# Fixed Receiver Bi Static Sar Biology Essay

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The aim of this work is to study the fixed-receiver bistatic SAR image formation using c/a code and golobal back-projection algorithm and comparing the performance with the monostatic caes based on the results obtained using a MATLAB simulation.

The next chapter, chapter 2, gives an overview of the GPS which includes in details the description of the c/a code which will be used alongwith this work.

Chapter 3 desribes the RADAR fudamentals , also it describes the SAR and some concepts related to the SAR.

Chapter 4 gives an introduction to the SAR data processing algorithms. Also it gives an overview of the GBA and describes the principle of working .

Chapter 5 describes the simulated models and the assumptions used in the simulation. In addition it presents the results of the simulation .

Finally chapter 6 presents the conclusions and recommendations for future work .

The development of satellite systems for three dimensional position and time information with optimal requirements such as global coverage, anywhere in the world, anytime (continuous), and any weather condition (clouds, rains, sun, etc) with high accuracy used to be a hot research issue for several U.S. government organizations such as the Department of Defense (DOD) and the National Aeronautics and Space Administration (NASA) since the early 1960s [1].

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The Global Positioning System (GPS) was developed by the U.S. Department of Defense in the early 1970s; the system meets the optimum requirements previously mentioned.

Although it is a Global Navigation Satellite System which was mainly developed for military purposes, the GPS has been widely used in several civilian applications and now it can be accessed by civilians as well as military people [1] - [3]. The following paragraphs describe the GPS.

## GPS Overview

The GPS consists of three main parts: space segment, control segment, and the user segment. The following paragraphs give a general description to these three segments.

## Space Segment

The space segment consists of a minimum of 24 GPS satellite distributed in six earth-centered orbital planes with four GPS satellite in each plane [1]. The orbits are Semi-circular with orbital radius of 26,600km and inclination of 55o .The orbital period is 11 hours,58 minutes and 2 sec [1][3].

The operating GPS satellites transmit signals that provide the positioning and timing information in addition to information about data, status, and corrected orbit parameters [1].

## Control Segment

The control segment ensures that the system satellites are working properly. It consists of a Master Control Station (MCS) which is responsible of the system operation, provision of commands, and control functions for the satellite constellation and a six worldwide monitor stations to continuously track the satellites [3].

## User Segment

The user segment is consists of the GPS receiver equipment, which capture and process the signals from the GPS satellites in view to calculate the user's position, time and velocity [3]. To do this, at least four satellite signals should be processed by the receiver.

## GPS Signal Structure

The GPS signal is combination of carrier wave, coarse / acquisition (C/A) code, P-code, and navigation message. The carrier waves generally involve L1 and L2 bands [1][2]. The different parts are briefly explained in the next paragraphs while C/A code is described in more details.

## C/A Code

The C/A code is also called pseudorandom number (PRN) code which is a succession of ones and zeros and is unique for every satellite. The frequency of the C/A code is [2] and the bandwidth is [4]. Depending on which PRN code is assigned to a particular satellite, PRN code or number is given to that satellite, i.e. a satellite is named as PRN-1, if the PRN (C/A) code 1 is assigned to that satellite[2].

The main characteristic of C/A codes is that they have the best correlation characteristic .i.e. the cross-correlation of any two different codes is much lower compared to the auto-correlation of each of the codes , also they are easy to generate but the synchronization is more difficult[2] .

## C/A code Generation

A unique C/A code is generated using two sets of gold codes ;an exclusive-or circuit is used to combine the two codes however in each case before doing the combination process , the output of the second code generator is delayed with respect to the first one . Each SV has a unique delay.

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For GPS there are two shift registers (G1 and G2) with length of 10-bits each one are used to generate a maximum length sequence of length = (all zeros state is the only not used state) and the output of the second generator (G2) is delayed then combined with the first generator. The shift registers architecture is described by the following characteristic polynomials:

these polynomials describe the sequences and present the shift registers feedback used to generate the C/A code. The initial states of the individual register stages are ten ones (1111111111) at a time instant known as X1 epoch [1].

There are about 37 C/A codes; the first 32 C/A codes are used in the space segments while the rest (five codes) are reserved for other uses [1]. The C/A code is 1 ms long and this due to the code length is 1023 and the frequency of the C/A code is 1.023 MHz so the repetition period is (1023/ (1.023*10^6 Hz) =1ms). Fig. 2.1 depicts the C/a code generation

Figure 1: C/A code generator [1]

## C/A code correlation

The autocorrelation function is one of the greatest importance signal characteristics for the satellite navigation applications. The auto-correlation function for constant power low pass signal is given by equation (2.1)

where * denotes complex conjugation.

