momentum) [7], C T 2 the temperature structure constant and L 0 is the spatial outer scale. An update model of the refractive index structure constant has been recently presented taking into account the conservative passive additive property of potential temperature ș [8] and applied to FSO [14]. If T is absolute temperature (K) and p is pressure (hPa), then potential temperature T is defined by [5]: ߠൌ൬ ݌ ଴ ݌ ൰ ோ ஼ ೛ Τ (2) where p o is the reference pressure (at 1000 hPa), R is the air gas constant, c p is the specific heat capacity (with R/c p = 0.286). The rigorous final expression of C n 2 then becomes [8], [14]: ܥ ௡ ଶ ሺݖǢ ߠሻൌ ቆ ͺͲݔͳͲ ଺ ݌  ߠ ቇ ଶ ܥ ఏ ଶ ሺݖሻ (3) where potential temperature structure constant is given by: ܥ ఏ ଶ ሺݖሻ؆ ଶ ሺ ܭ ு ܭ ெ Τ ሻ ܮ ଴ ସଷ Τ ൬  ߠ  ݖ ൰ ଶ (4) In the weak-fluctuation scintillation theory the Rytov log- amplitude variance parameter is expressed by [6]: ߪ  ʹ ൌ ͳǤʹ͵ ͹͸ Τ න ܥ  ʹ ܮ Ͳ ሺݎሻ ݎ ͷ͸ Τ  ݎ(5) This work has been carried out within JLAP project between ISCOM- MISE (Rome, Italy) and DIET Sapienza University of Rome (Italy) and within the COST-IC1101 OPTICWISE framework. Copyright 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Postprint. Original IEEE article: F.S. Marzano, D. Carrozzo, S. Mori, and F. Moll, "Clear-air Turbulence Effects Modeling on Terrestrial and Satellite Free-Space Optical Channels," in 2015 4th International Workshop on Optical Wireless Communications (IWOW), pp. 36-40, Sept. 2015 doi: 10.1109/IWOW.2015.7342261