A model to estimate in real time rain attenuation from BER measurements and its application to Italsat experimental attenuation time series during rain

Real time estimate of the signal–to–noise ratio (SNR) is very useful in any communication system because, according to its quasi–instantaneous values, important system parameters (bit rate, coding and modulation, transmitter power etc.) can be varied for ensuring constant or minimum quality to the user. In digital links, the bit error ratio (BER) provides a direct and fundamental measure of system performance because it determines the quality of the communication link. Because the SNR is a function of the theoretical probability of bit error p , if we estimate the BER in an interval T (e.g. 1 second), and assume that it is also an estimate of p (relative frequency approach) of the physical channel (i.e., before channel decoding), and define an appropriate physical channel model, we could theoretically also estimate the quasi–instantaneous physical channel SNR in the interval T , and from it, the slow changing tropospheric fading. In [1], we have shown that in additive white–noise gaussian channels, the conditional probability of the BER x , measured in T seconds, can be modeled as a lognormal distribution. From this model and standard calculations, we have also shown that the physical channel SNR, g 2 (i.e., before decoding), conditioned to the average probability p , can be modeled as a Gaussian random variable for BPSK, QPSK and QAM schemes. These theoretical results can be used for estimating the fading due to slow tropospheric phenomena, such as attenuation due to rain (when this phenomenon is responsible for the excess attenuation), water vapor, oxygen and clouds. In this paper, we estimate the total tropospheric attenuation from simulated BER time series, according to the experimental rain attenuation time series measured during the Italsat experiment in Spino d’Adda at 18.7 and at 39.6 GHz, slant path elevation angle 37.7°. Our preliminary analysis considers singles events, according to the following simulations. Since we do not have time series of the BER, we first simulate a Poisson process according to the instantaneous total tropospheric attenuation A (dB) measured in 1 second (Italsat), and then we estimate A from the BER obtained from the simulation, and compare it with the measured value. The results are extremely good.