In this paper, we propose an active calibration algorithm to tackle both gain-phase errors and position perturbations. Unlike many other active calibration methods, which fix the array while changing the location of the source, our approach rotates the array but does not change the location of the source, and knowledge of the direction-of-arrival (DOA) of the far-field calibration source is not required. The superiority of the proposed method lies in the fact that measurement of the direction of a far-field calibration source is not easy to carry out, while measurement of the rotation angle via the proposed calibration strategy is convenient and accurate. To obtain the receiving data from different directions, the sensor array is rotated to three different positions with known rotation angles. Based on the eigen-decomposition of the data covariance matrices, we can use the direction of the auxiliary source to represent the gain-phase errors and position perturbations. After that, we estimate the DOA of the calibration source by a one-dimensional search. Finally, the sensor gain-phase errors and position perturbations are calculated by using the estimated direction of the calibration source. Simulations verify the effectiveness and performance of the algorithm.

A robust adaptive beamforming algorithm is proposed based on the precise interference-plus-noise covariance matrix reconstruction and steering vector estimation of the desired signal, even existing large gain-phase errors. Firstly, the model of array mismatches is proposed with the first-order Taylor series expansion. Then, an iterative method is designed to jointly estimate calibration coefficients and steering vectors of the desired signal and interferences. Next, the powers of interferences and noise are estimated by solving a quadratic optimization question with the derived closed-form solution. At last, the actual interference-plus-noise covariance matrix can be reconstructed as a weighted sum of the steering vectors and the corresponding powers. Simulation results demonstrate the effectiveness and advancement of the proposed method.

An offline sensor gain-phase errors calibration method for a linear array using a source in unknown location is proposed. The proposed method is realized through three steps. First, based on the observed covariance matrix, we construct a function related to direction, and it is proved that when the function takes the minimum value, the corresponding value should be the direction of the calibration source. Second, the direction of calibration source is estimated by locating the valley from the constructed function. Third, the gain-phase errors are obtained based on the estimated direction. The proposed method offers a number of advantages. First, the accurate direction measurement of the calibration source is not required. Second, only one calibration source needs to be arranged. Third, it does not require an iterative procedure or a two-dimensional (2D) spectral search. Fourth, the method is applicable to linear arrays, not only to uniform linear arrays (ULAs). Numerical simulations are presented to verify the efficacy of the proposed method.