1. IMPROVING RADAR IMAGES FOR SAR AND ISAR SYSTEMS BY USING THE Polynomial FT
Igor Djurović, LJubiša Stanković, Miloš Daković
Electrical Engineering Department,
University of Montenegro
Thayananthan Thayaparan,
Department of Defense, Canada

2. Introduction
ISAR (Inverse Synthetic Aperture Radar) images are commonly obtained by a 2D Fourier transform of the dechirped reflected signal.
Longer time interval gives better image resolution.
Target points with high velocity changes within the considered time interval are blurred.
By using time-frequency analysis methods sharpness of ISAR images can be improved without reducing resolution.

3. ISAR model

4. Analytic CW Radar Signal Model
Consider radar signal model in the form of series of M chirps:
Each chirp is a linear frequency modulated signal:

5. ISAR imaging
Demodulated filtered received signal component is of the form
The ISAR image P(m’,n’) is obtained by 2D DFT

6. Fourier transform of the Doppler part
Consider Doppler part of the received signal:
and its Fourier transform:
where w(t) is window defining the considered
Coherent Intergration Time (CIT).
Denote Fourier transform of the window w(t) by W(ω)

7. Time varying distance Taylor expansion of the time varying distance
reduces Fourier transform to
with spreading factor

8. SAR Model

9. SAR Model
SAR model is similar to the ISAR with difference that it is assumed that radar is moving and that target is non-moving.
Motion of target causes spreading of components but also dislocation from the proper position.
We will demonstrate technique for SAR imaging based on the polynomial FT with couple comments and simulations for ISAR images.

10. PFT – some basic informations
The polynomial FT (PFT) is introduced several times in science.
Detailed statistical study has been provided by Katkovnik.
It is defined as:
For polynomial phase signal: the PFT is ideally concentrated on w=a1, ai=ai, i=2,...,k.

11. PFT - Introduction
Since the PFT can be calculationally demanding we will consider the PFT of the second order:
We assume that the second-order nonlinearity is enough for compensating motion caused effects but also we propose the order adaptive PFT form in the case that we need to increase the PFT order.

12. Notation Set of received chirps will be denoted as: s0(t,m).
Standard radar image obtained by the 2D FT is:
where

13. SAR imaging algorithm For each m Let r(t,m)=s0(t,m) and I=1 and .
While radar return r(t,m) contains significant energy
Calculate SI(wt,m) =R(wt,m) for (wt,m) representing well-focused component (target) and SI(wt,m)=0 otherwise.
Non-focused components are updated as: R(wt,m)SI(wt,m)- R(wt,m). Then we calculate:
Set II+1.
For aL (for various chirp rates from set L)
Calculate:
Endfor 1 2 3

14. SAR Imaging algorithm Endfor Radar image is calculated as: Endwhile
Estimate the chirp-rate of the radar return:
Endwhile
Endfor
Radar image is calculated as:

15. Comments on the algorithm
A technique for determination of chirp returns with significant energy has been developed. This technique works accurately for images with small noise and for some noise environments. Chirps with small energy are not processed since it is assumed that they have not moving components.
Technique for determination of well-focused components has been developed. When we cannot detect highly concentrated component we can use the third order PFT to get better concentration:

16. Comments on the algorithm
Set of chirp rates L can be selected based on information of maximal velocity and acceleration of targets. Chirp-rates in the set could be non-equidistantly spaced.
This technique does not solve problem of displacement radar targets from proper position due to motion caused effects. For handling this problem some classical techniques for motion estimation from video-signals processing are commonly used. The PFT imaging does not require the estimation of chirp rates for each frame since it can be assumed that the chirp rates varies very slowly.

17. Examples
We considered model of Environment Canada’s airborne CV 580 SAR system.
Operating frequency 5.3GHz (C-Band of the CV 580 SAR).
Bandwidth 25MHz.
Pulse repetition time Tr=1/300s.
M=256 pulses within one revisit.
Platform (aircraft) velocity 130m/s.
Altitude 6km.
8 targets: 4 stationary and 4 nonstationary
Two trials: non-noisy trial and noisy trial.

18. Advanced TFR imaging but with spurious cross-terms
Standard imagining
All target are non-moving
4 moving targets
PFT imaging
Advanced TFR imaging but with spurious cross-terms

19. Standard imagining of noise image
All target are non-moving
4 moving targets
PFT imaging
Noise only chirps are removed from the image
Advanced TFR imaging

20. Application to ISAR
This technique can be applied to ISAR systems but with couple differences.
Radar target in the case of the ISAR radars could have several close reflectors on quite small distance.
It can happen that all reflectors of the target have the same chirp rates but for some complicate maneuvers chirp rates could be quite different.
Some combining of results achieved for various chirps is here desirable.

21. Application to ISAR
Other differences in the ISAR radars are velocity of target and different radar operating frequency and bandwidths in this case.
All these differences cause that some more robust concentration measure is required in the PFT technique applied on the ISAR and that some combination of information related to the chirp rates between adjacent radar chirps is also discussed.
Details of this research are published in: I. Djurović, T. Thayaparan, LJ. Stanković: "Adaptive Local Polynomial Fourier Transform in ISAR", Journal of Applied Signal Processing, vol. 2006, Article ID 36093, 2006.
Here we will demonstrate some of results.

22. Simulated example
Standard FT based radar image
Adaptive chirp rate and filtered adaptive chirp-rate
PFT based image

23. B727 Image

24. Simulated image with complicated motion
DFT based image
Segmentation based on two values of the algorithm parameter
Algorithm based on radar image segmentation applied.

25. Simulated image with complicated motion
Algorithm based on radar image segmentation with adaptive selection of segmentation algorithm parameter applied.