## 1. Introduction

[2] Atmospheric attenuation significantly affects radio wave propagation in satellite links operated in high-frequency bands, between 10 and 50 GHz. It is caused by several types of atmospheric component: gases (oxygen and water vapor), clouds and rain. Each of these components behaves quite differently, when considered in terms of its temporal and spatial variability. Moreover, the relative contribution of each component to the total attenuation varies with frequency.

[3] In the case of a satellite slant path, gaseous attenuation, due mainly to water vapor and oxygen, can exceed 3 dB at frequencies below 50 GHz and at low elevation angles. This form of attenuation can be considered to be homogeneous, over the horizontal range of a link. Liebe's model allows accurate modeling of gaseous attenuation up to 1000 GHz, by using vertical profiles of atmospheric parameters (temperature, pressure, humidity). For frequencies below 50 GHz, a water vapor absorption peak is observed near 22 GHz. Spatial and temporal variations in gas-induced attenuation are mainly due to spatiotemporal variations in water vapor quantity.

[4] Attenuation due to nonprecipitating clouds, composed of liquid water or ice particles, leads to a maximum of about 4 dB for low elevation angles at 50 GHz, and total cloud-induced attenuation increases nearly as the square of frequency. The Rayleigh approximation can be used to calculate its contribution at frequencies below 50 GHz, such that the resulting attenuation is proportional to the integrated liquid water content present along the link. As cloud coverage varies considerably in both the horizontal and vertical directions, and the corresponding liquid content varies substantially in space and time, cloud-induced attenuation can vary strongly.

[5] Rain is the strongest contributor to attenuation in radio wave propagation at frequencies above 10 GHz. It increases with rainfall rate and frequency [*European Cooperation in the Field of Science and Technology* (*COST*), 1999b] and becomes particularly significant in V band (36 dB for a slant path at 50 GHz, for a rainfall rate of 50 mm/h). At any given frequency, rain-induced attenuation depends mainly on the shape and size distribution profile of the raindrops. In order to perform accurate rain attenuation calculations, a good knowledge is needed of these characteristics at each point along the link. The rain rate varies noticeably in space and time, and thus leads to particularly dynamic properties in the propagation channel. The present study concerns the range 20–50 GHz, which is roughly extends over the Ka and Q bands. Most of the statements and conclusions made in this paper are only valid within this frequency range.

[6] Satellite telecommunication systems using these frequency bands need to compensate for atmospheric attenuation. One of the fade mitigation techniques used to combat these phenomena is uplink power control. The transmission power is adjusted in accordance with the state of the atmosphere. As an example, it may need to be increased very quickly during rainy conditions. The uplink always uses a higher frequency band than the downlink, and is thus more sensitive to atmospheric effects. In practice, the required changes in uplink power are determined by scaling the attenuation measured in the downlink. The frequency scaling technique is based on the determination of a relationship between the attenuation occurring at two or more different frequencies. As the various atmospheric contributions behave differently as a function of frequency, each contributor generates a different frequency scaling ratio. In cases where one contributor is considerably more significant than the others (typically, during a strong rain event), the total scaling ratio is determined uniquely by that relevant to the main contributor. Consequently, in the case of very strong attenuation, the total scaling ratio can be approximated by the scaling ratio due to rain. However, if accurate attenuation frequency scaling is needed over a large range of attenuation and frequency values, as will be the case for new services which plan to use frequencies above 35 GHz, each of the individual atmospheric contributors will need to be accounted for. Under these conditions, a specific scaling ratio [*COST*, 1999a, 1999b] will be used for each of the atmospheric contributors, in order to determine an overall scaling ratio for the propagation channel in question.

[7] Separation of the different atmospheric contributions (also called separation effects) is an essential step in the study of the dynamics of the propagation channel. In addition, it is known that each of the atmospheric components is subject to temporal variations, which are individually specific. As a result, the prediction of global attenuation at time *t* + Δ*T*, based on known attenuations at time *t*, will certainly be improved by considering separately the attenuation predictions of each contribution.

[8] Our aim in this paper is to present a statistical model able to separate out the respective roles played by the three types of atmospheric contributor. An artificial neural network (ANN) is trained to estimate the respective contributions from gases (oxygen and water vapor), cloud and rain, to the overall attenuation measured at one or more frequencies. This training is performed in a supervised manner, and involves the development of a training base. In this manner, a very large database containing the ANN input data and corresponding targets is simulated from a wide set of atmospheric profiles, corresponding to different sets of meteorological conditions. The first section of this paper deals with the development of ANN models and the development of the simulated database. The second section is devoted to the performance of different separation models on simulated and real measurements. Finally, in the third section, we apply the models to frequency scaling applications, and performance is assessed using attenuation measurements acquired during the Olympus experiment.