For the purposes of rough surface scattering analysis it is often desirable to model the rough surface by a joint probability density function (JPDF). To date a considerable amount of work in this area has been done using a Gaussian and an exponential-type JPDF. Unlike the Gaussian JPDF, the exponential-type JPDF fails to meet the requirement that the random variables (which represent surface heights) become independent when uncorrelated. An exponential JPDF which splits into the product two sided exponential PDFs has been derived by applying certain nonlinear transformation to the square of the envelope and the phase of a narrowband Gaussian random process. The application of this JPDF is presented.
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