## Influence of Rain on Propagation

The emergence of new telecommunication needs, associated with the increasing congestion of the radio spectrum, have led radio system designers to become interested in increasingly high frequencies and more specifically to frequencies in the millimetre wavelength range, ranging from 30 to 300 GHz. Given the bandwidth available in this frequency band, considerably increased data transmission rates exceeding some hundreds of Mbits/s can be obtained. At these frequencies however, atmospheric precipitations in the form of rain, snow or hail cause important disturbances on the propagation of radio waves. System designers need therefore prediction methods predicting the effects induced by these disturbances in order to offer reliable transmission supports under any meteorological conditions.

Two different experiments were thus conducted at France Telecom R&D in order to study the influence of rain on the propagation of radio waves (Gloasguen 1993; Veyrunes 2000). The first experiment was intended at measuring the bistatic scattering of electromagnetic waves by rain particles along a 312 metre path at the 94 GHz frequency in vertical polarisation (Gloasguen 1993). This experiment was conducted using two transmitting and receiving rotating antennas, which could both be rotated independently in the horizontal plane, thereby allowing the meas urement of bistatic scattering angles ranging from - 120° to +120°. The size distributions of raindrops were measured by a disdrometer at a close distance from the propagation path (Gloasguen 1995). Since narrow beam antennas were employed for this experiment and the path length was relatively short, the scattering volume was small and the rain statistics could be assumed to be homogeneous over the scattering volume. The authors demonstrate that at the 94 GHz frequency the first order multiple scattering approximation suffices for the description of the lateral scattering by rain. The computations performed using the first order multiple scattering approximation and Mie theory for spherical particles were found to be in agreement with experimentally measured values (Gloasguen 1996a, 1996b).

The second experiment was intended at simultaneously measuring the meteorological conditions and the variations of the radio field at the 30, 50, 60 and 94 GHz frequencies along an 800 metre path in line-of-sight. The statistical study of the resulting experimental data, concerning for instance the interactions occurring between electromagnetic waves and different phenomena of atmospheric and meteorological nature, or the development of propagation prediction models, will be described hereafter.

### 5.8.1 Experimental Device

The experimental device, set up in rural medium near the town of Belfort in 1998, consisted of a ensemble of four transmitters and four receivers operating at the 30, 50, 60 and 94 GHz frequencies in vertical polarisation and of a ensemble of meteorological sensors distributed along the radio propagation channel in order to allow an accurate characterisation of the propagation channel.

Theoretical Results

By their very nature, wave propagation problems are essentially electromagnetism problems, and in theory their determination supposes the resolution of Maxwell's equations. Unfortunately, due to the complexity of natural propagation media, the resolution of these equations can only be performed once the problem has been simplified, sometimes to the point of being far removed from reality. An ideal model describing the attenuation by rain of electromagnetic waves has thus been developed (Veyrunes 2000).

Fig. 5.32 presents a comparison between the values of attenuation predicted by this model and the experimentally measured values at the 30 and 50 GHz frequencies during a very intense rain event.

Fig. 5.32. Comparison between the predicted and the measured values of specific attenuation at the 30 and 50 GHz frequencies

Fig. 5.32. Comparison between the predicted and the measured values of specific attenuation at the 30 and 50 GHz frequencies

Fig. 5.34. Comparison between experimentally measured, ITU-R predicted and optimised values of the specific attenuation in dB/km at the 94 GHz frequency as a function of the rainfall rate in mm/h

Fig. 5.34. Comparison between experimentally measured, ITU-R predicted and optimised values of the specific attenuation in dB/km at the 94 GHz frequency as a function of the rainfall rate in mm/h

### Statistical Results

System designers are interested in the statistical description of disturbances induced by hydrometeors for a determined link in space and time. The statistical study of the experimental results was therefore concerned with different problems which are discussed hereafter.

Statistical Distribution of Rain Intensities. An essential characteristic of the rain regime in a given place as regards telecommunication services is the statistical distribution of the rain intensities R (mm/h). The determination of the probability of rain occurrence, expressed as the probability for a given threshold R to be reached or exceeded, is essential in this context. As an example, Fig. 5.33 presents the monthly cumulative distributions of rain precipitation intensities (Veyrunes 2000).

