# Static and Moving Target Imaging Using Harmonic Radar
## 3 Imaging of Moving Targets
### Data Acquisition and Analysis  
Data were taken over the 81 fundamental and 81 harmonic frequencies for each of the target locations. The raw data were zero padded in both the slow time and frequency domain. This was done to interpolate the range-Doppler plot. Figure 7 shows the MTI results. In order calculate the Doppler speed axis, a data collection rate of 48 Hz was chosen.  
The image in Figure 7a shows the linear response of the mixer moving at the fundamental frequency, while the image in Figure 7b shows the nonlinear response of the mixer moving at the harmonic frequency. Figure 7 exhibits side lobes in both the range and Doppler domains. Therefore, a Hamming window is applied in both the frequency and the slow time domains to reduce the ringing caused by the sidelobes. The result is shown in Figure 8 for both the linear and nonlinear cases.  
Figure 6: Photographs of the test setup: (**a**) Radar transmitter; (**b**) Radar antennas; (**c**) Radar receiver.  
Figure 7: Range-Doppler plots of the nonlinear moving target at: (**a**) Fundamental frequency; (**b**) Harmonic frequency.  
The effect of windowing is that the side lobes are reduced, albeit at the cost of widening the peaks. The linear (\(n=1\)) MTI plot shown in Figure 8a shows a strong response at zero range and zero Doppler, which can be ascribed to transmit-receive antenna coupling. Although the data were taken in an anechoic chamber, there is a response from the back wall at about 7.6 m (25 feet). Since the wall is stationary, the resulting response is located at zero Doppler. There are also other linear responses from the environment between the antennas and the back wall. The target can be seen between 4.6 and 6.1 m (15-20 feet) and \(-1\) m/s. The linear response from the target is small and would otherwise be lost in the antenna coupling and clutter, but because it is moving, MTI processing is able to distinguish it from stationary targets.  
For the second harmonic response, shown in Figure 8b, there is no antenna coupling at zero range and zero Doppler. In addition, the target response stands out as the largest object in the scene, and linear clutter is virtually eliminated. There is a second response from a target at a further distance and slower Doppler speed. This is likely due to multipath, as explained in [63].  
Figure 9 clearly delineates different phenomenological mechanisms that more clearly expound upon the conclusions drawn above.  
We did not perform any Doppler measurements outside the anechoic chamber. In realistic outdoor scenarios, radio frequency interference (RFI) can cause degraded performance since the level of these signals at the desired harmonic bands may overwhelm the low level harmonically scattered signals  
Figure 8: Range-Doppler plots of the nonlinear moving target with Hamming window applied at: (**a**) Fundamental frequency; (**b**) Harmonic frequency.  
Figure 9: Explanation of Figure 8 features for: (**a**) Fundamental frequency; (**b**) Harmonic frequency.  
being processed by the radar. In addition, multipath may cause the formation of ghost targets in the image.