Approximate distribution of the parameter of a complex first-order autoregressive process

A simplified model for the joint probability density function (PDF) of the magnitude and phase angle of the reflection coefficient of a first-order autoregressive (AR) process is proposed. The distribution is based on the inversion of the moment generating function (MGF) of the estimated autocorrelations under two simplifying assumptions: (a) the process is circular, and (b) the sample size is moderately large. The first hypothesis simplifies the computation of the MGF, and the second one allows to employ saddlepoint methods to approximate the integrals involved in the derivation, resulting in a fairly simple expression for the PDF. Further work on this is carried out so as to obtain the marginal distributions of both the magnitude and the phase of the parameter. These latter PDFs are compared favorably to the usual asymptotic (Gaussian) approach