Modified Rice distribution for signals with limited available power

Signals consisting of a constant signal together with a number of superimposed randomly scattered complex signals have amplitudes that conform to the well-known Rice probability distribution. A property of the Rice distribution is that it is infinite, i.e., it knows no bounds in amplitude but has a tail that stretches to infinity. Infinite amplitudes, of course, defy reality because there is always a maximum available power, which translates to a maximum amplitude. In many cases the infinite tail of the Rice distribution causes no significant problems because the cumulated probability beyond the maximum amplitude is very small. However, there are situations where the maximum amplitude is not much higher than the average amplitude of the signal. In such cases, the amplitude distribution significantly differs from the Rice distribution. A finite probability distribution, derived from the Rice distribution and based on the linearity characteristics of the system, is presented. A measurement example with a linear system demonstrates good agreement to measured data. It is also demonstrates how to generate random variables that conform to the presented distribution.