Coherent Integration for Cooperative Bistatic Radar with Joint Time-Domain Waveform Agility
Highlights
- The coherent integration loss mechanism of a cooperative bistatic radar for ISAR with simultaneous pulse width (PW) and pulse repetition interval (PRI) agility is analyzed in bistatic radar coordinates.
- PW agility introduces pulse compression mismatch and deterministic residual phase in fast time, while PRI agility causes nonuniform slow-time phase sampling, which destroys the phase consistency required for coherent integration.
- A joint PW and PRI agile processing method is developed to recover coherent gain by coupling fast-time waveform mismatch compensation with nonuniform slow-time phase accumulation.
- Multiple scenario simulations verify improved target focusing, multi-target separation, and motion parameter estimation under the proposed coherent integration method for waveform diversity in the time domain.
Abstract
1. Introduction
- We establish a bistatic-range-domain signal model for cooperative bistatic radar with simultaneous and agility. Unlike monostatic formulations that describe phase history through slant range and radial velocity along a single line of sight, the proposed model describes delay, Doppler, and higher-order phase terms through the transmitter–target–receiver bistatic range and the bistatic projection vector.
- We characterize the effects of simultaneous and agility on coherent integration in a unified processing view. Existing -agile methods [11,18] address nonuniform slow-time sampling but assume uniform pulse compression; the present analysis additionally reveals the -induced fast-time effect through the fixed-bandwidth LFM instantiation considered here, showing that agility leads to nonuniform slow-time sampling while agility produces pulse-dependent compression displacement and deterministic residual phase.
- We develop a joint coherent integration method that combines pulse-wise fast-time compensation with nonuniform slow-time phase accumulation on the actual pulse times. This joint processing chain is new: prior bistatic methods [18] compensate only slow-time nonuniformity, and monostatic staggered-/ methods [17] do not account for bistatic geometry. We also give bistatic-range-coordinate ambiguity and grid-design rules and validate the method through controlled single-target, two-target, and grid-based estimation experiments.
2. Materials and Methods
2.1. Cooperative Bistatic Geometry
2.2. CPI-Local Polynomial Parameterization
2.3. Dual-Agile Waveform Schedule and Calibrated Echo Model
2.4. Proposed Joint Fast-Time and Slow-Time Coherent Integration Method
| Algorithm 1 Joint coherent integration for dual-agile cooperative bistatic LFM radar. |
Require: Pulse-compressed data , waveform schedule , hypothesis set
|
2.5. Ambiguity, Grid Design, and Implementation Discussion
2.5.1. Doppler and Range Ambiguity Under Dual Agility
2.5.2. Bistatic-Specific Parameter-Grid Design
2.5.3. Implementation and Computational Remarks
3. Results
3.1. Simulation Setup
3.2. Coherent Integration in Single-Target Scenario
3.3. Coherent Integration in Multi-Target Scenarios
3.4. Detection Performance
3.5. SNR-Dependent Parameter-Estimation Accuracy
4. Discussion of the Simulation
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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| Symbol | Meaning | Remark |
|---|---|---|
| transmitter and receiver positions | known during one CPI | |
| bistatic range | ||
| equivalent bistatic range | for display | |
| propagation delay | ||
| bistatic range rate | ||
| bistatic Doppler | ||
| width of the pth pulse | agile from pulse to pulse | |
| preceding the pth pulse | defines the slow-time grid | |
| chirp rate of the pth pulse | for fixed bandwidth | |
| emission time of the pth pulse | generally nonuniform | |
| search hypothesis vector |
| Parameter | Value |
|---|---|
| Carrier frequency | 5 GHz |
| Bandwidth B | 20 MHz |
| Number of pulses in CPI | 128 |
| Range of agile PRI | ms |
| Range of agile PW | µs |
| Sampling rate | 40 MHz |
| Baseline bistatic angle for design study | = 60° |
| Range grid spacing | 12 m |
| Velocity grid spacing | 10 m s−1 |
| Acceleration grid spacing | 2.6 m s−2 |
| Jerk grid spacing | 104 m s−3 |
| Number of Monte Carlo trials | 50 |
| Method | PSLRρ (dB) | ISLRρ (dB) | PSLRv (dB) | ISLRv (dB) | Peak (dB) |
|---|---|---|---|---|---|
| Proposed | |||||
| PW-only | |||||
| PRI-only | |||||
| Radon-FFT |
| Scene | Target Count | Bistatic-Range-Domain Parameters |
|---|---|---|
| Single target | 1 | (200.00 km, 3200 m s−1, 40 m s−2, −12 m s−3) |
| Same velocity | 2 | (199.86 km, 3000 m s−1, 40 m s−2, −12 m s−3) and (200.18 km, 3000 m s−1, 40 m s−2, −12 m s−3) |
| Same range | 2 | (200.00 km, 2840 m s−1, 40 m s−2, −12 m s−3) and (200.00 km, 3220 m s−1, 40 m s−2, −12 m s−3) |
| Close pair | 2 | (199.97 km, 2960 m s−1, 35 m s−2, −10 m s−3) and (200.05 km, 3040 m s−1, 35 m s−2, −10 m s−3) |
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Share and Cite
Liu, Y.; Yin, J.; Kong, Y.; Hu, W. Coherent Integration for Cooperative Bistatic Radar with Joint Time-Domain Waveform Agility. Remote Sens. 2026, 18, 2081. https://doi.org/10.3390/rs18132081
Liu Y, Yin J, Kong Y, Hu W. Coherent Integration for Cooperative Bistatic Radar with Joint Time-Domain Waveform Agility. Remote Sensing. 2026; 18(13):2081. https://doi.org/10.3390/rs18132081
Chicago/Turabian StyleLiu, Yiyue, Jiapeng Yin, Yukai Kong, and Weidong Hu. 2026. "Coherent Integration for Cooperative Bistatic Radar with Joint Time-Domain Waveform Agility" Remote Sensing 18, no. 13: 2081. https://doi.org/10.3390/rs18132081
APA StyleLiu, Y., Yin, J., Kong, Y., & Hu, W. (2026). Coherent Integration for Cooperative Bistatic Radar with Joint Time-Domain Waveform Agility. Remote Sensing, 18(13), 2081. https://doi.org/10.3390/rs18132081

