Advancements in Compressed Sensing for Antenna Far-Field Gain Calibration in an Extrapolation Range

In this study, we apply Compressed Sensing (CS) for far-field extrapolation calibration of high-gain aperture horn antennas. In earlier work, we successfully applied CS to dipole antennas, which exhibit different k-space characteristics. Dipoles show significant components related to chamber reflections but lack the third-order component observed in horn antennas, which arises from strong multipath interactions. This third-order component leads to sparser k-space data for horn antennas, making them well-suited for CS-based recovery. By employing pseudo-random undersampling, CS effectively recovers key spectral coefficients while dramatically reducing the amount of data required for accurate calibration. In contrast, traditional methods necessitate dense sampling to prevent aliasing, which can be time-consuming. Since the extrapolation process relies on curve fitting to the primary antenna response, it is crucial to first remove higher-order terms and chamber reflections. Filtering in the k-space is a natural approach to isolate the main response terms. However, horn antennas exhibit much stronger near-field effects compared to dipoles, resulting in significant curvature in the response even after normalization by 1/r (where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r$</tex> is the distance between antennas). This curvature leads to pronounced edge effects after filtering. To address this, we introduce a novel normalization process that detrends the raw data with a low-order polynomial before transforming it into k-space, effectively reducing edge artifacts. Our method demonstrates that CS can achieve accurate far-field gain extrapolation using as little as 8% of the original data, significantly reducing test time while maintaining calibration accuracy.