Slepian-Bangs formulas for parameterized density generator of elliptically symmetric distributions

This paper mainly deals with an extension of the matrix Slepian-Bangs (SB) formula to elliptical symmetric (ES) distributions under assumption that arbitrary density generator depends on unknown parameters, aiming rigorously quantify and understand impact this ES distributed parametric estimation models. SB is derived in a unified way within framework real (RES) circular (C-CES) or noncircular (NC-CES) complex elliptically distributions, then compared obtained fully known completely generators. new involves common structure existing one simple corrective coefficient. Closed-form expressions coefficient are given for Student’s t generalized Gaussian each according different knowledge generator. allows us conclude parameterization, Cramér-Rao bound (CRB) may be very sensitive super-Gaussian contrary sub-Gaussian distributions. Finally, we prove parametrization scale factor, CRB other parameters scatter does not depend type latter result remains true specific noisy linear mixture data model where parameter interest characterized by range space mixing matrix.