The correlation properties of gamma and other non-Gaussian processes generated by memoryless nonlinear transformation

The autocorrelation function (ACF) of a non-Gaussian random process, obtained by the memoryless nonlinear transformation of a Gaussian process with a known ACF, is calculated as a power series with coefficients expressed as one-dimensional integrals. In general these must be evaluated numerically; two analytically tractable special cases are also considered. In cases of practical interest the series has been found to converge rapidly. These results are then used in the simulation of a non-Gaussian process with a specified ACF, which can take values less than the square of its mean. Our approach is compared with other methods in the open literature. Examples are given of time series and random fields with gamma single-point statistics that provide controlled models of high-resolution radar clutter.