A simple method for combining probability distribution functions relevant to radar and communications systems

We provide a mathematical proof that the convolution or “faltung” method of adding probability distributions is equivalent to the characteristic function method that is widely accepted by mathematicians and described in almost all texts on probability and statistics. We further show by a simple example that the convolution method provides a much simpler approach to the combination of distributions and actually enables the computation of these combinations that would have been very difficult, if not impossible, using the characteristic function approach.