IMPROVING RADAR IMAGES FOR SAR AND ISAR SYSTEMSBY USING THE Polynomial FT

Igor Djurović, LJubiša Stanković, Miloš DakovićElectrical Engineering Department, University of Montenegro

Thayananthan Thayaparan, Department of Defense, Canada

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.

ISAR model

Analytic CW Radar Signal Model

ConsiderConsider radar signal radar signal model in the form ofmodel in the form of series of series of M chirps: chirps:

Each chirp is Each chirp is a a linear frequency modulated signal:linear frequency modulated signal:

ISAR imaging

The ISAR image The ISAR image P(m’,n’) is obtainedis obtained by by 2D 2D DDFTFT

DDemodulated emodulated filtered filtered received signalreceived signal component is of the form component is of the form

Fourier transform of the Doppler part Consider Doppler part of the received signalConsider Doppler part of the received signal::

aand its Fourier transformnd its Fourier transform::

where where w(t) is window defining the considered is window defining the considered Coherent Intergration Time (Coherent Intergration Time (CIT).).

Denote Fourier transform of the window Denote Fourier transform of the window w(t) by by W(ω)

Time varying distance Taylor expansion of the time varying distanceTaylor expansion of the time varying distance

reduces reduces Fourier transformFourier transform to to

with spreading factorwith spreading factor

SAR Model

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.

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 =a1, i=ai, i=2,...,k.

22 2( ; ,..., ) ( )exp( ... )kk k

t

X x t j t j t j t

1( ) exp k l

llx t A j a t

21 2( , ,..., )

ˆ ˆ( ,..., ) arg max | ( ; ,..., ) |k

k ka a X

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.

2( ; ) ( )exp( )t

X x t j t j t

Notation

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

0

0

( , ) ( , )exp( )

( , )exp( )

t m t mt m

t mm

S s t m j t j m

S m j m

where

0 0( , ) ( , )exp( )t tt

S m s t m j t

SAR imaging algorithm

• For each m– Let (t,m)=s0(t,m) and

I=1 and .– While radar return (t,m) contains significant energy

• Calculate SI(t,m) =R(t,m) for (t,m) representing well-focused component (target) and SI(t,m)=0 otherwise.

• Non-focused components are updated as: R(t,m)SI(t,m)- R(t,m). Then we calculate:

• Set II+1.• For (for various chirp rates from set )

– Calculate:

• Endfor

( , ) ( , )exp( )t ttR m t m j t

ˆ 0I 1

2

2ˆ( , ) { ( , )exp( )}t It m IFT R m j t

3

2( , ) ( , )exp( )t tt

R m t m j t j t

SAR Imaging algorithm• Estimate the chirp-rate of the radar return:

– Endwhile• Endfor• Radar image is calculated as:

( , )ˆ ˆ( , ) arg max | ( , ) |

It

I t tR m

ˆ( , ) ( , )It tR m R m

1

( , ) ( , )exp( )I

t m J t mJ m

S S m j m

Comments on the algorithm1. 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.

2. 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:

2 3ˆ , ˆ( , ) ( , )exp( )I t t I

t

R m t m j t j t j t ˆ ,( , )

ˆ ˆ( , ) arg max | ( , ) |I I

tI t tR m

2 3ˆˆ( , ) { ( , )exp( )}t I It m IFT R m j t j t

Comments on the algorithm

3. Set of chirp rates can be selected based on information of maximal velocity and acceleration of targets. Chirp-rates in the set could be non-equidistantly spaced.

4. 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.

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.

Standard imaginingAll target are non-moving 4 moving targets

PFT imaging Advanced TFR imaging but with spurious cross-terms

Standard imagining of noise imageAll target are non-moving 4 moving targets

PFT imaging

Noise only chirps are removed from the image

Advanced TFR imaging

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.

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.

Simulated example

Standard FT based radar image

Adaptive chirp rate and filtered adaptive chirp-rate

PFT based image

B727 Image

Simulated image with complicated motion

Algorithm based on radar image segmentation applied.

DFT based image

Segmentation based on two values of the algorithm parameter

Simulated image with complicated motion

Algorithm based on radar image segmentation with adaptive selection of segmentation algorithm parameter applied.