# Dual-Probe Near-Field Phaseless Antenna Measurement System on Board a UAV
## 2 System Description
### Near Field Measurements Processing  
As explained in Section 1, the system proposed in [9; 11; 20] makes use of the NF measurement data collected on two or more surfaces surrounding the AUT. These measurements are post-processed by means of phase retrieval techniques to recover phase information. The iterative phase retrieval methods, such as the ones presented in [15; 16; 17; 18], require the NF measured on the two acquisition surfaces to have different spatial distribution, taking advantage of the fact that the field distribution in the NF region depends on the distance to the AUT [13]. The UAV-based systems for on-site antenna measurements are limited by the life of the batteries that feed the systems on board the UAV. The use of a dual-channel radiofrequency power detector connected to two probes mounted on different positions on the UAV enables the simultaneous acquisition of the NF on two different surfaces. Furthermore, geo-referring uncertainties have the same impact in both acquisition surfaces, avoiding cumulative errors if the measurements on each acquisition surface were conducted in two different flights. The latter would increase the measurement time and thus, the operational cost. As shown in Figure 1, the two 3D-printed plastic structures designed and manufactured to mount the two probe antennas on the UAV frame achieve a maximum separation between the probes of 80 cm. The probes and the two channels of the power detector were tested on the ground to ensure that they exhibited the same performance in terms of dynamic range and sensitivity. However, the calibration  
Figure 2: Scheme of the hardware devices associated to the dual-band global navigation satellite systems-real time kinematics (GNSS-RTK) unit, highlighting the software modules that were developed for its integration into the unmanned aerial vehicles (UAV) controller (single board computer). procedure explained in Section 2.1 was conducted to correct the unbalance between the channels of the power detector. The NF measurements acquired on the two measurement surfaces were post-processed using the phaseless sources reconstruction method (pSRM) [16]. This method is based on minimizing a cost function (\(F\)) relating the measured NF samples on each acquisition surface (\(E_{\text{NF,p1}}\), \(E_{\text{NF,p2}}\)) to the NF radiated by an equivalent currents distribution (\(M_{\text{eq}}\)) that characterizes the AUT. The pSRM iterates until finding an equivalent currents distribution that radiates the same NF as the measured one. Concerning the cost function to be minimized, there are two main approaches. On the one hand, the forward-backward implementation of the pSRM is based on the minimization of a linear cost function, which requires working with the complex representation of the NF. Thus, an initial guess of the phase distribution on the measurement surfaces is required. A description of the forward-backward implementation technique is presented in [16] and revisited in [18] in order to assess its performance for on-site antenna measurement. On the other hand, a non-linear cost function relating the amplitude of the measured NF (\(|E_{\text{NF,p1}}|\)\(|E_{\text{NF,p2}}|\)) and the amplitude of the NF radiated by the equivalent currents can be set, as illustrated in Figure 3. In this case, the initial guess is done on the equivalent currents, which is simpler than estimating an initial guess for the phase of the NF in the measurement surfaces. The better performance of the pSRM based on non-linear cost function minimization over the forward-backward technique has been analyzed and discussed in [18]. Once convergence is achieved, or the maximum number of cost function minimization iterations has been reached, the output is an equivalent currents distribution that is used to compute the phase of  
Figure 3: Flowchart of the phaseless sources reconstruction method (pSRM) based on the minimization of a non-linear cost function [12; 18]. the NF on the measurement surfaces.