Asymptotic performance of optimal gain-and-phase estimators of sensor arrays (Q2734438)

This paper deals with the asymptotic behavior of optimal gain-and-phase estimators of sensor arrays. Three well-known algorithms for estimating angles of arrival are the following: (i) weighted noise subspace fitting (WNSF), (ii) unconditional maximum likelihood (UML), (iii) conditional maximum likelihood (CML). These algorithms can also be used for estimating and adjusting the gains and phases of sensor arrays under the assumption that the angles of arrival are known. It is shown that the WNSF algorithm with an optimal weight has the same statistical efficiency as the UML algorithm, but it is more efficient than the CML algorithm. This was known for angles of arrival estimation, and the paper confirms it for gains-and-phases calibration. The principal contributions of this paper are: (i) relaxed conditions on the array model, (ii) the covariance matrices of the estimators, (iii) the Cramer-Rao bound for gain-and-phase estimation, (iv) an efficient implementation of the WNSF algorithm.