A Calibration Method for Displaced Hemispherical Vehicular Antenna Based on Blind Phase Center Estimation

This letter presents an effective calibration method for displaced vehicular antennas based on blind phase center estimation. The proposed method first uses spherical-to-planar projection and convolution–deconvolution method to calculate the sum of the phase differences under different plane positions along the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$y$</tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$z$</tex-math></inline-formula> axes. Then, the virtual phase center with a minimum sum of the phase differences is determined. Next, the offset calibration method is used to compensate for the measurement offset between the real measurement center and the virtual phase center. Finally, the simulation and measurement results, whose maximum accuracy improvements are nearly 9% and 10%, respectively, both reveal that the proposed method can accurately reconstruct the far-field pattern with great convenience and wide applicability compared with the previous research.