# An Efficient Algorithm for De-Interleaving Staggered PRI Signals
## 3 Simulation and Analysis
### Comparative Experiments  
This section analyzes the algorithm's performance under different PRI jitter, missing pulses, and radiation source numbers. The signal de-interleaving algorithm is based on sequence correlation [11], and the signal de-interleaving algorithm is based on CMM [19] as the latest results were used for comparison. The parameters used for the simulation are as follows: the number of pulses of a single pulse sequence is 100; the stagger number is set to 3; the PRI range is [100 \(\upmu\)s, 500 \(\upmu\)s]. Measure five times consecutively, and the de-interleaving result with the lowest number of correctly extracted radiation sources among the five tests was selected as the final result. The simulations are shown in Tables 2 and 3. As shown in Tables 2 and 3, the following hold. 1. The algorithm proposed in this research can correctly de-interleave five radiation source signals arriving simultaneously when the PRI jitter rate is \(\pm\)12% and the pulse missing rate is 5%. The algorithm proposed in this research can correctly de-interleave four radiation source signals arriving simultaneously when the PRI jitter rate is \(\pm\)3% and the pulse missing rate is 15%. The proposed approach for signal de-interleaving is highly suited to PRI jitter and pulse missing. 2. The signal de-interleaving algorithm based on sequence correlation is sensitive to PRI jitter. In addition, the performance of the sequence correlation algorithm for fixed PRI signals de-interleaving decreases as the pulse missing rate increases. When the pulse missing rate increases, the peak of the line histogram corresponding to the true PRI decreases, and the peak of the line histogram corresponding to the PRI harmonics increases, so the harmonic components of the true PRI are detected, resulting in de-interleaving errors. Due to the characteristics of staggered signals, pulse loss has less impact on the de-interleaving of the staggered PRI signal. Even if the pulse loss is severe, the line histogram peak corresponding to the frame periods is still high. Figure 5: Sub-PRIs estimation result of staggered PRI signal. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Pulse Sequence 1** & **Pulse Sequence 2** & **Pulse Sequence 3** & **Pulse Sequence 4** \\ \hline PRI modulation type & Staggered & Jittered & Fixed & Fixed \\ Frame period (μs) & 166 & - & - & - \\ Sub-PRIs (μs) & 11, 20, 33, 45, 57 & - & - & - \\ PRI value (μs) & - & 441 & 780 & 1151 \\ Noise error (μs) & \(\pm\)0.5 & \(\pm\)0.5 & \(\pm\)0.5 & \(\pm\)0.5 \\ Jitter bound & 0 & \(\pm\)10\% & 0 & 0 \\ Missing rate & 10\% & 15\% & 20\% & 20\% \\ Observation time (μs) & 50,000 & 50,000 & 50,000 & 50,000 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of Mixed Pulse Stream 1. 3. The CMM-based signal de-interleaving algorithm is sensitive to PRI jitter. The effectiveness of the CMM-based signal de-interleaving algorithm declines as the pulse missing rate and number of radar radiation sources rise. When the pulse missing rate is considerable, the sequence retrieval is greatly affected by the interference of different pulse sequences, resulting in wrong pulse separation and consequently to de-interleaving errors. 4. As the pulse missing rate and the number of radiation sources increase, the performance of the proposed algorithm is better than the algorithms in [11; 19]. The proposed algorithm adopts two measures to improve de-interleaving success rate. The probability of misidentification is reduced by combining the improved SSWI algorithm and sequence retrieval algorithm. Moreover, based on the matched filter theory, a sequence retrieval algorithm is proposed, enhancing the pulse sequence's separation accuracy.