Micro-Doppler measurement of insect wing-beat frequencies with W-band coherent radar

The wingbeat frequency of insect migrant is regarded potentially valuable for species identification and has long drawn widespread attention in radar entomology. Principally, the radar echo signal can be used to extract wingbeat information, because both the signal amplitude and phase could be modulated by wing-beating. With respect to existing entomological radars, signal amplitude modulation has been used for wingbeat frequency measurement of large insects for many years, but the wingbeat frequency measurement of small insects remains a challenge. In our research, W-band and S-band coherent radars are used to measure the insect wingbeat frequency. The results show that the wingbeat-induced amplitude modulation of W-band radar is more intense than that of the S-band radar and the W-band radar could measure the wingbeat frequency of smaller insects. In addition, it is validated for the first time that the signal phase could also be used to measure the insect wingbeat frequency based on micro-Doppler effect. However, whether the wingbeat frequency measurement is based on the amplitude or phase modulation, it is found that the W-band coherent radar has better performance on both the measurement precision and the measurable minimum size of the insect.


Signal processing method
Signal processing of high resolution range profile. The resolution of range profile determines the distinguishability of two targets along the range direction. The high resolution is beneficial to separate the effective target from the ambient clutter. In our experiments, the frequency modulated continuous wave (FMCW) and stepped-frequency pulse-train (SFPT) waveforms are adopted as the transmitted signal in W-band radar and S-band radar, respectively. For a point target, taking FMCW as an example, the block diagram of signal processing of high resolution range profile is shown in Fig. S1. At the beginning, the original received radio frequency (RF) signal can be expressed as where t represents the time variable. The r K is the frequency sweep rate. The backscattered signal of the target is denoted as ( ) s t . The echo delay of target is denoted as , where ( ) R t stands for the range between the radar and the target, and c is the light speed. In addition, rect{} ⋅ represents the rectangular function with the width of T which can be considered as the signal repeated period, and n is the index of rectangular function.
First of all, the down conversion is performed by multiplying   nT represents the carrier phase of the target. It can be found that the range displacement of 1.5 mm can lead to phase variation of 180 degree for W-band. Therefore, the carrier phase is quite sensitive to micro-vibration, especially for insect body flexing or vibrating caused by wingbeat.
Next, the beat-frequency processing between the baseband signal and the signal reference is implemented, where the signal reference is selected as the transmitted signal in general. Thus, after simplification, the output signal can be written as Then, the beat-frequency signal is arranged to 2D signal format according to signal repeated period index. Fast Fourier transformation (FFT) is applied on each individual signal to achieve the high resolution range compression. Finally, the high-resolution range profile can be expressed as where sinc{} ⋅ is the sinc function and its resolution is determined by signal bandwidth of r K T , f is the transmitting frequency. In addition, note that the signal repeated period T is usually in microsecond order of magnitude, which is 0.5 ms for our W-band radar. As thus, With respect to SFPT, the whole block diagram from the raw received radar signal is the same and the only difference is the range compression processing. The signal processing of range compression in detail refers to ref [1].
Target detection based on wingbeat frequency measurement. As the suspended insect is mostly in flat flight, the direction of which is perpendicular to the radar line of sight, the returned signal from insect after range compression could not migrate through a range resolution cell during radar observation interval. Thus, the signal integration can be directly done along the same range resolution cell without range migration correction, and subsequently the target detection was performed to identify the effective range cell ( Fig.   S2(a)). Owing to the clutter in the experimental environment, two targets were detected in the same range profile. As the insect has wingbeat behavior while the clutter target does not, it is possible to identify the insect target from the signal spectrum of amplitude or phase. In our experiment, the signal carrier phase is extracted to measure the wingbeat frequency as shown in Fig. S2(b). Based on signal phase spectrum analysis, the insect target is able to be identified according to its wingbeat frequency. Compared to wingbeat, the clutter and insect body movement can be considered as stationary or changing slowly. Thus, the received signal from the clutter and insect body can be removed by high-pass filtering. However, it can be found from (7) that the received signal modulated by wing-beating also has the low-frequency component while 1 n =  . After high-pass filtering, (5) can be written as From equation (8), it can be seen that the second item in equation (5) which represents the low-frequency component is removed by high-pass filtering.
With respect to wingbeat frequency extraction, the Fourier transform can be directly applied on (8). The wingbeat frequency can be obtained based on harmonic-pairs positions in signal spectrum, because the wing-beating can make the signal generate a series of harmonic pairs with the frequency interval of wingbeat frequency (See equation (7)).
Besides, the signal phase analysis of wing-beating can be also used for wingbeat frequency extraction. The signal phase of (8) can be expressed as  where 2 w s is the variance of the white Gaussian noise and N is the signal sampling number.
It is found that for the same radar parameters, the Cramer-Rao lower bound of amplitude-based wingbeat frequency estimate is about three times than that of phase-based method when the vibration amplitude induced by wing-beating is at sub-millimeter order level.
According to the above two equations, it can be found that wingbeat frequency estimate is influenced by several factors, including radar wavelength, sampling rate, sampling number, the backscattered signal intensity of wings, the effective vibration amplitude of wing-beating and noise level. Generally, the shorter wavelength, longer observation time, stronger backscattered signal, larger vibration amplitude and lower noise level are beneficial for wingbeat frequency estimate for phase-based method and potential to achieve better precision.  10 mm-40 mm. Moreover, the scattering mechanism is significantly different that Rayleigh scattering mainly happens to S-band experiments while the scatterings of these insects for W-band locate in resonance or optical region. Based on signal power analysis of high resolution range profiles, the ratio between the received signal power from wing-beating and signal noise power is approximately from 10 -1 to 1 for W-band radar while this ratio is one order of magnitude smaller for S-band radar in general (see Table 1 in the text). In addition, the effective vibration amplitude can be derived from the wingbeat phase undulation, which is about millimeter order of magnitude or even smaller.
From simulation results, it can be seen that the W-band coherent radar theoretically has better estimate accuracy, which is consistent with our experimental results. However, our wingbeat frequency measurement precision does not achieve CRLB in the experiments, probably due to non-optimal estimate method. Therefore, theoretically, wingbeat frequency measurement based on coherent radar could realize higher precision and thus the optimal estimate method still needs to be investigated further.