Semi-empirical modelling of subtropical rain attenuation on earth-satellite microwave links.

Abstract

The exponential rise in demand for high fidelity content on multiple platforms has in recent years made increased use of the higher echelons of radio communication frequency inevitable. At these high frequencies, wavelength becomes small enough to compare with the size of rain drops and in some cases smaller than drop size. This implies that the impairment due to rain, which already usually forms the most severe form of impairment at higher radio frequency bands, will become even more acute and require rigorous parameterization. This thesis investigates both by rigorous measurements and by theoretical approaches, the attenuation effect of rainfall in a subtropical climate (Durban, South Africa) on a microwave earth-satellite link operating at 12.6 GHz. The link was set up and the received signal level monitored via spectrum analyser sweeps conducted every minute. A Joss-Waldvogel impact disdrometer was installed such that its diaphragm is located a few meters away from the link’s receive antenna. From such a location, all precipitation recorded by the disdrometer are assumed to have some effect on the link. The monthly variation in the received signal during clear air was investigated by taking into consideration the average monthly values of temperature, relative humidity and atmospheric pressure. By employing multiple regression, a linear expression was obtained that can be used to predict the change in received signal level in clear air over the link given the values of these three atmospheric parameters. The attenuation due to the rain events was extracted from the data by carrying out an even-by-event matching of rain rate spikes with the corresponding drop observed in the received signal level at and around the time of the precipitation. The average monthly received signal level during clear air was extracted from the spectrum analyser data and used as the base channel power to which the received signal during rain in the particular month is compared. The difference between the two is stored as the attenuation due to rain in that instant of measurement time. The attenuation data thus accumulated were entered into a computer algorithm and a regression fitting procedure carried out to deduce an empirical set of logarithmic and power law models that relate the total path attenuation to rain rate. The models were then validated by a largely favourable comparison with four existing models, one of which is the in-force ITU-recommended model for slant path attenuation estimations. Random number properties of rain attenuation statistics obtained from the measurement model were exploited to develop a Markov chain approach by which seasonal and annual slant path rain attenuation time series can be generated. By investigating the nature of the probability distributions of the seasonal and annual measured path attenuation statistics, which was found to be lognormal, the state probability matrix necessary for implementing a Markov chain prediction model for future patterns of rain attenuation on a similar link was obtained as the lognormal probability density function. The state transition probability vector for each time period was developed by extracting the fade slope statistics of the measured attenuation. The discrete-time Gaussian distributed fade slope PDF forms the basis for the state transition probability matrix. With these, Markov-generated time series of seasonal and annual slant path attenuation for up to five iterations were obtained. The results make useful data that can be used for long-term planning for rain fade mitigation in a subtropical climate easier to generate without the expense of measurements. The theoretical approach called the Synthetic Storm Technique was also applied to investigate the nature of slant path rain attenuation in Durban. Based on the rainfall pattern captured by the disdrometer, SST approximations for the four seasons of the subtropical year and for years of rain data collection were carried out. The results were compared with the values generated from the measurement model. It reveals that the two models exhibit significant agreement because in a majority of the cases, the A0.01 values obtained are very close. Comparison of the performance of SST as a theoretical model with that of the ITU-recommended method also reveals that the ITU performs slightly better as an alternative to measurement than the SST model. It was observed that during certain precipitation events, the satellite link registers significant attenuation levels several minutes before the disdrometer records any precipitation on the ground. This anomaly was investigated in this work and a few conclusions drawn. By proceeding on the assumption that the observed delay was due to the migrating rain cell interacting with the satellite beam several minutes before reaching the receive antenna, it was demonstrated that the time of delay between precipitation and attenuation is related to the rain height during that particular rain event. A simple mathematical analysis is presented that enables the rain height to be estimated from the delay time. The results obtained range between 1.4 km to 6.7 km which is similarity to rain height values obtained by the ITU model which range from 1.36 km to 6.36 km.