An Efficient Algorithm for De-Interleaving Staggered PRI Signals
Abstract
:1. Introduction
- An efficient algorithm is proposed to de-interleave staggered PRI signals from the mixed signals. The algorithm can adjust to a broad PRI range and dense pulse signals with negligible computational costs.
- An improved square sine wave interpolation (SSWI) function is constructed, making the algorithm adapt to staggered PRI signal and PRI jitter.
- A threshold criterion is designed for the improved SSWI algorithm, which decreases the interference between the sub-PRIs and the frame period.
- A sequence retrieval algorithm incorporating matched filter theory is proposed, enhancing the separation accuracy of radar pulse sequences.
2. Problem Formulation and Proposed Algorithm Description
2.1. The TOA Model of the Mixed Pulse Sequences
2.2. The Principle and Flow of the Proposed Algorithm
- The problem of suppressing the interference between the sub-PRIs and the frame period.
- The problem of extracting the staggered PRI sequence from the mixed pulse sequences.
- The problem of computing efficiently.
- (i)
- Input the discrete signal , initialize , c indicates the difference grade. Calculate the improved SSWI function, and execute the fast Fourier transform (FFT) on the interpolation result. Then, determine the estimated PRI values according to the threshold criteria, and go to Step (ii).
- (ii)
- Use the proposed sequence retrieval algorithm to extract the pulse sequence from the mixed discrete signal by the estimated PRI. If sequence search does not succeed, . If c is greater than , go to Step (iii); otherwise, go to Step (i). If sequence search succeeds, the residual pulses are set as a new . If the residual pulse number exceeds the de-interleaving threshold , go to Step (i); otherwise, go to Step (iii).
- (iii)
- Extract the staggered sequence and estimate the sub-PRIs.
2.3. Improved Square Sine Wave Interpolation Algorithm
2.3.1. SSWI Function and Spectral Characteristic Analysis
2.3.2. Improved SSWI Function
- (i)
- Let be the i-th subclass after clustering, the center value of the i-th subclass, the elements number of the i-th subclass, and P the subclasses number after clustering;
- (ii)
- Initialization: Pulse interval sequence indicates the c-th grade difference sequence of the discrete signal , ; , , and indicates the difference interval number;
- (iii)
- For , calculate the relative error between the difference interval and each cluster center
- (iv)
- Find the minimum of relative error vector . , and is the position corresponding to the minimum value of . If , go to Step (v); otherwise, go to Step (vi). indicates the error threshold, determined by the PRI jitter upper limit;
- (v)
- Update subclass, update the pulse interval number, and go to Step (vii);
- (vi)
- Generate a new subclass and update the number of subclasses, update the pulse interval number, and go to Step (vii);
- (vii)
- If , go to Step (iii), proceed to the next clustering; otherwise, the clustering algorithm ends, so go to Step (viii);
- (viii)
- Correct the difference interval sequence according to the clustering result, and generate an improved SSWI function from the corrected difference sequence.
2.3.3. A Threshold Criterion
2.3.4. The Flow of the Improved SSWI Algorithm
Algorithm 1: The flow of the improved SSWI algorithm |
Input:
Improved SSWI and FFT:
Generate the SSWI function according to the corrected difference interval; End
Threshold Criterion:
Output: The estimated PRI is q. |
2.4. Sequence Retrieval Algorithm Based on Matched Filter
- (i)
- Initialization: , , , reference pulse ; , , where , and , and determine the search scope, determined by the PRI jitter upper limit; is for counting;
- (ii)
- According to reference pulse and PRI value q, calculate the search scope:If , this round is complete, so go to Step (vi); else, go to Step (iii).
- (iii)
- Search for the next pulse that meets the condition:
- (iv)
- Screen the next pulse by the class-matched filter operation.According to Formula (22), is the sampling signal of the reference pulse , is the sampling signal of the pulse set , is determined by the class-matched filter operation; go to Step (v);
- (v)
- Update the PRI value based on the searched next pulse:
- (vi)
- If exceeds , end the pulse sequence search; else, . If i is greater than , end the pulse sequence search; otherwise, update reference pulse, ; initialization , ; go to Step (ii).
2.5. Extract the Staggered PRI Sequence and Estimate the Sub-PRIs
3. Simulation and Analysis
3.1. Simulation Experiments
3.2. Comparative Experiments
- (i)
- The algorithm proposed in this research can correctly de-interleave five radiation source signals arriving simultaneously when the PRI jitter rate is ±12% and the pulse missing rate is . The algorithm proposed in this research can correctly de-interleave four radiation source signals arriving simultaneously when the PRI jitter rate is ±3% and the pulse missing rate is . The proposed approach for signal de-interleaving is highly suited to PRI jitter and pulse missing.
- (ii)
- 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.
- (iii)
- 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.
- (iv)
- 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.
