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The Rayleigh problem is everywhere!

In this work, we discuss a variety of problems that can be cast as specific instances of the superposition of random amplitudes times random phase functions, the Rayleigh problem. A wide number of problems that occur in sensor domain are equivalent to specific instances of this problem. Using characteristic functions, it is possible to determine how to mathematically characterize the probability density function or equivalently the characteristic function for the general Rayleigh problem.