# Using a Pair of Different-Sized Spheres to Calibrate Radar Data in the Microwave Anechoic Chamber
## 2 Materials and Methods  
The RCS value of a target can be measured in an anechoic chamber or the outfield. In the outfield, the measuring tools are real radar systems [5], while in an anechoic chamber, a vector network analyzer (VNA) acts as the \"radar\" system [3]. Network analyzers are convenient tools for onsite RCS measurements [8]. They measure the S-parameter matrix of a system. The transmitting antenna is connected to source port 1 of the network analyzer; the receiving antenna is connected to source port 2. The parameter S21 (unit: dB) describes the ratio of the transmitted power to the received power. This value represents radar echoes from the measured targets in the anechoic chamber. Thus, based on S21, the Equation (1) is given as  
\[\sigma_{m}^{\ \prime}=S_{m}-S_{r}+\sigma_{r}^{\ \prime} \tag{3}\]  
where \(\sigma_{m}^{\ \prime}\) is the RCS value of the measured target (unit: dBm\({}^{2}\)), \(\sigma_{r}^{\ \prime}\) is the known RCS value of the standard object (unit: dBm\({}^{2}\)), \(S_{r}\) is the received power of the standard object (unit: dB), and \(S_{m}\) is the received power of the measured target (unit: dB). We conducted a serial measurement in an anechoic chamber in 2019. The anechoic chamber belongs to Marine Equipment Inspection & Testing in Qingdao, China ([[http://www.chinammei.com/](http://www.chinammei.com/)]([http://www.chinammei.com/](http://www.chinammei.com/)), accessed on 10 June 2022). The inner room of the anechoic chamber is 7.890 \(\times\) 3.517 \(\times\) 3.3 m, as shown in Figure 1. The antennas are double-ridged broadband horn antennas, BBHA 9120 D, manufactured by Schwartzbeck from Schonau, Germany. The size of an antenna is 245 \(\times\) 142 \(\times\) 408 mm. The detailed VNA used in this analysis was PNA-NS224A, which was manufactured by Keysight Technologies (Santa Rosa, CA, USA). Figure 1b shows the photo of the internal environment in the microwave anechoic chamber. The wedges are wave absorption wedges. We used the swept frequency measurement of the VNA to obtain radar data with a high-range resolution profile (HRRP). The VNA antennas used vertical polarization to transmit signals and receive echoes. If the measured band is \(B\), the sampling data are \(N\), and the parameters can be calculated as  
\[f_{\text{e}}=\frac{B}{N} \tag{4}\]\[t_{\rm e} =\frac{1}{f_{\rm e}} \tag{5}\] \[R_{\rm e} =\frac{c}{2B}\] (6) \[L =\frac{ct_{\rm e}}{2} \tag{7}\]  
where \(c\) is the propagation velocity of the electromagnetic wave, \(f_{\rm e}\) is the frequency resolution, \(t_{\rm e}\) is the time dynamic range, \(R_{\rm e}\) is the range resolution, and \(L\) is the maximum measurement range. The advantage of HRRP technology is that it can separate radar echoes from different target structures [9]. Table 1 shows the setup parameters of the VNA when measuring data in the S-band, X-band, and Ku-band. Figure 2 depicts the data from the background environment when no object was on the foam holder. In this case, the data from everything in the anechoic chamber except the tested object belonged to the background clutter. The horizontal axis on the screenshot of the VNA is time, which was also the measured distance from the network analyzer. The distance must account for the length of the RF (radio frequency) cables that connect the antennas and the network analyzer. The test area of the foam holder was calculated to be approximately 11.5 m based on the data, which indicates that the foam holder was 11.5 m from the VNA, including the cable length. We used two different sized spheres to calibrate the radar data and ensure that the test environment matched the conditions. The radius of the large sphere was 0.15 m, while that of the small sphere was 0.05 m. Theoretically, the RCS values of the two spheres (\(\sigma_{\rm a10}=0.05\) m, \(\sigma_{\rm a30}=0.15\) m) in the optic region can be calculated using Equation (2), resulting in values of approximately \(-21.0491\) dBm\({}^{2}\) and \(-11.5067\) dBm\({}^{2}\), respectively.