An Online Calibration Method using Hadamard-Fourier Clustering and Neural Network for Large-Scale Phased Arrays

This paper proposes a novel online calibration method based on clustering for large-scale phased array antennas. The proposed clustering method (called HaF clustering) leverages Hadamard and Fourier transform features, resulting in increased output power variation (suitable for large phased array calibration), noise robustness, and fewer measurements compared to traditional methods. Additionally, it eliminates the need for extra phase measurement instruments as it relies solely on power measurements. Analytical closed-forms are derived to demonstrate the effectiveness of HaF clustering. In this method, the mean phase error ( MPhE ) in each cluster is determined by a combination of Hadamard features and the extended rotational electrical vector field method (eREV). Using a trained multi-layer perceptron neural network and feeding it with each cluster's MPhEs , the direction of arrival (DOA) error is determined. Subsequently, antenna phase errors are estimated based on the DOA error, and new calibration coefficients are applied to the array. To validate the proposed online calibration method, Monte-Carlo simulations, and experimental measurements were conducted on a 1024-element modular planar phased array receiver within the frequency range of 18 GHz - 21 GHz and an angle of elevation range between -70 to 70 degrees. The simulation and experimental results indicate a mean absolute error (MAE) value of approximately 6 degrees for phase error determination and a DOA estimation error of less than 0.1 degrees using the multi-layer perceptron (MLP). Furthermore, the array can be calibrated with a maximum calibration error of less than 0.1 degrees within a period of 3 milliseconds.