As an example, the baseband DSSS signal shown in Fig.2.2 , has the autocorrelation function described in equation (2.2)

and it is illustrated in Fig. 2.3.

Figure 2: A random binary code producing [1]

Figure 3: the autocorrelation function for fig3 [1]

The C/A codes correlation characteristics are interesting in this work; they have the best correlation characteristic .i.e. the cross-correlation of any two different codes is much lower compared to the auto-correlation of each of the codes. Fig. 2.4 shows the auto-correlation of PRN-1 .The cross correlation between PRN-1and PRN-2 is presented in Fig. 2.5.

Figure 4 Auto-correlation of the first Sat C/A code

Figure 5 Cross-correlation between two Sats C/A codes

## P-Code

P-code consists also of zeros and ones and is generated using a set of Gold Codes. The Y-code is used to encrypt the P-code [2]. The frequency of P-code is 10.23 MHz and is generated using four 12-bit shift registers (X1A, X1B, X2A, and X2B). More details of the P-code generation and operation can be found in [1].

The initial states and the polynomials are presented in Table 2.1 for both P-code and C/A code generator shift registers [1] while a high-level block diagram for the two codes is depicted in Fig. 2.6.

Table 1: GPS Code Generator Polynomials and Initial States

Figure 6: GPS code generators [1]

## DATA NAVIGATION

Navigation data consist also of zeros and ones, however they are based at a low rate which is 50 bits per second and the main use of it, is to send the information to the user from the satellite since every satellite receives a message from the master control station which contains information about the state of the clock, the orbital parameters and another temporal data. More details can found in [1] and [4].

## L1 band

The GPS L1 band frequency is 4. (wave length around 19 cm) which is derived from a fundamental frequency of with a multiplication factor of 154, hence, . L1 band has C/A code, P-code and navigation data [2] which can be shown in equation (2.3).

Fig.2.7 presents a general schematic to generate an L1 band signal as represented by the equation shown in the figure for C/A code [2].

Figure 7: Schematic showing the generation of L1 band GPS signal.

The equation is the mathematical representation of C/A code in L1 band [2]

## L2 band

The GPS L2 band frequency is (wave length around 24 cm) which is derived from a fundamental frequency of f0= 10.23 MHz with a multiplication factor of 120. . L2 band has only P-code and navigation data [4] which can be shown in equation (2.4).

L2 band and the encrypted P-code are used in military applications and the encryption codes are not accessible to the civilian community.

## Frequency down Conversion

A frequency down conversion is a fundamental part in many communication systems such as satellite communication. Frequency down conversion allows the frequency band of interest to be moved down the spectrum so the sampling rate can be reduced and the processing on the signal of interest become more easily. In GPS case, the carrier frequency is f1= 1.57542 GHz and the signal bandwidth is 1MHz. it can be digitized with a sampling rate over 3.5G sample per second. The frequency down conversion allows selecting the 1MHz bandwidth and shifting its frequency down to base band or lower frequency and in doing so reduce the sampling rate to 3 MHz would be fine. Fig (8) shows simple frequency down converter

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Figure 8: frequency down converter

The basic operation idea is based on the following trigonometric identity

So multiplying the carrier frequency by an intermediate frequency the low-pass filtering gives the required low frequency.

## GPS Positioning Services

There are mainly two types of services, provided by the GPS system, which distinguish the military from the civilian use.

## The Precise Positioning Service PPS

The PPS is primarily used in military applications since it predicts the positions with high accuracy. P-code in the two frequency bands (L1 and L2) is used with this service. The use of this service is only permitted to the authorized users [5].

## The Standard Positioning Service SPS

The SPS is used in civilian applications and is free and available to all users worldwide. It is used to determine the positions with an acceptable accuracy using C/A code and L1 frequency band [5].

CHAPTER 3: Radio Detection and Ranging (RADAR)

Radio Detection and Ranging is well-known as RADAR and it was originally developed for military purposes during World War II. It is a good application of electromagnetic radio waves to detect targets and determine the target range. Scottish scientist Robert Watson-Watt defined radar as follows - "Radar is the art of detecting by means of radio echoes the presence of objects, determining their direction and ranges, recognizing their character and employing data thus obtained in the performance of military, naval, or other operations.".

