## 5 Experimental Verification and Analysis  
To verify the proposed LPSA algorithm for fast pulse compression, we built an experiment, as shown in Figure 8. In the experiment, the input frequency bandwidth ranged from 1.8 GHz to 2.4 GHz. The frequency of the expander chirp signal ranged from 2.5 GHz to 3.7 GHz, the chirp rate was 60 MHz/us, and time duration was 20 us. These two signals were generated by an arbitrary waveform generator (AWG7082C). The measured signals with four point frequencies at 1.8 GHz, 1.9 GHz, 2.0 GHz and 2.1 GHz were generated from the second channel of the AWG. After the mixer and band-pass filter, the IF chirp signals had a frequency bandwidth from 700 MHz to 1300 MHz. A digital phosphor oscilloscope (DPO) with 2 GHz bandwidth was used to sample and store the output IF chirp signal for the final digital pulse compression. Figure 9 shows the output pulses calculated by the classical time-domain pulse compression method (a) and the novel LPSA algorithm (b) at a 8 G sampling rate. Two periods of output pulses can be observed in Figure 9. The horizontal axis is time, which can be converted to frequency by multiplying with the chirp rate. The time interval between the output pulses was about 1.667 us, so the corresponding frequency interval was about 100 MHz, considering a chirp rate of 60 MHz/us. It can be seen that a big amplitude difference (up to 1.14 dB) existed between the different output pulses in both of the two pictures. Figure 8: Experimental verification of the novel LPSA algorithm for pulse compression. Output IF chirp signals from the band-pass filter were first sampled and stored by a 2 G bandwidth DPO and then compressed by the classical time-domain pulse compression method and the LPSA algorithm in Matlab. This was mainly caused by the different conversion loss for different input frequencies of the mixer that were used in the experiment. This fixed error introduced by the mixer could be calibrated with the conversion loss characteristic of the mixer. The amplitudes of the output pulses calculated by the classical time-domain pulse compression method were slightly higher than those calculated by the LPSA algorithm, and the noise level in (a) was smaller than that in (b). These differences in amplitudes and noise levels were introduced by the approximate choice of the orthogonal sampling points with fixed sampling rate; the differences can be further reduced by increasing the sampling rate and choosing more reasonable orthogonal sampling points. Figure 10 shows the output pulses obtained by the SAW filter. In the experiment, a S2P file was created in MATLAB to replace the SAW filter for pulse compression. It can be seen that the amplitudes compressed by the SAW filter were smaller than those in Figure 9, while the average noise level was bigger. This was due to the limited time-bandwidth \((T_{c}B_{c})\) of the SAW filter, which could only achieve a compression gain ratio of \(D=\sqrt{T_{c}B_{c}}\). This is an obvious disadvantage of the analog compression method, as it will degrade the sensitivity of the system. In addition, the mismatch in the dispersion characteristics between different SAW filters will also influence the amplitude accuracy and the frequency resolution. Compared to this analog pulse compression method, the novel LPSA algorithm can avoid mismatch problem and increase the sensitivity of the system. Figure 9: Experiment results with four input frequencies calculated by the classical time-domain pulse compression method (**a**) and the LPSA algorithm (**b**) at 8 G sampling rate. The total calculations of the classical time-domain compression method comprised 1.2 \(\times\) 10\({}^{8}\) multiplications and 1.2 \(\times\) 10\({}^{8}\) additions, while that of the LPSA method with two-stage frequency resolution subdivision comprised just 2.48 \(\times\) 10\({}^{5}\) additions and 268 multiplications. Figure 11 shows the frequency resolutions obtained by the LPSA algorithm and the digital time-domain pulse compression method.