# Dual-Polarization Observations of Slowly Varying Solar Emissions from a Mobile X-Band Radar
## 3 Deriving Solar Flux Values Using Observations of a Mobile Radar Working at the X-Band
### The Swiss Confederation Dual-Polarization X-Band Weather Radar
It is important to note that this incoming signal is the sum of the solar power plus an unknown noise power so that the corresponding value at the output of the A/D converter S\({}_{\rm{adu}}\), which is expressed in analog-to-digital units (adu), contains both the informative and the parasitic signal. The amount of spectral power that reaches the reference point, which is the Rx front-end at the LNA input, depends on the antenna gain and receiver chain (waveguides, circulator, T-R limiter,...) plus radomeloses. The given amount of received power (mW), which also depends on the bandwidth of the Rx transfer function, is transformed to a given digital unit value by the linear A/D \begin{table}
\begin{tabular}{c c c} \hline
**Rx Chain Performance** & **Horizontal Pol.** & **Vertical Pol.** \\ \hline Rx Losses including radome & 2.15 dB & 2.25 dB \\ Antenna Gain & 42.6 dB & 42.6 dB \\ \hline \end{tabular}
\end{table} 
Table 1: Nominal receiver (Rx) Losses and antenna Gain of the X-band weather radar. converter. In short, the sun(+Noise) signal detected by the radar induces a given level at the output of the A/D converter, where S\({}_{\rm dBadu}\) is the log-transformed value in the analog-to-digital-units (dBadu) at the output of the A/D converter. The radar establishes the exact power of any signal by comparing it with a known reference power: this is the key radar calibration concept (see Section 3.2.1). Once the incoming solar power at the reference point has been assessed by means of electric calibration it is possible to retrieve the corresponding log-transformed incident solar spectral irradiance at the 3.2 cm wavelength, I\({}_{3.2}\), that hits the antenna. This can be achieved through two additional steps together with a few conceptual assumptions (Sections 3.2.2 and 3.2.3). As stated, this original, \"raw\" spectral irradiance has two components: the solar radio noise (which is informative for us) plus an unknown noise component. Every 30 min, in addition to the (Sun + Noise\({}_{\rm{unk}}\)) component (antenna beam axis hitting the center of the sun), a simultaneous estimate of the noise is retrieved by measuring an angular offset of 2\({}^{\circ}\) with respect to the center of the solar disc. This estimated signal is then subtracted from the original, \"raw\" signal in order to get a better estimate of the solar power. The closer is the estimated noise to the unknown noise, the better is the estimate of the true solar signal after noise subtraction. For both the noise and the sun+noise, the estimate is based on 11,000 samples, namely 1100 (100) samples in range (Azimuth): the Azimuthal resolution is 0.1\({}^{\circ}\) (PRF = 2000 Hz, angular velocity set to 2\({}^{\circ}\)/s), while the range resolution is 50 m (echoes from 20 to 75 km are used). 2.1 Converting the Solar dBADU Level into (Log-Transformed) Power (dBm) at the Entrance Reference Point  
Owing to the linear behavior of the radar receiver over a huge dynamic range, the incoming solar value, S\({}_{\rm dBadu}\), in dBadu, can be converted into (log-transformed) power (in dBm) after a simple comparison with the corresponding value of the injected reference signal. In the case of the mobile X-band radar operated by MeteoSwiss, the reference signal is obtained from a monochromatic signal provided by an Internal Test Signal Generator (ITSG): ITS\({}_{\rm{rp}}\) is the injected, reference power value in dBm, while ITS\({}_{\rm{GdBadu}}\) is the corresponding level at the output of the A/D converter. Let S\({}_{\rm{rp}}\) be the power of any received solar signal that one would like to determine, and S\({}_{\rm{dBadu}}\) its corresponding level, as read at the output of the A/D converter. Then one obtains:  
\[\rm{S_{rp}}=\rm{ITSG_{rp}}+\rm{S_{dBadu}}-\rm{ITSG_{dBadu}}, \tag{3}\]  
where [ITSG\({}_{\rm{rp}}\)] = [S\({}_{\rm{rp}}\)] = dBm, while [ITSG\({}_{\rm{dBadu}}\)] = [P\({}_{\rm{dBadu}}\)] = dBadu.