# Terahertz Frequency-Scaled Differential Imaging for Sub-6 GHz Vehicular Antenna Signature Analysis
## 1 Introduction  
The future generation of connected vehicle, along with the autonomous vehicle it evolves into, will require significantly increasing the number of antennas on its surface operating at different frequency bands from sub-6 GHz to millimeter-wave (mmWave), as effective communication and environment sensing are ensured in this way in respect of other vehicles and different base-stations [1]. The operation of these antennas and a focus on a 3D spatial angular response (3D radiation pattern) may be significantly influenced (perturbed) by the nearby vehicular structure. The task of studying these effects may require ascertaining the distribution of the currents induced by the antenna on the vehicular surface by means of numerical or experimental methods. The process of obtaining these currents for realistic vehicle geometries, especially when using experimental techniques, may require complex and bulky setups. The new imaging systems operating in terahertz frequencies provide a very interesting tool that is applicable for solving the stated problem in relation to the estimation of the induced currents on the vehicular structure by the antenna. This imaging system provides the reconstructed image and shape obtained via the scattered field of metallic or non-metallic targets [2]. The concept of using terahertz frequencies and imaging techniques has been reviewed in order to confirm its applicability to the present problem. In [3], the ultrawide-band (UWB) imaging radar system used in this paper is tested at mmWave and terahertz bands, validating the spatial resolution on the order of millimeters and its imaging capabilities. The work presented in [4] is an imaging system that inspects a polymer radome in the frequency range of 70-170 GHz, reporting good performance in resolution and proposing to increase the frequency up to 300 GHz for improved resolution. Continuing with frequencies around 300 GHz, the three-dimensional (3D) imaging system presented in [5] is a synthetic aperture radar (SAR) operating at 340 GHz, utilizing the Fourier transform in two dimensions for the reconstruction process. In [6], the operating frequency is increased to 522 GHz. Finally, to conclude the background review, a novel reconstruction process in time domain operating in the microwave and mmWave frequency bands is presented in [7]. Extensive discussion has focused on the structural scattering and the scattering of an antenna's radiation mode [8]. It is intended to reconstruct the currents associated with scattering of the radiation mode of an antenna. The main objective of this paper is to investigate the distribution of currents induced by the antenna on the vehicular surface by means of differential image reconstruction processes, and using a previously developed multi-frequency system [3] operating in the terahertz frequency band and extending this concept to explore an area. This experimental method is a non-invasive way of obtaining the induced currents without placing the antenna in the supporting structure. A frequency-dimension scale translation is applied to reduce complexity from an experimental point of view. As the defining aspect, a differential imaging concept is exploited to process the images captured during the experiment. In this specific case of measurements, it could be applied to the study and optimization of the co-location of several antenna systems in vehicles. To the authors' best knowledge, the uniqueness of this paper concerns dealing with a differential imaging method to obtain the current distribution without influencing the measure. As discussed previously, the terahertz imaging radar system makes it possible to obtain the spatial distribution of the reflectivity of an object for the analytical and experimental assessment of induced currents in the vehicle structure. This system uses a double focal system with an independent transmitter antenna and receiver antenna, being connected to both ports of a vector network analyzer (VNA) to obtain the scattering parameters over a defined frequency range [3].