CRB-Based Design of Linear Antenna Arrays for Near-Field Source Localization

This paper is devoted to the Cramer Rao bound (CRB) on the angle and range of a narrow-band near-field source localized by means of an arbitrary linear array using the exact expression of the time delay parameter. First, we prove that the conditional and unconditional CRBs are proportional for an arbitrary parametrization of the steering vector (that may include, but is not limited to, the source DOA, range or polarization). Then, a Taylor expansion of the CRB is conducted to obtain accurate nonmatrix closed-form expressions of the CRB on angle and range. In contrast to the existing expressions, our expressions are simple, interpretable and more general because the sensors are only constrained to be placed along some axis. Our analysis leads to the characterization and design of a class of centro-symmetric linear arrays with improved near-field angle and range estimation capabilities.