Attenuation due to Rain Intensity. A most fundamental parameter to consider for the understanding of the characteristics of the attenuation due to hydrometeors is the relation between the specific attenuation A (dB/km) and the rainfall rate R (mm/h). The comparison of experimentally measured values of attenuation with the values predicted by the ITU-R model (A = kRa) led to the conclusion that the parameter k was underestimated and the parameter a overestimated at the frequencies considered by this model. The optimisation of these parameters leads to enhanced performances, more specifically in the case of rain intensities higher than 20 mm/h (Veyrunes 2000).

Several different models can be found in the literature. A synthesis of these models was carried out within the COST255 framework (COST255 1999). The most powerful such models are described in Appendix I devoted to rain attenuation.

Frequency Scaling. The determination of frequency scaling law of rain attenuation along a propagation path may turn out to be necessary for extending long term measured attenuations statistics to other frequencies at which the necessary data cannot be collected, either out of time constraints or for economic reasons. The aim of the long term frequency scaling law is to derive a long term cumulative distribution of attenuation at the considered frequency from the distribution available at another frequency. A frequency scaling model of the attenuation due to rain and snow was developed in the frequency band ranging from 30 to 94 GHz.

Fig. 5.34 presents a comparison between the frequency scaling of rain attenuation at the 94 GHz frequency and rain attenuation at the 30 GHz frequency (Veyrunes 2000).

Specific attenuation at the 30 GHz frequency (dBftm)

Specific attenuation at the 30 GHz frequency (dBftm)

Fig. 5.35. Modelling of the correlation between the specific attenuation at the 94 GHz frequency and the specific attenuation at the 30 GHz frequency. Comparison with the ITU-R P.530-8 model

Fig. 5.36. Monthly cumulative distributions of the specific rain attenuations at the 94 GHz frequency

Fig. 5.36. Monthly cumulative distributions of the specific rain attenuations at the 94 GHz frequency

Statistical Distribution of Attenuation. A most important parameter in the development of communication systems is the statistical distribution of attenuation. This parameter indicates the percentage of time that the selected value of attenuation is reached or exceeded. In order to investigate this parameter, hourly, monthly, annual and worst month distributions were studied and modelled.

Fig. 5.36 represents the evolution of the experimentally determined monthly cumulative distributions of the specific rain attenuations at the 94 GHz frequency (Veyrunes 2000).

Statistics for Fade Duration. The dynamic characteristics of the attenuation due to rain were also considered in the course of this experiment. Although these characteristics have been little investigated in the past, radio system designers are now becoming increasingly interested in their study, which concern the following parameters:

- the fade durations. This parameter provides information about the distribution of the cut-off times for the link. Fig. 5.37 presents an example of seasonal cumulative distributions of rain fade durations exceeding the attenuation thresholds 2, 4, 6, 8 and 10 dB/km at the 60 GHz frequency (Veyrunes 2000).

- the intervals between individual fades. This parameter allows determining the availability of the signal, i.e. its correct operating time with respect to its specifications. Fig. 5.38 presents an example of seasonal cumulative distributions of the times between individual rain fades at the 94 GHz frequency (Veyrunes 2000).

- the fading rates. The study of the variations of this parameter allows evaluating the desired speed of the error control systems used for the link. Examples of seasonal cumulative distributions of the fading rates associated with rain attenuation at the 30, 50, 60 and 94 GHz frequencies are presented here in Fig. 5.39 (Veyrunes 2000).

The modelling of these different cumulative distributions has led to a significant improvement of the quality of prediction in the 30-94 GHz frequency band.

These studies lead to a better understanding of the complexity of propagation phenomena in natural media and to the possibility of drawing statistical distributions of the occurrence of the parameters involved in these phenomena. Theses statistics address the new needs of communication system designers, and should therefore enable the design of reliable transmission supports for high rate binary proximity links.

The analysis of the measurements was conducted over a 20 month period. Conducting similar experiments in regions with different rain characteristics should allow to compare the experimental results thus obtain and to extend the models.

The propagation models described here were developed for relatively short paths along which precipitations are almost homogeneous. This condition however is rarely fulfilled in practice, especially in the case of links with a length of a few kilometres. It would therefore be of interest to conduct experiments on longer links in order to develop a model for an average effective length and thus extend the results obtained for 800 metre links to longer links.

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