Fractal analysis and synthesis of rain fields for radio communication systems
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) (mmIhr) 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.