## 1 Introduction  
Antenna measurements play a critical role in the framework of antenna characterization, since they allow one to examine the real-world performance of the antenna under test (AUT) and ensure that it meets the specified requirements and standards for the planned application in its intended environment. In particular, numerous approaches are used for obtaining the AUT far-field (FF) pattern and are generally divided in FF and near-field (NF) methods. Although FF methods allow for the direct determination of the AUT FF parameters of interest, they exhibit several downsides. First, the well-known FF condition, which requires a minimum distance from the probe antenna to the AUT, must be satisfied. Obviously, especially when dealing with electrically large antennas, this requirement necessitates the use of very large measurement facilities, usually making it impossible to characterize the AUT indoor. Furthermore, due to the long measurement distances required, it may be necessary to perform FF measurements outdoor, thus heavily influencing the accuracy of the results due to the unavoidable impact of external factors, such as environmental reflections and/or weather conditions. This led, during last decades, to the development of NF measurements techniques [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. In particular, these techniques allow one to bypass the requirement on the minimum separating distance so that the acquisition can be accomplished in a climate- and electromagnetic-controlled environment of the measurement facility [7], the anechoic chamber. More specifically, NF measurements generally require the collection of the NF data for two orthogonal polarizations of the antenna field on a geometrical surface enclosing the AUT, which depends on the specific measurement facility and fixes the corresponding scanning method to be implemented. In particular, these approaches are usually classified in spherical, cylindrical, and planar NF scans, with the acquisition taking place on a sphere, a cylinder, or a plane, respectively. Following the collection of the samples, the NF data are manipulated using ad hoc NF/FF transformation (NF/FFT) techniques, which allow one to obtain the FF pattern of the AUT by properly post-processing the samples depending on the specific geometrical surface on which they are acquired. Spherical NF (SNF) methods [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30] are the most accurate ones, providing for the determination of the entire FF pattern of the AUT without introducing any truncation error. They rely, save for those based on the source reconstruction method [17; 21], on a modal expansion of the field on the measuring sphere, the so-called spherical wave expansion (SWE), afterward a proper spherical NF/FFT technique is performed. However, SNF measurements can be very time consuming, thus entailing high related costs, since the amount of NF data, in particular when dealing with electrically large AUTs, can become huge. This is why, nowadays, the scientific community pays so much attention to the development of novel NF techniques that address the problem of reducing the high number of required samples, such as the non-redundant (NR) representations theory [31], compressive sensing [27; 29], or adaptive sampling [26]. In particular, among these, the NR sampling representations of the electromagnetic (EM) fields [31] stand out due to their unique features. Indeed, by utilizing the spatial band-limitation properties of the EM field [32], these techniques allow for a significant reduction in the number of samples needed to effectively reconstruct the near field radiated by the AUT or, equivalently, the voltage collected by a non-directive probe [16; 24], whose spatial bandwidth is almost the same of the AUT field one [33]. In particular, by properly choosing a rotational surface modeling the AUT, the NR representations require the acquisition of only a minimum number of samples, substantially coincident with the number of degrees of freedom of the field [34].