Asymptotic performance of optimal gain-and-phase estimators of sensor arrays

For estimating angles of arrival, there are three well known algorithms: weighted noise subspace fitting (WNSF), unconditional maximum likelihood (UML), and conditional maximum likelihood (CML). These algorithms can also be used for estimating/calibrating the gains-and-phases of sensor arrays, assuming the angles of arrival are known. We show that the WNSF algorithm with an optimal weight has the same statistical efficiency as the UML algorithm but more efficient than the CML algorithm. This conclusion was known for angles of arrival estimation and is now confirmed for gains-and-phases calibration. Computationally, the WNSF algorithm is shown to be more attractive than the other two as it can be implemented via a quadratic minimization procedure for arbitrarily shaped arrays.