Identifiability analysis of local oscillator phase self-calibration based on hybrid Cramér-Rao Bound in MIMO radar

The identifiability of local oscillator phase perturbation self-calibration in multiple-input multiple-output (MIMO) radar is analyzed in this paper. There are four cases, the absolute phase perturbation (APP) and phase perturbation difference (PPD) in MIMO radar with widely separated antennas (SMIMOR), the APP and PPD in co-located MIMO radar (CMIMOR), discussed in this paper. The hybrid Cramér-Rao bound (HCRB) matrix of phase perturbation is derived and used to analyze the identifiability of phase perturbation. Under the assumptions of approximately orthogonal waveforms and a common geometry of targets and sensors, it is proved that only the PPD in CMIMOR is identifiable. The closed-form HCRB of PPD is obtained and verified by numerical simulations. In addition, the problem in this paper is a special case in which HCRB is asymptotically tight for nonlinear observation models containing unknown deterministic and random parameters with known prior probability distribution.