Identifiability analysis for array shape self-calibration in colocated multiple-input multiple-output radar using Cramér-Rao bound

In this study, parameter identifiability in array shape self-calibration in colocated multiple-input multiple-output radar is addressed under a deterministic framework. In contrast to the random model used in the previous analysis, some distinct identifiability conditions are established through deriving and then analysing the Cramer–Rao bound on self-calibration accuracy of antenna positions using far-field targets whose directions of arrival and scattering coefficients are initially unknown. It is proved that at least three non-collinear targets are needed to precisely self-calibrate the positions of antennas of arbitrary geometry when there exist a position reference and a direction reference. The sole exception is an actually linear array for which self-calibration is impossible.