The principle of working is similar to the principles of measuring the distances by sound echoes but radio waves are used instead of sound. The system works by transmitting a radio pulse from the transmitter, this pulse reaches the target with a constant speed close to the speed of light; a part of this pulse will be reflected back to the RADAR receiver. The distance calculated by means of time and the velocity of propagation.

## The RADAR can be classified according to the positions of the transmitter and receiver in the design of the system. RADAR in which the transmitter and receiver are separated is called Bistatic-RADAR; in other hand RADAR in which the transmitter and receiver are collocated is called Monostatic-RADAR.

The amount of power returning to the receiving antenna is given by the radar equation for the Bistatic case

where is the transmitting power, is the gain of the transmitting antenna, is the gain of the receiving antenna, Ïƒ is the radar cross section of the target, is the wave length, is the distance from the transmitter to the target, is the distance from the target to the receiver. Thus, the longer the target is illuminated, the more energy will be reflected back to the receiver. In Monostatic-RADAR, whereby the transmitter and the receiver are at the same location, , thus the equation of the radar is reduced to the expression

this shows that the received power declines as the fourth power of the range, meaning that the reflected power from distant targets is very small.

RADAR can be used in various applications such as meteorological detection of precipitation, measuring ocean surface waves, air traffic control, police detection of speeding traffic, and for military purposes.

## Synthetic Aperture Radar (SAR)

SAR is a coherent RADAR system which makes an image of the earth surface with high resolution. The SAR is installed in planes or space platforms .In SAR there is a big antenna synthesized through the composition of successive and a coherent signal received as echoes from the signals transmitted by a smaller antenna along its flight track. The signal processing uses the magnitude and phase of the received signal of the different pulses in order to create the image. With the movement of the antenna or real aperture through the different positions along the flight track the synthetic aperture is made as it is shown in figure 7 .

Figure 9: Concept of SAR

## Modes of SAR Operation

This section describes different modes of SAR operation which can be within a single system or it can be with different systems.

## Stripmap SAR

In this mode of operation, antenna pointing is fixed relative to the flight line. The beam sweeps along the ground and a continuous image is formed. The antenna length limits the azimuth resolution.

## Scan SAR

This mode is a variation of Stripmap SAR, the sensors steers the antenna beam to illuminate a strip of terrain at any angle to the path of motion. In this mode, a much wider swath is obtained with the cost of low azimuth resolution.

## Spotlight SAR

In this mode, the sensor steers its antenna beam to continuously illuminate the terrain patch being imaged. Comparing this mode with Stripmap mode, the resolution is improved by increasing the angular extent of the illumination on the area of interest (a spot on the ground). In this mode of operation the coverage is not contiguous i.e. only one spot on the ground is imaged at a time.

Figure 10 SAR operation modes: stripmap, scan and spotlight [3]

## Inverse SAR

In this case, the target is moving and the RADAR system is stationary. The signals are similar since the relative position and motion between the sensor and the scene being imaged is important. The processing required to produce an image is similar also. An example is the tracking of satellites from ground-based RADAR.

## Bistatic SAR

In remote sensing SARs, the transmitter and the receiver are usually placed in the same location which is referred to as monostatic; if the transmitter and the receiver are at different locations, this mode of operation is called Bistatic.

## Interferometric SAR (InSAR)

In this mode of operation, post-processing is used to extract terrain height or displacement from the complex images.

## SAR GEOMETRY

Understanding the SAR operation need a clarification to some terminologies and concepts which are defined in this section and illustrated in fig() .

The basic element should be exist is a target, which is the part of the Earth's surface that the SAR system is imaging. A single representative point is considered when developing the SAR equations. This point is called "point target" or "point scatterer" or simply "target" or "scatterer". During the transmission of a particular pulse, the RADAR antenna projects a beam onto an area of the ground referred to as the beam footprint. The footprint is the part of the Earth's surface that is illuminated by the RADAR beam. Range of closest approach is the minimum range i.e. when the zero Doppler line crosses the target. It is denoted as. Zero Doppler time is The time of closest approach, measured relative to an arbitrary time origin. Nadir is the point directly beneath the SAR i.e. the satellite projection on the earth. Swath is the width of the part of the Earth's surface that viewed by the satellite antenna. The range is direction of the SAR to target. Slant Range is the distance from the satellite to the target. Ground range is the projection of Slant Range in the Earth's Surface or the direction in 90â-¦ to the azimuth direction. Near range is the edge of the swath nearest to the nadir track .Far rang is the edge of the swath furthest to the nadir track. the integration angle in the SAR geometry is presented in fig ().

