Breaking the Nyquist Law Using Machine-Learning Empowered Interpolation Method in Planar Near-Field Antenna Measurements

Abstract

This work presents a machine-learning empowered interpolation method to break the Nyquist sampling law for the planar near-field antenna measurements. In this way, the measurement time can be reduced significantly. Specifically, the proposed method uses a complete dataset X <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> to interpolate the incomplete dataset X <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> to realize the data supplementation and the reconstruction of the antenna far-field pattern, with less initial measurement data and time cost. This method uses K-means classification and Voronoi cell to cluster the initial dataset X <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and accomplish the deep and shallow interpolation. Then, the truncation error of the interpolated planar near-field data can be reduced after using the Gerchberg-Papoulis (GP) algorithm. Since the proposed method uses a complete dataset X <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> with small data size to achieve the interpolation process, the sampling interval of X <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> can be larger than half-wavelength, and accordingly the sampling time can be further reduced without sacrificing the reconstruction accuracy within the confidence area.