Conditional Cramér–Rao Lower Bounds for DOA Estimation and Array Calibration

This letter aims at deriving the Cramér-Rao lower bounds (CRLB) of the direction-of-arrival (DOA) estimation and array calibration precisions in the case of determined and unknown signals based on the assumptions of small array perturbations. The analysis begins with a comprehensive perturbed array output formulation, and it is effective for various kinds of perturbations, such as mutual coupling, gain/phase uncertainty and sensor location error. The CRLB of the DOA and array perturbation parameters are well separated from each other in the letter, which facilitates their usage in performance evaluation of the self-calibration methods. However, the CRLB are finally given in the form of the inverse of the corresponding Fisher information matrices (FIM) as the inversion process can hardly be implemented mathematically. Simulation results are provided to compare the obtained conditional CRLB with the parameter estimation precision of the maximum likelihood estimators (MLE) and the unconditional CRLB.