3.3. Computational Costs
3.4. Semi-Physical Simulation Experiments
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Pulse Sequence 1 | Pulse Sequence 2 | Pulse Sequence 3 | Pulse Sequence 4 | |
---|---|---|---|---|
PRI modulation type | Staggered | Jittered | Fixed | Fixed |
Frame period (�s) | 166 | - | - | - |
Sub-PRIs (�s) | 11, 20, 33, 45, 57 | - | - | - |
PRI value (�s) | - | 441 | 780 | 1151 |
Noise error (�s) | ||||
Jitter bound | 0 | 0 | 0 | |
Missing rate | 10% | 15% | 20% | 20% |
Observation time (�s) | 50,000 | 50,000 | 50,000 | 50,000 |
PRI Jitter Rate | Missing Rate | Input Radiation Source Conditions | De-Interleaving Results | ||
---|---|---|---|---|---|
Sequence Correlation | CMM | Ours | |||
1 staggered PRI | 1/1 | 1/1 | 1/1 | ||
1 staggered PRI and 1 fixed PRI | 1/2 | 1/2 | 2/2 | ||
1 staggered PRI and 2 fixed PRI | 1/3 | 1/3 | 3/3 | ||
2 staggered PRI and 2 fixed PRI | 2/4 | 2/4 | 4/4 | ||
2 staggered PRI and 3 fixed PRI | 2/5 | 2/5 | 5/5 | ||
1 staggered PRI | 1/1 | 1/1 | 1/1 | ||
1 staggered PRI and 1 fixed PRI | 1/2 | 1/2 | 2/2 | ||
1 staggered PRI and 2 fixed PRI | 1/3 | 1/3 | 3/3 | ||
2 staggered PRI and 2 fixed PRI | 2/4 | 2/4 | 4/4 | ||
2 staggered PRI and 3 fixed PRI | 2/5 | 2/5 | 5/5 | ||
1 staggered PRI | 1/1 | 1/1 | 1/1 | ||
1 staggered PRI and 1 fixed PRI | 1/2 | 1/2 | 2/2 | ||
1 staggered PRI and 2 fixed PRI | 1/3 | 1/3 | 3/3 | ||
2 staggered PRI and 2 fixed PRI | 2/4 | 2/4 | 4/4 | ||
2 staggered PRI and 3 fixed PRI | 2/5 | 2/5 | 5/5 |
Missing Rate | Input Radiation Source Conditions | De-Interleaving Results | ||
---|---|---|---|---|
Sequence Correlation | CMM | Ours | ||
1 staggered PRI | 1/1 | 1/1 | 1/1 | |
1 staggered PRI and 1 fixed PRI | 2/2 | 2/2 | 2/2 | |
1 staggered PRI and 2 fixed PRI | 3/3 | 3/3 | 3/3 | |
2 staggered PRI and 2 fixed PRI | 4/4 | 4/4 | 4/4 | |
2 staggered PRI and 3 fixed PRI | 5/5 | 5/5 | 5/5 | |
1 staggered PRI | 1/1 | 1/1 | 1/1 | |
1 staggered PRI and 1 fixed PRI | 2/2 | 2/2 | 2/2 | |
1 staggered PRI and 2 fixed PRI | 3/3 | 3/3 | 3/3 | |
2 staggered PRI and 2 fixed PRI | 3/4 | 4/4 | 4/4 | |
2 staggered PRI and 3 fixed PRI | 4/5 | 4/5 | 5/5 | |
1 staggered PRI | 1/1 | 1/1 | 1/1 | |
1 staggered PRI and 1 fixed PRI | 2/2 | 2/2 | 2/2 | |
1 staggered PRI and 2 fixed PRI | 3/3 | 3/3 | 3/3 | |
2 staggered PRI and 2 fixed PRI | 2/4 | 3/4 | 4/4 | |
2 staggered PRI and 3 fixed PRI | 3/5 | 3/5 | 4/5 |
Sequence Correlation | Part1 | |
Part2 | ||
Part3 | ||
Total | ||
CMM | Part1 | |
Part2 | ||
Part3 | ||
Total | ||
Ours | Part1 | |
Part2 | ||
Part3 | ||
Total |
PRI Range | Radiation Sources | Sequence Correlation | CMM | Ours |
---|---|---|---|---|
100–300 | 2 | 2.21 s | 4.15 s | 0.91 s |
100–300 | 4 | 6.73 s | 7.22 s | 1.13 s |
100–300 | 6 | 10.25 s | 13.57 s | 1.37 s |
100–600 | 2 | 3.62 s | 8.62 s | 0.92 s |
100–600 | 4 | 10.51 s | 12.51 s | 1.11 s |
100–600 | 6 | 16.33 s | 19.25 s | 1.35 s |
100–1000 | 2 | 5.51 s | 14.22 s | 0.95 s |
100–1000 | 4 | 16.62 s | 17.52 s | 1.21 s |
100–1000 | 6 | 24.33 s | 24.76 s | 1.39 s |
Sequence 1 | Sequence 2 | Sequence 3 | |
---|---|---|---|
PRI modulation type | Staggered | Jittered | Fixed |
Frame period (µs) | 222 | - | - |
Sub-PRIs (µs) | 47, 66, 109 | - | - |
PRI value (µs) | - | 555 | 887 |
Jitter bound | 0 | 0 |
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Cheng, W.; Zhang, Q.; Dong, J.; Wang, H.; Liu, X. An Efficient Algorithm for De-Interleaving Staggered PRI Signals. Appl. Sci. 2023, 13, 7977. https://doi.org/10.3390/app13137977
Cheng W, Zhang Q, Dong J, Wang H, Liu X. An Efficient Algorithm for De-Interleaving Staggered PRI Signals. Applied Sciences. 2023; 13(13):7977. https://doi.org/10.3390/app13137977
Chicago/Turabian StyleCheng, Wenhai, Qunying Zhang, Jiaming Dong, Haiying Wang, and Xiaojun Liu. 2023. "An Efficient Algorithm for De-Interleaving Staggered PRI Signals" Applied Sciences 13, no. 13: 7977. https://doi.org/10.3390/app13137977