Compact Cramer-Rao bound expression for an extended signal model

Previously, Stoica and Nehorai (1989, 1990), and Yau and Bresler (see ibid., vol.40, no.5, p.1508, 1992) have developed compact expressions for the Cramer-Rao (CR) bound on frequency covariance for a class of spectral estimation problems. These expressions are very useful in that they support identification of fundamental performance limitations that otherwise would be difficult or impossible to obtain. This article extends the foregoing CR bound results to a more general data model. The work is motivated by direction-finding (DF) scenarios that cannot readily be represented by the data models of Stoica, Nehorai, Yau, and Bresler. The utility of the extended result is illustrated by specializing it to provide a new compact formula for the CR bound on directional variance for DF scenarios involving polarization-agile sources