# Error Correction of Water Vapor Radiometers for VLBI Observations in Deep-Space Networks
## 2 WVR Design  
Microwave radiometers are different from conventional radar or communication receivers. The signal received by a microwave radiometer is usually much lower than the noise power of the receiver. The antenna of a microwave radiometer receives incoherent thermal radiation signals from the target or scene under test and the transmitting medium, which are processed by the radiometer receiver and usually converted to an output voltage. In theory, as long as the receiver is in the use of a square law detector and linear amplifier, the receiver output voltage is linear with the antenna-received power or antenna temperature. When the microwave radiometer aims at the target or scene, we can calculate the antenna temperature based on the calibration equation and the output voltage of the  
Figure 1: WVR next to the Shanghai Tianma telescope. radiometer and can retrieve the radiation brightness temperature or other parameters of the target or scene. This is the basic principle of the microwave radiometer. Modern radiometer designs include [PERSON] and total power modes with a reference source to achieve calibration [6; 7; 8; 9]. Figure 2 shows the schematic diagram of the HZD-X water vapor radiometer. It mainly includes an antenna feed system, receiving system, calibration blackbody, servo system, temperature control system, etc. The antenna system of the water vapor radiometer consists of a 0.8 m antenna and a feed. The multi-channel receiver sends the antenna output and synchronous gain correction noise source to the down-converter through the digital synthesis local oscillator for IF (intermediate frequency) processing and low-pass filtering, and finally converts the signal to its voltage value. The data acquisition system converts the measured voltage values into a sky brightness temperature and transmits them to the user through the network. The temperature control system is designed to ensure the stability of the receiver. The specifications of the water vapor radiometer are shown in Table 1.  
The schematic of the receiver system is shown in the dashed box in Figure 2. At the receiver input, the directional coupler allows for the injection of two precise noise signals generated by the single-pole double-throw (SPDT) switch. The two noise signals are used to determine the system noise temperature drift and system nonlinearity. Standard noise 1 has a temperature of approximately 300 K and standard noise 2 has a temperature of approximately 400 K. A low-noise amplifier (LNA) boosts the input signal before it is split into 16 branches, with only two being used for VLBI delay measurements. The splitter implements a waveguide bandpass filter (BPF), with the bandwidth and center frequency listed in Table 1.  
The core concepts of the receiver design are as follows:  
(1) The receiver design is centered on maximum thermal and electrical stability, compact layout, minimal connectors, and thermal drift elements;  
(2) A temperature control system and air circulation system are added to ensure a constant temperature of \(45\pm 0.05\) degrees Celsius, which is the key to achieve a temperature accuracy of 0.2 K absolute brightness; \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Specifications** \\ \hline Operating Frequency & 23.8 GHz, 31.2 GHz \\ channels & 2 \\ IF Bandwidth & 100 MHz \\ Antenna Sidelobe Level & \(-27\) dB \\ Calibrated Brightness Temperature Accuracy & 0.2 K \\ Measurement Resolution & 0.05 K \\ Operating Temperature Range & \(-50\) to 65 deg C \\ Mass & 200 kg \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Key radiometer specifications. Figure 2: The schematic diagram of the HZD-X water vapor radiometer. (3) Even after taking various measures, the measurement accuracy of the receiver will inevitably vary with the environment and other factors. Therefore, it is important to analyze and compensate for errors;  
(4) When clouds cross the field of view, the wet delay is a rapidly changing quantity. Therefore, the receiver is designed to measure multiple channels in one second.