1. PARALLEL FREQUENCY RADAR VIA COMPRESSIVE SENSING
IGARSS 2011
PARALLEL FREQUENCY RADAR
VIA COMPRESSIVE SENSING
You Yanan, Li Chunsheng, Yu Ze
BEIHANG UNIVERSITY 201 LAB

2. OUTLINE 1. INTRODUCTION 2. background of compressive sensing
3. PARALLEL FREQUENCY RADAR BASED ON
COMPRESSIVE SENSING
4. simulation results
5. CONCLUSION

3. 1. INTRODUCTION
Traditional radar utilizes Shannon-Nyquist theorem for high bandwidth signal sampling, which induces the complicated system.
Compressive sensing (CS) indicates that the compressible signal using a few measurements can be reconstructed by solving a convex optimization problem.

4. 1. INTRODUCTION
The structure of compressive sensing radar with frequencies transmitted in parallel is firstly presented in On compressive sensing applied to radar
Parallel frequency radar theoretically cannot degrade the resolution compared with a traditional radar system and effectively reduces the sampling rate.

5. 2. BACKGROUND OF COMPRESSIVE SENSING
sparse scene S
convex problem
Basis Pursuit (BP) , Matching Pursuit (MP) and Orthogonal Matching
Pursuit (OMP) can solve this convex problem
Sparse scene S can be reconstructed by the above algorithms.

6. 3. PARALLEL FREQUENCY RADAR BASED ON
COMPRESSIVE SENSING
3.1 Observation mode
The radar platform moves along track (azimuth) direction with constant velocity.
two-dimension observation scene is limited with the along track (azimuth) direction and the cross track (range) direction.
Parallel frequency radar synchronously transmits M single frequency pulses in each azimuth and then received the phase shift echoes.

7. 3. PARALLEL FREQUENCY RADAR BASED ON
COMPRESSIVE SENSING
3.2 Resolution and sampling rates
Ground observation grid
Azimuth
Range
Range resolution of traditional pulse compressive radar
Parallel frequency radar synchronously transmits M single frequency pulses in each azimuth with the constant
Range resolution of parallel frequency radar via compressive sensing
Conclusion ：If we set the appropriate M and ≈

8. ＞ 3. PARALLEL FREQUENCY RADAR BASED ON COMPRESSIVE SENSING BM/D B
3.2 Resolution and sampling rates
The sampling rate of parellel frequency radar is M/T complex samples per second. Define the time-bandwidth product to be D=BT, B is the total bandwidth of M single frequency pulses. Then, the sampling rate is shown as BM/D.
Conclusion：If we set the appropriate M and D ＞
BM/D B
Traditional radar system
Parallel frequency radar system

9. 3. PARALLEL FREQUENCY RADAR BASED ON
COMPRESSIVE SENSING
3.3 Imaging based on compressive sensing
The phases of echo signal contain the information of the targets.
The kth echo in a certain azimuth is
The phase information of the target is
The discrete representation is
Y is identity matrix

10. 3. PARALLEL FREQUENCY RADAR BASED ON
COMPRESSIVE SENSING
Ka estimation
The targets will be focused on the respective zero Doppler by Ka.
Ka is calculated precisely before compressing the azimuth phases.
Ka varies with the range cells and the signal frequencies.

11. 3. PARALLEL FREQUENCY RADAR BASED ON
COMPRESSIVE SENSING
F construction
1D observation grid
M echoes
phase
detector
M single frequency pulses
M frequencies
3D prior F
Prior F
Measurement matrix is constructed by prior phase information using discrete grids.

12. Observation scene reconstruction
3. PARALLEL FREQUENCY RADAR BASED ON
COMPRESSIVE SENSING
Observation scene reconstruction
Observation scene
Observation grids
M echoes
phase
detector
M frequencies
M single frequency pulses
Na×Nr
Prior F
recover
1×Nr
OMP
M×Nr
M frequencies

13. 3. PARALLEL FREQUENCY RADAR BASED ON
COMPRESSIVE SENSING
Illation
Echo equation 1
Instantaneous range
Approximate representation
Echo equation 2
Demodulating and detecting the phase shift

14. 4. simulation results
The parameters in simulations: M = 30, △f = 5MHz, RMAX = 20km and N = 512.
Azimuth cross section(amplitude)
Imaging result of point target of the parellel frequency radar via compressive sensing
Range cross section(amplitude)

15. 4. simulation results
Imaging results of pulse compression radar and parallel frequency radar via compressive sensing with single or several point targets
Range
Range
RD algorithm of pulse compression radar
Compressive sensing algorithm of parallel frequency radar
Parallel frequency radar via compressive sensing
Pulse compression radar

16. Parallel frequency radar via compressive sensing
4. simulation results
Imaging results of traditional SAR and parallel frequency radar via compressive sensing with the same data amount
Parallel frequency radar via compressive sensing
Traditional SAR

17. Parallel frequency radar via compressive sensing
4. simulation results
Parallel frequency radar via compressive sensing
Pulse compression radar
Range
Amplitude
Azimuth
Amplitude
Range
Azimuth
Range
Azimuth
Azimuth
Range
Conclusion: Sampling rate is reduced by narrow-bandwidth of single frequency pulse. The sparse scene is reconstructed using 10% original data. Side lobes of the range disappear via compressive sensing.

18. 4. simulation results
The ability of distinguishing the adjacent targets in the range direction
Pulse compression radar
Parallel frequency radar via compressive sensing

19. 5. CONCLUSION
This presentation introduces parallel frequency radar and imaging approach based on compressive sensing.
The novel radar can reduce data rate and maintain range resolution with the premise of the appropriate parameters.
The measurement matrix F is composed of the priori phases. The observation scene is reconstructed by OMP.

20. 5. CONCLUSION
The imaging approach based on compressive sensing avoids side lobes of the range.
The noise in received signal is not taken into account in the simulations, it is not ignored in practice.
More researches are required on the capability resisting the noise interference of the signal processing based on compressive sensing in the future.

21. Thank you for your attention!
IGARSS 2011
Thank you for your attention!
BEIHANG UNIVERSITY 201 LAB