Figure 11 SAR GEOMETRY

Figure 12 Integration angle

## SAR Resolution

The SAR resolution is defined as the smallest distance between two targets that allows the two targets still can be discerned. Since the SAR produce a two dimensional image, there are two resolutions, range resolution and azimuth resolution. The range resolution is determined by the transmitted pulse width (the length of the pulse in time), i.e. fine range resolution is obtained using a narrow pulses. If the pulse length is too large, the echoes from two targets may be detected as one. The azimuth resolution is perpendicular to range. It is defined by the sharpness of the beam (the lobe width) which is calculated by the wave length divided by the physical size of the antenna. Fine azimuth resolution is obtained using high frequency or a wide antenna.

## .

CHAPTER 4: SAR Image Forming Algorithms

SAR image forming algorithms are classified into two main types, frequency domain algorithms and time domain algorithms. This chapter gives a brief introduction to the two types and describes in more details the Global Back-Projection (GBA) algorithm [1] since it has been chosen as an image formation algorithm in this project.

## Frequency-Domain Algorithms

The early SAR systems mostly use Fast Foruier Transform (FFT) based algorithms or frequency-domain algorithms due to their computational efficiency. They have a main drawback that they are valid only for a linear aperture (flight track) which is an assumption that is not applicable for an ultra-wideband system[1][2]. Some of the common frequency-domain algorithms are Range Doppler (RD) algorithm[3 from viet], Range Migration (RM) algorithm[4], Chirp Scaling (CS) Algorithm[5][6].

## Time -Domain Algorithms

The time-domain algorithms are also known as back-projection algorithms. Time domain algorithms are used to solve the frequency-domain algorithms drawbacks in a cost of the computational efficiency. Some of the common time-domain algorithms are Global Back-projection (GBP)[1], Fast Back-projection (FBP)[7], and Fast Factorized Back-projection (FFBP)[8].

## Comparative Features of Imaging Algorithms

This section describes the relative advantages and disadvantages for the algorithms in both domains.

Regarding the used band, FFT-based algorithms produce good image quality and try to reduce the processing load for non-wideband SAR while the image quality is not good in case of Ultra Wide Band (UWB) SAR. This is due to the long integration times needed by UWBSAR which require motion compensation for a good image quality. The FFT-based algorithms can provide motion compensation but very convenient to perform, so they are not suitable for UWBSAR. The time-domain algorithms can provide the adequate motion compensation therefore they can work satisfactorily for UWBSAR systems[2][9].

Another drawback of FFT-based algorithms is that most of them require interpolation of data in frequency domain and this may lead to some errors that degrade the resulting image quality[7].

For the FFT-based algorithms the dimension of the data is related to the size of the image scene and this needs a large memory space since it process big data[9].

Generally it can be said that the relative merits of time-domain algorithms over the frequency-domain algorithms are: wide bandwidth, unlimited scene size, perfect motion compensation, and ability to handle long integration angles while the relative drawback, they require heavy computational load. So the images can be produced with back-projection methods in the time domain or with FFT-based methods in the frequency domain and the choice is a trade-off between accuracy and computational load[9].

## Global Back-projection

The Global Back-Projection (GBP) algorithm is the first time-domain algorithm which is a point-by-point reconstruction method and it has been introduced with several advantages and it is considered as the root of all time-domain algorithms in the area of UWBSAR image scene construction. GBP is adapted to general aperture configure, and compensating for range migration easily in the time domain and it is characterized by the high resolution and low efficiency. Usually the evaluation of any new time-domain algorithm is performed by a comparison of the performance of GBP with the proposed algorithm[1][2].

The main steps in GBP are:

Compressing the range by any compression method.

Dividing the scenes into cells, according to resolution and computational efficiency.

Calculating the transmitter-cells-receiver range by getting the first echo data.

Projecting the scatter coefficients of each cell, according to the transmitter-cells-receiver range. Here, interpolation can be used. Linear interpolation, nearest neighbor interpolation, and cubic spline interpolation can be chosen as the interpolated functions.

