Cramér-rao bound of the direction-of-arrival estimation using a spatially spread electromagnetic vector-sensor

A new spatially-spread electromagnetic vector-sensor consisting of six non-collocating dipoles / loops is proposed in [1] to (i) reduce the mutual coupling across antennas, (ii) adopt the Poynting-vector estimator to estimate the direction-of-arrival of the source, and (iii) improve the direction-finding accuracy by extending the spatial aperture. The improvement in estimation accuracy was characterized by the Cramér-Rao bound for one pure-tone signal in [1]. In contrast, this paper will derive a new Cramér-Rao bound by modeling the incident source as a zero-mean complex Gaussian random sequence. This signal model is applicable when there is no prior knowledge of the incident source's time-frequency structure.