This set of two companion papers aims at providing a statistical framework to quantify the inter-annual variability observed on the statistics of rain attenuation or rainfall rate derived from Earth-space propagation measurements. This part I is more specifically devoted to the theoretical study of the variance of estimation of empirical complementary cumulative distribution functions (ECCDFs) derived from Earth-space rain attenuation or rainfall rate time series. To focus the analysis on the statistical variability but without loss of generality, synthetic rain attenuation time series are considered. A large variability on the ECCDFs, which depends on the duration of the synthetic data, is first put into evidence. The variance of estimation is then derived from the properties of the statistical estimator. The formulation is validated numerically, by comparison with the ECCDF variances derived from the synthetic data. The variance of the fluctuations around the CCDF is then shown to be dependent on the average of the correlation function of the time series, on the probability level and on the measurement duration. This variance of estimation is needed as a prerequisite in conjunction with the knowledge of the climatic variability to characterize the yearly fluctuations of propagation statistics computed from experimental time series. The extensions from simulations to experiments as well as the application to system planning are detailed in part II.
The design and optimization of propagation impairment techniques for space telecommunication systems operating at frequencies above 20 GHz require a precise knowledge of the propagation channel both in space and time. For that purpose, space-time channel models have to be developed. In this paper the description of a model for the simulation of long-term rain attenuation time series correlated both in space and time is described. It relies on the definition of a stochastic rain field simulator constrained by the rain amount outputs of the ERA-40 reanalysis meteorological database. With this methodology, realistic propagation conditions can be generated at the scale of satellite coverage (i.e., over Europe or USA) for many years. To increase the temporal resolution, a stochastic interpolation algorithm is used to generate spatially correlated time series sampled at 1 Hz, providing that way valuable inputs for the study of the performances of propagation impairment techniques required for adaptive SatCom systems operating at Ka band and above.
This set of two companion papers aims at providing a model for the inter-annual variability of earth-space propagation statistics and for the inherent risk and CIs. In part I, it was proposed to model the yearly variance σ² of empirical complementary CDFs so that σ 2 p ð ÞC the inter-annual climatic variance and p the long-term probability. Particularly, an analytical formulation of σ 2 E was derived and parameterized from synthetic rain attenuation data. Considering the statistical framework developed in part I, this part II is specifically devoted to the parameterization of the variance of estimation σ 2 E from experimental data of rain attenuation and rainfall rate. Then, a methodology to model and parameterize worldwide the inter-annual climatic variance σ 2 C is presented. The model of yearly variance of the empirical complementary CDFs σ 2 ¼ σ 2 C þ σ 2 E is finally compared against yearly experimental variances derived from data collected worldwide. The knowledge of this variability is very useful for system design as it allows the risk on a required availability and associated with a given propagation margin to be quantified.
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