## 4 Simulation and Analysis
### Simulation Results and Analysis  
Three input signals were measured: single frequency signal, five frequencies signals and signals with eleven frequencies. Figure 3 presents the output results using the classical time-domain compression method and the novel LPSA algorithm with a single input frequency of 6.4 GHz based on CTS system. The left picture (a) shows the output pulse calculated by the classical time-domain compression method. The right one (b) shows the output pulse obtained using the new LPSA method with two-stage frequency resolution (3.1 MHz-100 kHz). It can be observed that near the 6.4 G input frequency, the noise level of the novel method was a little higher than that of the classical time-domain pulse compression method. This was mainly caused by the subsampling of the orthogonal points, which could be improved by increasing the sampling rate, i.e., by adding more orthogonal sampling points. For the first stage of 3.1 MHz frequency resolution, the compression time was 0.1 us and the number of the orthogonal sampling points was 100. The calculation for the spectrum measurement under 3.1 MHz frequency resolution included 64,600 additions and 323 multiplications. For the second stage of 100 kHz frequency resolution, the compression time was 10 us and the total number of the orthogonal sampling points was 15,000 (sampling rate from 1 GHz to 2 GHz and 100:1 attenuation of the amplitudes extension). As there was only one channel with signals, only 500 sampling points were selected for the calculation (sampling rate from 33.3 MHz to 66.6 MHz and 18:1 attenuation of the amplitudes extension). The calculation for the spectrum measurement under 100 kHz frequency resolution included 31,000 additions and 31 multiplications. So, the total calculations for the LPSA method comprise 95,600 additions and 354 multiplications. For the classical time-domain pulse compression method, the total calculations under 100 kHz frequency resolution comprise 8 \(\times\) 108 additions and 8 \(\times\) 108 multiplications. As shown in Figure 4, we zoomed in on the pulses at 6.4 GHz in Figure 3. It can be seen that the frequency resolutions of 3 dB bandwidth were both about 100 kHz, i.e., close to the inverse of the duration time (\(\frac{1}{T_{c}}\)) of the compressor. The novel LPSA algorithm introduced a relatively higher sidelobe compared to the classical time-domain pulse compression method. This was caused by the total number of the selected sampling points used for the calculation and phase approximation in (31). Another five input frequencies from 5.6 GHz to 6.4 GHz with 200 MHz frequency interval and identical amplitudes of 0.14 V were measured. The output pulses were calculated by the classical time-domain compression method and the novel LPSA algorithm with two-stage frequency resolution (3.1 MHz-100 kHz), as shown in Figure 5. In the second-stage frequency resolution subdivision, the subsampling rate (33.3 MHz-66.6 MHz) with only 500 orthogonal sampling was adopted for the measured spectrum. It can be seen the frequency components obtained by the two digital pulse compression methods were almost the same. The noise level had a slightly difference. This can be improved by increasing the linear sampling rate in the second-stage frequency resolution subdivision at the expense of some increased calculations. The amplitudes were a little different between the output pulses calculated by the two methods. The fixed sampling rate of 5G determines the location and maximum number of the orthogonal points satisfied (16) and (17), and it is the major factor that influences the amplitude accuracy of the output pulses. The choice of the sampling rate was determined by the amplitude accuracy requirements. In this simulation, the total computation of the novel method comprised 219600 additions and 478 multiplications, while the total number of calculations for the classical time-domain pulse compression method still comprised 4 \(\times\) 10\({}^{8}\) additions and 4 \(\times\) 10\({}^{8}\) multiplications.