Assumption-Free Active Calibration of mm-Wave Phased Arrays using Excitation Estimation via Far-field Measurements

This paper proposes an active calibration method for millimeter-wave beamforming arrays by estimating elements' excitations under realistic operating conditions. The method leverages far-field transmission coefficient measurements collected while the array is rotated toward different angles. From these measurements, the complex excitations are estimated without imposing assumptions on the beamforming circuitry behavior. With all elements active during measurements, effects such as mutual coupling are inherently captured, which element-wise calibration fails to account for. The method is validated on a 4x4 phased array operating at 38.5 GHz. Radiation patterns reconstructed from the estimated excitations match the measurements with a normalized root-mean-square error (NRMSE) of -30 dB compared to an NRMSE of -8 dB from element-wise measurements. For boresight-beamforming, the proposed method improves the gain by 1.4 dB relative to passive calibration and reduces sidelobe level imbalance by 2.4 dB. Finally, for null-steering, the method achieves 21.2 dB deeper null-depth than passive calibration.