Theoretical analyses of gain and phase error calibration with optimal implementation for linear equispaced array

In array signal processing, high-resolution direction-of-arrival (DOA) estimation algorithms are known to be sensitive to system errors. In practice, the system should be properly calibrated before DOA estimation. In this paper, a calibration method of gain and phase errors of linear equispaced arrays (LEAs) is considered. A class of simplified calibration algorithms based on different diagonal lines of the covariance matrix is proposed. The statistical performance analyses of the calibration algorithms due to finite data perturbations are presented. Expressions for average bias (Abias) and square root of average variance (SRAV) of the calibration algorithms are derived using first-order approximation. These statistical and computer simulation results reveal and explain why the more diagonal lines that are used for gain and phase error estimations, the more inferior performance that may be obtained. Based on this conclusion, the simple and optimal gain and phase error calibration algorithms for such model are obtained.