Joint Sparse Estimation Method for Array Calibration Based on Fast Iterative Shrinkage-Thresholding Algorithm

Existing array calibration methods rely on the geometric characteristics of the array or signal matrix, which limits their flexibility and robustness. This study addresses this challenge by proposing a novel joint sparse estimation method for array gain and phase calibration. By leveraging the sparsity of calibration signals and the dictionary mismatch model, the proposed method, based on the fast iterative shrinkage-thresholding algorithm (FISTA), jointly estimates the discrete on-grid azimuths and continuous off-grid offsets of the direction of arrival (DOA) of calibration signals. The method employs a spatial domain filtering technique based on the maximum a posteriori probability to mitigate the bias induced by phase errors in the calibration signal estimation, enhancing calibration accuracy. Furthermore, the iterative estimation framework was optimized to extend the applicability of the method from linear to uniform planar arrays. The results demonstrated that the root mean squared error (RMSE) of the beam pattern for various array types decreased by one to two orders of magnitude after calibration. Compared with existing state-of-the-art methods, the proposed approach exhibited stable performance and superior estimation accuracy under conventional signal-to-noise ratio conditions. Moreover, the proposed method maintained high stability and lower RMSE as the gain and phase error values increased.