## 4 Simulation and Analysis
### Comparison and Analysis of Simulation Results  
In the model with ideal devices, the measured discrete sinusoidal signals with linearly increased frequency interval are ultimately compressed into four pulses, as shown in the left side of Figure 7. The repetition period of the obtained pulses is 10 us. It can be seen that the time spans of the four compressed pulses are 1.25 us, 2.5 us, and 3.75 us, which correspond to the frequency spans of  
the digital process of data accumulation for noise elimination in practical application. Figure 8 is an enlarged comparison version of one single pulse at 31.26 us from the two CTS models. The measured maximum value of the single pulse is 0.998 V and 1.076 V for the classical CTS and the single-channel structure, individually. The little difference in the amplitudes is mainly caused by the added mixer and the signal splicing of the up-conversion and down-conversion of the modulated chirp signal. It is obvious that the envelope of the pulse has the shape of a sinc function, and the measured 3 dB pulse widths of 1.667 ns corresponding to the spectral resolution of 100 kHz are the same. The match of the temporal relations, pulses' amplitudes, and spectral resolution between the two CTS models verifies that the novel single-channel structure has the same performance as the classical CTS system.  
In the model with nonideal devices of the novel structure, the four measured signals with identical frequency span (100 MHz) are also compressed into four pulses. Accordingly, the output pulses have identical time intervals (1.667 us), as shown in Figure 9. The added nonideal power splitter and combiner in the novel structure introduce the amplitude unbalance that can be seen at points of m1, m2, m3, and m4. The overall amplitudes of m5, m6, m7, and m8 are smaller than that of m1, m2, m3, and m4. This is mainly caused by the added nonideal mixer. As the dispersion of real mixer is usually less than 1 nanosecond, which is much smaller than the time resolution of output pulses, its influence on signal resolution can be ignored.  
There are some differences of pulse amplitudes in the simulation results with ideal elements (Figure 8) and with nonideal devices (Figure 9). For the simulation with ideal elements, the ideal concept mainly means the ideal mixer without insertion loss. However, the frequency response of the bandpass filter is nonideal, that is, there is transitional band in the simulation model of the bandpass filter, which may cause the amplitudes inconsistency of the output pulses. For the big amplitudes differences in the simulation with nonideal devices, the main reason is the insertion loss of the nonideal mixer and the difference insertion loss for the up-conversion and down-conversion. The downloaded S2P files of the power splitter and combiner from the website of Mini-Circuit have nonideal frequency  
Figure 8: An enlarged comparison version of one single pulse at 31.26 us from the classical CTS system (**left**) and the single-channel system (**right**).  
Figure 7: Compressed pulses resulting from the classical CTS system (**left**) and the single-channel system (**right**) with four measured signals. The devices used in both models are ideal.  
response, which may also have a slight influence on the amplitudes. These differences introduced by the nonideal devices with insertion loss can be calibrated in the subsequent signal processing.