Fractal analysis and synthesis of rain fields for radio communication systems

  • Sarah Anne Callaghan

Student thesis: Doctoral Thesis


This thesis has the aim of introducing fractal methods for the analysis and synthesis of rain fields into the field of radio communication systems. To this end, the fractal nature of rain rate contours as measured by meteorological radar was verified, using different techniques including the area-perimeter relationship, the box-counting dimension, and power spectral density function analysis. The fractal dimension of these contours was found to be -1.2, and the different methods of calculation agreed with each other. Scaling results were also exhibited by the distribution of number of contours with respect to their enclosed area.
Multifractal analysis of the radar measured rain fields showed that rain rate fields display multifractal behaviour, as described in the literature. However, log rain rate fields have a straight line K(q) function, indicating that for these fields mono fractal methods of analysis and synthesis may be used. This is of particular interest to the communications engineering community, who are not concerned with the extreme events that require multi fractals to correctly categorise them, and are already accustomed to dealing with observables on a logarithmic basis.
A study of the physical and phenomenological aspects of rain was conducted, with particular emphasis on the impact of measuring device resolution and scaling limits on the calculation of the fractal dimension of rain fields. Also investigated were the differences between stratiform, convective and frontal rain events, the results of which led to the inclusion of climatologically based parameters into the rain field simulator proposed. The simulator uses a discrete additive cascade process to produce simulated mono fractal log rain rate fields, which are visually and statistically realistic. The calculated value for one of the parameters, H = 1/3, related to the power spectral density function exponent, shows that log rain rate is antipersistent, and that log rain rate has long range anticorrelation.
The procedure required to convert from rain rate fields R(x,y,z,t) (mm/hr) to attenuation along a path AdB (p,t) (dB) was detailed. It was found that the Met Office's Nimrod rain radar database does not have a spatial resolution high enough to be able to accurately use radar derived attenuation data as a substitute for measurements made on site diversity links -1 Okm apart. The fractal rain field simulator can scale the data in space to any size resolution required, without adversely affecting the statistics and spatial behaviour of the simulated field.
Attenuation time series derived from the simulated rain fields were created. In order to compare them statistically with measured attenuation time series, cumulative distribution functions were calculated from a database of measured and simulated events. The results give reasonable agreement, but emphasise the need for more measured data in order to more accurately characterise the wide range of variability present in attenuation events. Similar conclusions were drawn from the results of the diversity gain comparison performed between the measured and simulated data. The time series were also applied to the case study of a switching algorithm for an Earthspace radio system using site diversity as a fade mitigation technique. The inputs into such a switching algorithm were defined and discussed, including a simple short-term attenuation predictor. The behaviour of the switching algorithm with the simulated data was contrasted with the behaviour with measured site diversity data, with similar results. Finally, potential areas of improvement and further work were identified
Date of AwardMar 2004
Original languageEnglish
Awarding Institution
  • University of Portsmouth
SupervisorDavid Ndzi (Supervisor) & David Sanders (Supervisor)

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