Representing a Cascade of Complex Gaussian AR Models by a Single Laplace AR Model

In this letter, we consider the problem of modeling a system consisting of two cascaded subsystems, each of which represented by a second-order complex Gaussian autoregressive (AR) process, by a single AR process. Such combined representation of cascaded systems has a potential of simplifying the simulations of the cascaded processes and easing the complexity of estimating the model parameters. When deriving the combined model, we use the fact that the marginal probability density functions (pdfs) of the real and imaginary parts of the combined process are Laplace pdfs. This fact enables us to represent the combined process with a complex Laplace AR process whose parameters are selected to capture the statistical characteristics of the combined processes. Specifically, we design the Laplace AR process to attain identical statistical temporal variation to that of the combined process using autocorrelation matching. Our derivations provide details on how to compute the parameters of the complex Laplace AR process to meet the statistical characteristics of the combined processes.