# Measurement and Analysis of Radar Signals Modulated by the Respiration Movement of Birds
## 3 Results  
The measured LRRP data of the duck indicated that respiration caused 1 dB-level signal fluctuations. Figure 4 compares the data of a living duck and a dead duck with LRRPs in Table 1. The duck's chest faces the radar wave (i.e., head view). The duck's echoes were at 11.8 m in the range data (Figure 4). There were no apparent signal fluctuations within any test radar bands of the dead duck, but the signal fluctuations were approximately 1 dB within the S-band and 3 dB within the X-band and Ku-band. Neither of them was larger than the 10 dB level for the data of the living duck. Compared to the LRRPs of the duck, the HRRPs of the duck present clearer radar signatures posed by respiration. Figure 5 compares the HRRPs. The duck chest echoes were at 11.8 m in the range data. The signal fluctuations of the dead duck were no more significant than 1 dB within any measured radar band. However, the respirations of the chest caused different levels of signal fluctuations in radar data within the three radar bands. LRRPs cannot exclude inference from the ducks' movements in the test, but HRRPs can capture detailed echoes from a specific part of the bird and the surrounding environment. Thus, it can mark the contributions from the measured part over other parts of the bird. For example, the radar reflection from the duck could reflect the surrounding environment and then be received by the antenna and produce the different HRRP curves. The shapes of the HRRP curves are different, even within the same band, and there were other fluctuations (e.g., fluctuations at 11.6 m and 11.7 m in Figure 5) around the chest of the bird. These fluctuations were not from the duck's movement because the bird stayed still, and its neck was curled up to the tail, as shown in Figure 2. These \"ripples\" contain waves because of the multipath effect or even the vortex [26; 27] due to respiration and other unknown reasons. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Content** & \multicolumn{2}{l}{**Parameters**} & & & & & \\ \hline
**Bands 1** & **S-Band** & & **X-Band** & & **Ku-Band** & \\ \hline Range profile 2 & HRRP & LRRP & HRRP & LRRP & HRRP & LRRP \\ Frequency (GHz) & 2–4 & 9–9.1 & 8–12 & 10–10.1 & 14–18 & 16–16.1 \\ Bandwidth (GHz) & 2 & 0.1 & 4 & 0.1 & 4 & 0.1 \\ Resolution (cm) & 7.5 & 150 & 3.75 & 150 & 3.75 & 150 \\ \hline \hline \end{tabular} 1  
\end{table} 
Table 1: Measured parameters of experiments. Statistical results of both LRRPs and HRRPs are shown in Table 2. The mean value is the mean number, and the scope is the difference between the maximum and the minimum one, which describes the fluctuation level of the signals. First, the mean values of the S-band were the largest, and those of the X-band were the second largest, and then those of the Ku-band were the smallest, no matter whether it was the living duck or the dead duck. Second, the scope level was less than 1 dB within the S-band and approximately 4 dB within the X-band and the Ku-band. Similar to LRRPs, neither was larger than the 10 dB level. Figure 5: The comparison of HRRPs of a living duck and a dead duck 1. (**a**) HRRPs of a dead duck, (**b**) HRRPs of a living duck. 1 The ducks were in positions around 11.8 m of the range profiles. In addition to range profiles, the signal fluctuations in the time series could also measure apparent intervals due to respiration. We extracted the data of 11.8 m in Figure 5, drew the continuous frames of radar data in the cross-range profile, and calculated their corresponding spectrum in Figure 6. As we stated in Section 2, although the sampling period is approximately 3 s, our sampling frequency of 10 Hz is larger than the required sampling frequency of 1.66 Hz, following the Nyquist theorem. There are two peaks in the X-band HRRPs, with a time interval of 1400 ms. These numbers within the Ku-band, and S-band are also about 1400 ms. The calculated respiration rate of the duck was approximately 42 breaths/min (i.e., 0.7 Hz). The respiration rate could also be tracked in the spectrum.