# Calibration of a Low-Cost 8\(\times\)8 Active Phased Array Antenna
## 3 Active Phased Array Calibration
### Active Antenna Measurement  
As mentioned in the previous section, the prototype antenna manufactured does not exhibit the same behavior for each of the columns. The calibration of the phased array antenna is performed using the methods explained in [16]. In [16], three different calibration methods are proposed and analyzed: the REV method, Fast Amplitude-Only Method and Complex Amplitude Calibration Method. The REV method [18; 23] is a phased array element excitation extraction method that is able to retrieve the excitation coefficient of each phased array element in its operation state. Therefore, this method takes into account the degradation induced by the phased array element's mutual coupling. However, in some antenna structures, the significance of this interaction can be disregarded in favor of more simple phased array excitation extraction techniques. The REV technique can retrieve each element individual excitation by sweeping that element phase shifter. Since the programmed phase shift for a given amplitude measurement is known a priori, through the mathematical procedure describe in [18] the  
Figure 6: Comparison of simulated and measured reflection coefficient. Figure 7: (a) Normalized measured amplitude of the subarray respect Col 5. (b) Normalized measured phase of the subarray respect Col 5.  
initial element excitation is calculated [18; 23]. The proposed phased calibration need 2 \(\times\) N measurements. The measured set up is shown in Figure 8: a standard gain horn antenna (SGH) is used as a probe in the far-field conditions (550 cm) to obtain the S\({}_{21}\) parameter for each of the columns, deactivating the rest of the columns using the beamformer control. During the calibration process, the temperature of the facility is controlled (22 \({}^{\circ}\)C) and there is no temperature dependence for the calibration. In the proposed method, the phase is considered to be a calibration variable, so that the amplitude variation, when changing phase state (PM-AM performance), is not affected in the calibration process, thereby reducing the number of calibration measurements and iterations. The proposed calibration flow diagram is shown in Figure 9. The process is detailed as follows:  
1. The amplitude and phase control of the column under test are programmed to behave with maximum gain state and zero-state for the phase. 2. The rest of the channels are disabled with the amplitude control set to maximum attenuation state (30 dB). 3. The S\({}_{21}\) parameter between the SGH and the column under test is measured. For each measurement, a frequency sweep for 17.7 GHz to 20.2 GHz is measured for each column. In the first iteration after N measurements, select an arbitrary column and normalize the phases with respect to the chosen column and obtain the phase difference between columns. In the second iteration, using the phase differences obtained in the iteration one, compensate the phase difference by changing the phase shifter state of the beamformer for each column to reach the same phase. The obtained initial phase stage result is shown in Figure 10a. Again, the phase unbalance is normalized to column 5, and it can be observed that the unbalanced phase  
Figure 8: Calibration set up for the active phased array. Figure 9: Flowchart of the calibration process. differs from the passive antenna, indicating that the beamformer and the cables also introduce additional phase errors. In order for the columns to exist in the same phase state, the center frequency 18.95 GHz is used as the calibration frequency. By varying the states of the beamformer phase shifters, the S\({}_{21}\) phase states depicted in Figure 10b can be obtained. It can be seen that the phase error has been significantly reduced; while it cannot be zero, the phase error is smaller than the phase step of the beamformer. The calibration frequency and the selected reference column are arbitrary; any frequency and any column can be selected as reference, as we can see in Figure 11a.