High-Accuracy, Fast Calibration of Large-Scale Phased Antenna Arrays via Novel Constellation Modeling Method

This article presents a novel constellation modeling method for fast and accurate calibration of beamforming integrated circuits (BFICs) and radio frequency (RF) chains in large-scale phased antenna arrays. The proposed method efficiently models the gain and phase response of BFIC channels and RF chains as functions of control indices through a set of closed-form equations. To construct the model and characterize nonidealities and coupled gain-phase errors with the minimum number of measurements, a deterministic strategy is also introduced to optimally select a subset of constellation states that effectively captures the response across the entire control space. This enables the generation of calibrated look-up tables with the desired tuning resolution and comparable accuracy to the exhaustive search method while reducing the required number of measurements by orders of magnitude. Building upon the proposed modeling method, open-loop and closed-loop calibration routines are developed to offer different tradeoffs between speed and accuracy for the calibration of phased antenna arrays. The open-loop routine relies solely on model predictions to minimize measurement overhead, while the closed-loop routine incorporates adaptive verification to ensure accuracy. Furthermore, a taper-aware calibration method is proposed to enhance effective isotropic radiated power in scenarios requiring tapering. This is achieved by leveraging the proposed constellation modeling method to calculate the gain-tapering mask by explicitly accounting for intrinsic performance variations across array elements. Experimental validation using two commercial BFICs and two <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$</tex-math> </inline-formula> phased antenna arrays demonstrates that the proposed method achieves a phase and gain root-mean-square error of 0.45° and 0.03dB, nearly matching the exhaustive search method performance while reducing the number of required measurements by over a thousand times. Radiation pattern measurements further confirm the practical effectiveness of the proposed method by delivering superior scalability, measurement efficiency, and calibration accuracy.