# Projects:2018s2-226 Software Library for Inverse Synthetic Aperture Radar

Abstract here

## Contents

## Introduction

### Motivation

Radar is an electrical system which transmits radiofrequency (RF) electromagnetic (EM) waves toward a region of interest and receives the EM waves reflected from the targets for detecting and ranging the target. [1] For the modern radar system, it has much powerful features such as, tracking, classifying and imaging the target. Inverse synthetic aperture radar (ISAR) is such a useful technology to obtain high-resolution images of moving targets under conditions of all-weather and all-day, which has been wildly used in many field such to recognise and classify targets. This project aims to obtain a better understanding of ISAR and the principle of modern radar system.

### Objectives

The purpose of the project is to write a software library for ISAR system by using signal processing knowledge. Our project group need to write functions to achieve multiple radar features starting from building up a radar signal simulator and 3D point scatterer targets with arbitrary motions. Then the ISAR library will follow the design process of range-Doppler algorithm to generate ISAR image. Other functions such as = bistatic radar modelling and image auto-focusing are also included.

### Project team

#### Project students

- Alfred Lu
- Ting Jiang
- Nan Yang

#### Supervisors

- Dr Brian Ng
- Dr Hong Gunn Chew

## Background

### Radar

Radar is an electrical system which transmits EM waves toward a region of interest and receives the reflected signal from the targets for detecting and ranging it. The major components in a radar include transmitter which generates EM waves, transmit antenna which transmit the signal into propagation medium, receive antenna which receive the EM waves reflected from the target, a detector which can demodulate the carrier signal and finally a signal processor which can sort and analyse the received signal.

### SAR

Developed in 1950s, synthetic Aperture Radar (SAR), based on the principle of synthetic aperture, realises high-resolution microwave imaging. It has the characteristics of all-weather, high-resolution and wide-range etc. It was firstly mainly used in airborne and spaceborne platform. With the development of technology, missile-borne, ground-based SAR, UAV SAR, near-space platform SAR and hand-held SAR etc. have appeared. SAR equipped with various forms of platforms is widely used in military and civilian fields.

SAR transmits electromagnetic waves in turn. Radar antenna collects, digitalises and stores reflected echoes for later processing. As sending and receiving occur at different times, they are mapped to different locations. A good combination of received signals has constructed a virtual aperture which is much longer than the physical antenna length. This is why it is called “synthetic aperture”, giving it the attribute of imaging radar. The target direction is parallel to the flight path and perpendicular to the azimuth direction, also known as the orbit direction because it is in line with the position of the object in the antenna’s field of view.

### ISAR

Inverse synthetic aperture radar (ISAR) is a radar technique using radar imaging to generate two-dimensional high resolution image pf a target, which is an important branch in the development of SAR. ISAR is capable of imaging long-range targets with high resolution, so it has great potential for long- range targets. To achieve ISAR imaging, motion compensation must be carried out [2].

The basic principles of SAR and ISAR imaging are the same, which is to obtain high range resolution by transmitting broadband signal and high azimuth resolution by large observation angles. However, different from SAR which is installed on a moving platform to detect static targets, ISAR is a ground-based system to form images for moving objects. Due to the non-cooperation of targets, the development of ISAR was relatively slower than SAR. In 1980, C. C. Chen and Andrew in the United States published the first real ISAR image for an aircraft and researched about signal pre-processing, distance bending and motion compensation. After that, more and more publicly reported ISAR images appeared including Boeing 727, DC-9 and even Venus. In recent years, V. C. Chen and Jian Li had introduced micro-Doppler analysis into ISAR imaging to analyse target moving components. With the in-depth and extensive research of ISAR technology, ISAR has been able to obtain the detailed images of most moving targets (such as aircraft, ships, missiles, satellites and other targets), and has become an extremely important means of target recognition in strategic defence systems [3].

## ISAR Signal Modelling

### LFM Signal

Firstly, a chirp or LFM (Linear Frequency Modulation) signal model is built up as the radar transmitted signal.

For chirp signal, it has the features,

- The LFM signal can have wide bandwidth.
- The frequency of LFM pulse waveform changes linearly within a single pulse.

#### Transmitted Signal

The transmitted LFM signal with a rectangular envelope can be expressed as:

tx=ones(1,length(𝑡𝑥))∗exp(j2π(fc+beta/2*t)t)

Where fc is the carrier frequency

ones (1,length(𝑡𝑥)) is the rectangular envelope

beta is the frequency changing rate,

beta=bandwidth/𝑃𝑢𝑙𝑠𝑒𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛

Based on the formula, a transmitted signal function is defined as

function TX=Chirp_isar(fc,beta,t)

The function takes the carrier frequency, frequency changing rate and time vector as the input, and outputs a single chirp pulse as the transmitted signal.

#### Received Signal

The radar received signal arrives with a time delay of td. This time delay can be expressed as

td=2∗R/c

Where R is the distance from the signal transmitter to the target, c is the wave propagation velocity, constant 2 represents round trip travelling time. The LFM received signal with a time delay can be expressed as

Rx=ones(1,length(𝑡𝑥))∗exp(j2π(fc+beta/2(t−2R/c))∗(t−2R/c))

### Pulse Train

In the ISAR simulator, the radar system is designed to emit N number of chirp pulses to build up a discernible echo. And the sequence of pulses used to generate the multiple range profiles over slow time.

### Matched Filter

The transmitted signal is defined as tx (t), the filter matched to the signal, can be defined as the impulse response of the transmitted signal:

h(t)=k∗tx(Δ−t)

Where k is a constant representing the magnitude of the impulse response Δ is an arbitrary constant where range compression occurs The pulse compression occurs when processing the returned chirp signal through a matched Filter. If the signal is noisy, the matched filter can also filter out the noise.

