A Rain Attenuation Time-Series Synthesizer Based on a Dirac and Lognormal Distribution

Abstract

In Recommendation ITU-R P.1853-1, a stochastic approach is proposed to generate long-term rain attenuation time series , including rain and no rain periods anywhere in the world. Nevertheless, its dynamic properties have been validated so far from experimental rain attenuation time series collected at mid-latitudes only. In the present paper, an effort is conducted to derive analytically the first-and second-order statistical properties of the ITU rain attenuation time-series synthesizer. It is then shown that the ITU synthesizer does not reproduce the first-order statistics (particularly the rain attenuation cumulative distribution function CDF), however, given as input parameters. It also prevents any rain attenuation correlation function other than exponential to be reproduced, which could be penalizing if a worldwide synthesizer that accounts for the local climatology has to be defined. Therefore, a new rain attenuation time-series synthesizer is proposed. It assumes a mixed Dirac-lognormal modeling of the absolute rain attenuation CDF and relies on a stochastic generation in the Fourier plane. It is then shown analytically that the new synthesizer reproduces much better the first-order statistics given as input parameters and enables any rain attenuation correlation function to be reproduced. The ability of each synthesizer to reproduce absolute rain attenuation CDFs given by Recommendation ITU-R P.618 is finally compared on a worldwide basis. It is then concluded that the new rain attenuation time-series synthesizer reproduces the rain attenuation CDF much better, preserves the rain attenuation dynamics of the current ITU synthesizer for simulations at mid-latitudes, and, if it proves to be necessary for worldwide applications, is able to reproduce any rain attenuation correlation function.

Reliable M2M/IoT data delivery from FANETs via satellite

“…At the operating frequencies under investigation, ie, Ku‐ Ka‐ bands, rain is the dominant fading mechanism . Most models for rain attenuation time series synthesis and modeling of first order statistics refer to fixed ground stations . However, a characteristic of FANETs is that the user terminals are mobile, and therefore, the aforementioned models are not directly applicable.…”

“…19 Most models for rain attenuation time series synthesis and modeling of first order statistics refer to fixed ground stations. [20][21][22][23][24] However, a characteristic of FANETs is that the user terminals are mobile, and therefore, the aforementioned models are not directly applicable. In Matricciani, 25 the exceedance probability of rain attenuation for a mobile user (P MOB ) is related to this for a fixed user (P FIX ) through…”

Inter‐annual variability, risk and confidence intervals associated with propagation statistics. Part I: theory of estimation

“…Therefore, even if the synthetic rain attenuation time series do not have exactly the same statistical properties as the experimental ones, their use to put into evidence the high variability associated with empirical statistics is expected to give an appropriate order of magnitude as their parameterizations are derived from measured data. In the present paper, the channel model used to generate the synthetic rain attenuation time series is described in [17]. As for the model of ITU-R Rec.…”

“…To illustrate this point, 500 years of rain attenuation time series sampled every second have been generated from the channel model [17], considering an arbitrary rain attenuation CCDF such that P(A > 0) = 5% (a typical value for European climates). The dispersion of the ECCDFs computed for durations arbitrarily restricted to 1, 2, 5 and 10 years is illustrated on Figure 1.…”

“…ITU-R P.1853 to simulate rain attenuation time series lies first in the generation of a correlated Gaussian process G(t) with correlation c G (τ) = exp(Àβτ), where β = 2 × 10 À 4 s À 1 . The underlying Gaussian process G(t) is then turned into a rain attenuation process A(t) using the monotonic function f so that f(G(t)) = A(t) (see [17,18] or [19] for more details on the mathematical definition of the rain attenuation time series synthesizer). In such conditions, the Bernoulli process definition U(iΔt) = 1 if A(iΔt) > A* and U(iΔt) = 0 otherwise is strictly equivalent to U(iΔt) = 1 if G(iΔt) > α and G(iΔt) = 0 otherwise where α = f À 1 (A*).…”