In communications satellite systems, rain attenuation frequency scaling is a technique implemented to model rain fade phenomena affecting a telecommunications link, both statistically and instantaneously. Accurate predictions of rain attenuation are crucial both for the proper design of a satellite communication (SatCom) system, as the detrimental impact of hydrometeors present within the troposphere, mainly rain, on radio frequency signals, can lead to system failures (commonly known as network outage periods). Moreover, such analyses are essential for the implementation of adaptive fade mitigation techniques, such as uplink power control and variable rate encoding schemes, to increase the link availability. A scaling approach is particularly suitable in scenarios where the uplink and downlink, which typically share the same channel capacity and therefore operate at different frequency to avoid co-channel interference, are affected by the same rainfall event along the link. In such context, it may be advantageous to derive the attenuation due to rain at the higher frequency, called target frequency, by properly scaling concurrent attenuation measurements affecting the same link at lower frequency, called reference frequency. Furthermore, as rain attenuation measurements inherently embed key information about the rain event, such as the spatial distribution of the rain and the information on the raindrop size distribution (DSD), frequency scaling models provide an enhanced prediction accuracy if compared to statistical prediction models, which are typically fed with local pointfall rain data only. As proof, frequency scaling models applied to experimental SatCom systems operating within the geostationary orbit yield statistical errors of 12 - 15% in contrast to the 30 - 40% associated with statistical prediction models.
General definition Conceptually, the frequency scaling (FS) of rain attenuation, A R {\displaystyle {A}_{R}} , can be expressed as:
A ~ R , f U = R F S A R , f L (dB) {\displaystyle {\tilde {A}}_{R,f_{U}}=R_{FS}\ A_{R,f_{L}}\quad {\textrm {(dB)}}}
where the estimation of the rain attenuation at the target frequency f U {\displaystyle f_{U}} , namely A ~ R , f U {\displaystyle {\tilde {A}}_{R,f_{U}}} , is directly related to the corresponding attenuation measured at the reference frequency f L {\displaystyle f_{L}} (Hz), namely A R , f L {\displaystyle {A}_{R,f_{L}}} (dB), by means of the frequency scaling ratio, R F S {\displaystyle R_{FS}} , whose definition changes model by model. Several FS models have been proposed in the past, and they can be classified as either statistical (S-FS) models or instantaneous (I-FS) models. S-FS are typically empirically based and relate the attenuation values at f L {\displaystyle f_{L}} and f U {\displaystyle f_{U}} as function of the same frequency of exceedance, commonly referred to as the exceedance probability level p {\displaystyle p} %:
A ~ R , f U ( p ) = R F S A R , f L ( p ) (dB) {\displaystyle {\tilde {A}}_{R,f_{U}}(p)=R_{FS}\ A_{R,f_{L}}(p)\quad {\textrm {(dB)}}}
In this context, R F S {\displaystyle R_{FS}} is typically a constant only dependent only on the two operating frequencies. However, defining a fixed R F S {\displaystyle R_{FS}} limits the scaling prediction accuracy, as the value of R F S {\displaystyle R_{FS}} can vary significantly from one rain event to another, and even within the same event. I-FS models aim at overcoming this limitation by introducing a time-variant R F S ( t ) {\displaystyle R_{FS}(t)} :
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