Almost-Periodic Higher Order Statistic Estimation

In this paper, stochastic processes with higher order statistical functions decomposable into an almost-periodic function plus a residual term not containing finite-strength additive sinewave components are considered. These processes arise in mobile communications when almost-cyclostationary (ACS) processes pass through time-varying channels. They include as special case the generalized almost-cyclostationary processes which, in turn, include the ACS processes. In the paper, the problem of estimating the Fourier coefficients of the (generalized) Fourier series expansion of the almost-periodic component of higher order statistical functions is addressed. Estimators are proposed for cyclic temporal cross moment and cumulants. They are proved to be mean square consistent and asymptotically complex Normal under mild assumptions on the memory of the processes expressed in terms of summability of cross cumulants. Numerical results confirm the theoretical results and the derived rate of convergence to zero of bias and standard deviation of the estimators.