Bounds on uncalibrated array signal processing

Deterministic constrained Cramer-Rao bounds (CRBs) are developed for general linear forms in additive white Gaussian noise. The linear form describes a variety of array processing cases, including narrow band sources with a calibrated array, the uncalibrated array cases of instantaneous linear mixing and convolutive mixing, and space-time coding scenarios with multiple transmit and receive antennas. We employ the constrained CRB formulation of Stoica and Ng (IEEE Sig. Proc. Letters, vol.5, no.7, pp.177-179, July 1998), allowing the incorporation of side information into the bounds. This provides a framework for a large variety of scenarios, including semi-blind, constant modulus, known moments or cumulants, and others. The CRBs establish bounds on blind estimation of sources using an uncalibrated array, and facilitates comparison of calibrated and uncalibrated arrays when side information is exploited.