Asymptotic Frequency-Domain FIM for multidimensional stationary and cyclostationary compound-Gaussian processes: Application to DOA estimation

The classical Whittle formula provides a closed-form expression for the asymptotic Fisher information matrix (FIM) of stationary, zero-mean Gaussian processes (GPs) with finite-dimensional parameterizations, expressed in terms of their power spectra. While this result was recently extended to nonzero-mean, multidimensional, real-valued stationary compound-Gaussian processes (CGPs), its applicability remains limited. In this paper, we significantly broaden this theoretical framework with two primary contributions. First, we extend the Whittle formula to purely cyclostationary real-valued CGPs with parameterized cyclic spectra, and further generalize it to circular and noncircular complex-valued multidimensional stationary CGPs, encompassing both purely and almost cyclostationary CGPs. Second, we apply these novel Whittle-type formulas to evaluate the impact of source spectral characteristics on the Cramer-Rao bound (CRB) for direction-of-arrival (DOA) estimation, particularly in scenarios involving frequency offsets.