## 3 Experiments with Optical Fibers  
From the above, the major difference between periodic nonlinearity and phase-locked loop spuriousness is the clutter generated by them has different trends with the target delay. To investigate this tendency of the clutter used in the system and exclude environmental interference, a series of closed-loop experiments were carried out. In particular, the transmitted and received ports of the system were directly linked using different lengths of connecting wires to simulate target echoes. The physical picture of the closed-loop experimental used is shown in Figure 5a. Figure 5: Equipment for closed-loop experiments. (**a**) The physical picture of the radar system used; (**b**) The physical picture of the optical fibers and corresponding conversion modules; (**c**) The specific connection between the radar system and the fiber optic module. Optical fiber has the characteristics of long transmission distance, high anti-interference ability, and very low signal attenuation. Therefore, the optional fiber was selected as the connecting line for the closed-loop experiment. Figure 5b is the physical picture of the fiber optic module whose model number is R0F006 GEM-MA (It first appeared at Corning, NY, USA). Port RF_in is the RF input port for connecting to the transmitted port, and port RF_out is the RF output port for connecting to the received port of the radar system. The specific connection between the radar system and the fiber optic module is shown in Figure 5c. The length of the accessed optical fiber was varied to simulate changes in the target time delay. We collected data from the radar operating for a certain period, during which time more than one piece of data was obtained by constantly transmitting and receiving. The steps for processing the echo signal (also known as the beat signal) are as follows:  
* Signal pre-processing includes Hilbert transform and direct current signal removal operation on each piece of data;
* FFT is performed along range direction to obtain the range-slow time spectrum. This step is still included for every piece of data. Each piece of data is arranged into a matrix by column as the range-slow time spectrum. Figure 6a shows the range-slow time spectrum plot of a fiber with a length of 24 m. The maximum position of each column of data corresponds to the distance of 24 m;
* Two adjacent columns of the range-slow spectrum along the slow time direction are subtracted. The information of the clutter is highlighted due to its own instability. The energy of the main lobe is canceled out due to its stability. The processed result of the fiber with a length of 24 m is shown in Figure 6b where only clutter remains. To observe the characteristics of the clutter more clearly, the above-processed data were accumulated along the slow time direction. The cumulative result is shown in Figure 6c. Figure 6: Results of closed-loop experiments on an optical fiber with a length of 24 m. (**a**) The initial range-slow time matrix; (**b**) The range-slow time matrix with only clutter remaining; (**c**) The distribution of clutter along the distance. The positions of the two spikes in it are located at 18.69 m and 28.73 m. Both are exactly symmetric, about 24 m. This indicates that the positions of the clutter on both sides of the main lobe are symmetrical about the peak position of the main lobe. The clutter is defined as left clutter and right clutter based on its front-to-back position with the main lobe. Closed-loop experiments are conducted using optical fibers with lengths of 12 m, 16 m, 24 m, and 40 m, respectively. The above processing is performed for the echo signals and the results are plotted in Figure 7a. It is evident that the positions of left clutter and right clutter are symmetric about the corresponding optical fiber length. Peaks of the clutter on both sides are extracted and plotted as separate lines in Figure 7b. The magnitude of the clutter on both sides decreases as the length of the fiber becomes longer.