Constructions of particular random processes

This paper reviews how to construct sets of random numbers with particular amplitude distributions and correlations among values. These constructions support both high-fidelity Monte Carlo simulation and analytic design studies. A variety of constructions is presented to free engineering models from “white or normal” limitations embodied in many current simulations. The methods support constructions of conventional stationary and normally distributed processes, nonstationary, nonnormal signal and interference waveforms, nonhomogeneous random scenes, nonhomogeneous volumetric clutter realizations, and snapshots of randomly evolving, nonhomogeneous scenes. Each case will have specified amplitude statistics, e.g., normal, log-normal, uniform, Weibull, or discrete amplitude statistics; and selected correlation, e.g., white, pink, or patchy statistics, clouds. or speckles. Sets of random numbers with correlation, nonstationarities, various tails for the amplitude distributions, and multimodal distributions can be constructed. The paper emphasizes aspects of probability theory necessary to engineering modeling