# Model for the Prediction of Rain Attenuation Affecting Free Space Optical Links
## 1 Introduction  
Optical wireless communications are based on the transmission of data through the atmosphere using optical carriers within spectral windows that are free from molecular absorption. Optical links target very short-range (in the order of few cm), as well as long-range (hundreds of km), applications. Specifically, the terms free space optical communications or free-space optics (FSO) typically refer to outdoor terrestrial links operating over distances from a few tens of meters up to several kilometers. As optical wavelengths are very sensitive to atmospheric effects, FSO has been so far restricted to niche applications, such as inter-building connectivity in enterprise/campus environments, temporary links in emergency situations, or high-definition video transmission (typically from TV cameras to a broadcasting center) [1]. However, with the dramatic growth of broad-band services over wireless cellular networks for mobile users, FSO might emerge as a competitor of microwave wireless systems for backhauling in future 5G meshes, where the cell size, hence the distance between base stations, is relatively small [2]. Indeed, FSO presents several advantages over radiofrequency, including a very high-bandwidth, narrow-beam transmission (which, in turn, improves security, re-use capability, and electromagnetic compatibility issues), no licensing costs, and simple installation. On the other hand, the performance of FSO is strongly limited by atmospheric effects [3; 4]. In clear air, atmospheric turbulence is the cause of signal fluctuations (scintillations) that may affect FSO operation [5]. Spatial diversity at the receiver (by aperture averaging or multiple apertures) and/or at the transmitter (by multiple transmit beams)is a viable solution to reduce the detrimental effect of turbulence. Mitigation techniques also include adaptive transmission (where the transmit power, the modulation, and/or the coding are adjusted to the actual channel conditions), and cooperative transmission through multi-hop or parallel relaying [1]. Laser beam propagation through atmospheric particles (fog, rain, snow, etc.) may produce long and deep signal fades that result in link outage [6; 7; 8]. In this case, the techniques used for turbulence mitigation are ineffective due to the correlation scale of the process (in both time and space). Fog has the most detrimental impact on optical waves: specific attenuation due to dense fog is as high as 300 dB/km for a visibility of around 50 m [9]. Rain attenuation, although markedly dependent on the microphysics of precipitation, is of the same order of magnitude as at mm-waves. As a matter of fact, where fog occurrence is non-negligible, FSO is outperformed by microwave links in high-availability applications. On the other hand, in sites where fog is not present, such as inland tropical/equatorial regions, rain is the main atmospheric constituent limiting the length and performance of FSO links. It is therefore of key importance to properly investigate the impact of rain on FSO links. Several global models have been developed and proposed in the literature to predict rain attenuation on terrestrial links operating at frequencies in the millimeter-/micro-wave portion of the spectrum. The International Telecommunication Union--Radio communication sector (ITU--R) P.530-16 [10], the Brazilian [11], the Lin [12], and the Moupfouna [13] models are worth being cited as sample methodologies that aim at being globally applicable. On the other hand, although several works in the literature investigate the effects of rain on FSO, they focus on limited local data (no long-term statistically meaningful rain attenuation datasets) and do not attempt to propose expressions of more general applicability. For instance, optical attenuation has been predicted according to a scattering model and a theoretical DSD [14]. Alternatively, empirical best-fit expressions between optical attenuation and rain rate have been proposed [7; 15].