# Measurement and Analysis of Radar Signals Modulated by the Respiration Movement of Birds
## 2 Method and Materials
### Measurement Systems  
We designed a dynamic measurement system composed of a vector network analyzer (VNA) and a high-speed camera to capture the weak signal fluctuation. The spatial arrangement is shown in Figure 2a. The anechoic chamber belongs to the National Center Marine Equipment Quality Inspection. The camera is a Photron FASTCAM SA-Z, manufactured by Photron from Tokyo, Japan. The network analyzer Agilent PNA-N5224A (Santa Clara, CA, USA) uses vertical polarization to transmit signals and receive echoes [8]. Network analyzers have become convenient for onsite RCS measurements [22]. Network analyzers 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, which can be seen as the radar signals of the target, as the example in Figure 2b shows. The most practical approach for calibrating the RCS value of a measured target uses a standard object with a known RCS. It is known as the ratio method [12; 22; 23]. The process is described by  
\[\sigma_{m}=\frac{P_{m}}{P_{r}}\sigma_{r} \tag{6}\]  
where \(\sigma_{m}\) is the RCS value of the measured target, \(\sigma_{r}\) is the known RCS value of the standard object, \(P_{r}\) is the received power of the standard object, and \(P_{m}\) is the received power of the measured target. Considering that we measure the variation in the radar signals, the difference in the measured data can be described in dB units of dBsm. The unit of dBsm is defined as decibels received for a square meter target. We wrote a program to conduct the measurement automatically. There are synchronization signals to synchronize the measurement of PNA-N5524A and Photron FASTCAM SA-Z. The flow diagram of one measurement is described in Figure 3. PNA-N5524A provides an external source control feature, which can be used to control external sources automatically. We used the Trigger-Aux function of PNA-N5524A to send the synchronistical signals. It could input a trigger signal and then send out two synchronistical response signals (i.e., TTL signals) to external devices using the Handler IO of \"Aux Trig out 1\" and \"Aux Trig out 2\" on the panel PNA-N5524A. Then, we could track the dynamics of the detailed deformation of the bird's chest posed by respiration movement and other deformations, such as wing beats and head movements. Moreover, we waited until the duck was flapping its wings, and a program automatically triggered the recording process to capture the data. We used the Macros provided by the PNA-N5524A to conduct the measurement. Macros are executable programs that a user writes, loads into the analyzer, and runs from the analyzer. We recorded 30 frames (see legends in Figure 4) of radar echoes and photos in approximately 3 s.  
Figure 3: The flow chart of one measurement. Figure 2: Tests in the anechoic chamber. (**a**) Photos of birds using the high-speed camera 1, (**b**) a screenshot of the data measured by the Vector Network Analyzer, PNA-N5224A. 1 The number # x is the tracking ID. The target birds were ducks: a living duck and a dead duck. These two domestic ducks were bought from a local farm. Their masses were similar (0.955 kg). They also shared a similar appearance. From their beaks to their feet, the body heights were 38 cm. The wingspans were 75 cm, while the width of the wings was 14 cm. The respiration rate was approximately 30-50 breaths/minute [18,24]. Our sampling frequency was 10 Hz, larger than the required sampling frequency of 1.66 Hz based on the Nyquist Theorem. There were 30 continuous sampling frames in 3 s. Moreover, we sometimes used tape to fix wings, necks, and heads to avoid flapping motions, but we just placed the ducks on the  
Figure 4: The comparison of LRRPs of a living duck and a dead duck [1,2]. (**a**) LRRPs of a dead duck, (**b**) LRRPs of a living duck. [1] The ducks were in positions around 11.8 m of the range profiles.