## Target Simulation & Range Updating

### Target Design

In the ISAR radar library, several 2D and 3D targets are plotted. The targets will help with radar tests in different scenarios. The air plane models are designed as translational motion object; and a helicopter model is designed for rotational motion. Also, the simple targets are used for testing simulation results, and the large scale 3D objects are used for the exhibition.

### Rotate Function

In order to realise the target rotating motion, the next step is to design a 3D rotation function. For a certain target, such as aircraft, will have three motions, which are yaw, pitch and roll.

### Translational Motion Function

In the radar simulator, targets are defined as scattered objects. Therefore the range updating function have to track all scatters’ location of the target. The range update function can be expressed as 23

range(i)=r+scatterlocation(i)+V∗Time

Where r is the location of the target centre, scatterlocation is the scatter position in target’s own frame, i is the ith scatter of the target and V is the target translational velocity. Time is the target travelling time, in the radar system it can be expressed as

Time=PRI∗pulse_index(n)

Where PRI is the pulse duration interval of the target, Pulse index shows the target travels n number of PRI.

## Range & Cross-range Profile

### Range Profile

A range profile is the returned waveform reflected from a target that has been illuminated by the radar with sufficient frequency bandwidth [4]. For the LFM waveform, the reflected signal will have 1D characteristics, intensity versus range.

### Cross-range Profile

A cross-range profile can be formed by collecting the radar returns from a target at different look angles, and the aspect width of the look angles is used to resolve the required cross-range points to form the 1D cross-range profile.

## ISAR Imaging

This section will talk about the ISAR geometry, and generate an ISAR image by using a range profile. The 2D ISAR image is the display of range profile in one axis and the cross-range profile in the other axis [4]. The following figure shows the ISAR geometry, in which the target rotates around the rotating centre O with an angular velocity ω. The radar collects wideband reflected signals from moving targets at multiple aspects with chirp signal [5].

## Range Alignment

From previous ISAR design part, it can be found that the blurred ISAR image is induced by target radial translational motion. It is because the change of range value from profile to profile results in one scatter to migrate along multiple range bins.

### Cross Correlation Method

When target rotating speed is slow, the difference in phase shift between adjacent pulses will be small, which means there is strong correlation between the returned pulses. So cross correlation method can be used to estimate the time delay and compensation the time delay between pulses.

R12(τ)=∫u1(𝑡̂)u2(𝑡̂−τ), where τ is time delay

### Minimum Image Entropy Method

Miminum image entropy method firstly establishes an image entropy, which is the evaluation function of imaging effect. Then, it uses the estimated target motion parameters to compensate the target echo data and performs range Doppler imaging. Finally, the motion compensation is completed by optimizing the image entropy. Minimum image entropy is an iterative motion compensation method, which can achieve optimal imaging without any manual intervention. The motion parameter estimation method based on image entropy is to link the estimation of motion parameters with the image quality. An accurate motion compensation will produce images with good focusing effect and high resolution. The image quality depends on the ISAR image.

For instance, a target is moving towards ISAR LOS, the range is changing as

ΔR_t = R_t − 𝑅0 = 𝑣0 + 0.5 𝑎 ∗ 𝑡^2

Where R_t is the range of the target to the ISAR LOS at time t, R0 is the initial distance, v0 is the target’s initial velocity and a is the acceleration. ΔR_t can be used to compensate the target echo signals where the optimal solution spaces are v0 and a.

## Auto Focusing

After translational motion compensation ISAR image is still smeared due to phase errors induced by the target rotation and residual translation errors.

Two nonparametric auto focusing methods will be designed and tested, which are phase gradient alignment (PGA) and single prominent point processing (SPPP).

As the ISAR library is not capable of rational error compensation, it is not expected to work effectively on rotational error. However, the library has strong features of translational motion compensation, therefore the following design will more focus on eliminating residue translation errors.

## Results

Based on the implementations for ISAR simulator and motion compensation methods, the final ISAR images obtained using the Matlab sotware library is constructed. Figure f49 shows ISAR images for the B2 boomer. However, the ISAR images for a same target may be different when the object performs different movements.

## Conclusion

Through the ISAR software project, several important features of ISAR imaging are learned. Firstly the ISAR image depends on the target’s motion and RLOS, that different targets motion can generate different ISAR image. Secondly, in range-Doppler plane, the phase difference of the scatters located at the same range bin is proportional to the difference in cross range.

### Future Work

In this project, the rotation motion compensation function is not contained in the software library which can be built up in the future. Then in the radar simulator part, the target RCS and radar power dissipation are not considered. These features can be added to the software library to make the simulation more real.

## References

[1] “Project Proposals”, the University of Adelaide, Adelaide, 2018. Available at: https://myuni.adelaide.edu.au/courses/35933/files/3348540/download?wrap=

[2] “Inverse synthetic-aperture radar”, Wikipedia. Available at: https://en.wikipedia.org/wiki/Inverse_synthetic-aperture_radar.

[3] L. Zhang, “Study of high resolution ISAR Imaging for mono- and bistatic radar”, Xidian University, p. 1, Sep. 2011.

[4] C. Özdemir and C. èOzdemir, Inverse synthetic aperture radar imaging with MATLAB algorithms. Hoboken, NJ: Wiley, 2012.

[5] S. Li, G. Zhao, W. Zhang, Q. Qiu and H. Sun, "ISAR Imaging by Two-Dimensional Convex Optimization-Based Compressive Sensing", IEEE Sensors Journal, vol. 16, no. 19, pp. 7088-7093, 2016. Available: 10.1109/jsen.2016.2599540.