Getting the next echo data and repeating step(III) , until the last echo data are projected to the scenes.

In order to describe the global back projection in more details, consider a SAR raw data matrix generated from the sampled echoes from L SAR pulses. A row in the matrix corresponds to a particular pulse, in other words, to a platform position along the flight path; while a column corresponds to a particular target range. The task for GBP is the integration for each resolution cell in the output image, the instantaneous response that a target in that particular cell would have. This is shown in figure1, where the image of size MxN pixels is created. Every pixel of the MxN pixels in the resulting image is produced by L additions where N is the azimuth size, M is range size, and L SAR pulses correspond to the full radar integration length, or aperture. Thus the computational complexity is proportional to LMN[1][2].

Figure 13: Simplified illustration of global back-projection [1]

CHAPTER 5: Simulation Models and Results

The goal of this thesis work is to investigate the fixed receiver Bi-Static SAR image formation using C/A code and GBA. To perform this task, a MATLAB simulation was done. The performance of The bi-static SAR is compared with the monstatic SAR. Also, different receiver locations are taken into account. The following sections describes the simulation models and the results obtained from the simulation.

## Monostatic Image Processing and Formation

This part describes the monostatic SAR image formation model. It presents the system geometry, clarifying the location of the point target, the platform movement, the signals representation, and the relevant parameters.

## System Geometry

Fig. â€Ž5.1 .Monostatic SAR Geometry

Fig. 5.1. presents the mono-static SAR system geometry used in this work; it presents a point target (pt(x,y,z)) and SAR system. The platform flying is assumed to be in the same direction as the X-axis with constant speed (128 m/s) at constant altitude (2000 m) i.e. the flying path is assumed to be straight line. The point target is located on the ground, in the middle of the aperture length (L/2) and (1500m) away from the flying trajectory (ground range) i.e. pt(x,y,z) = pt(1035.5, 1500, 0). Table 5.1. shows the main parameters related to this model.

Table 1. Monostatic SAR Model Parameters

## Parameter

## Value

Altitude \ h

2000 [m]

Ground range

1500[m]

Integration angle

45[degrees]

Platform velocity\ v

128[m/s]

Pulse repletion frequency \PRF

100 [Hz]

Full aperture length

2070[m]

Number of aperture positions

1618

## Signals Representations

In the case under study, it is assumed that the system transmits a pulse and wait in the same aperture position to receive the scatter from the target, then move to the next position, transmits a new pulse and wait to receive the scatter, and so on.

The transmitted signal is the C/A code modulated with QPSK modulation technique, and the received signal is a delayed version of the transmitted signal; this operation is repeated for every aperture position. The delay for each position is related to the duple of the slant range of that position and it is given by:

where is time delay of the received signal at the position , is the distance between the target and the transmitter at the position and is the speed of light. is calculated using the following formula:

where , and are the platform coordinates at the position and , and are the target coordinates.

The channel effect (path loss, fading, attenuationâ€¦etc) has been ignored only the phase shift (due to the delay) is considered. Table 5.2. presents the frequencies and times considered during the simulation.

Table 2 Frequencies And Times

## Parameter

## Value

C/A code frequency \ fb

1.023[M Hz]

C/A code bit duration \Tb

0.9975[Âµ s]

C/A code length \ Tc

1[m s]

Light speed \ c

3x10^8 [m/s]

Carrier frequency \fc

10.23 [M Hz]

Sampling frequency \Fs

40.92 [M Hz]

Sampling time \Ts

0.024438[Âµ s]

## Data Acquisition And Processing

At each azimuth position, the received signal is compressed by correlating the received signal with a reference signal at the receiver; the result is stored as a row in a matrix. This operation is repeated for all azimuth positions, then, the SAR raw data matrix (two dimensional) is generated. A row in the matrix corresponds to a particular pulse while a column corresponds to a particular target range.

After data acquisition and generating the SAR raw data, the global back-projection algorithm is applied for this data in order to generate the final SAR image for a selected area of size (400 pixels x 400 pixels) considering that the point target in the middle of this area.

## Results And Analysis

Following the above descriptions, the system was simulated in Matlab. The following paragraph discusses the obtained results.

As previously mentioned, in the algorithm implementaion stage, the received signals had been compressed using cross-correlation method which correlate the received signals with a refrence signal generated in the reciever and this operation is performed at every aperture position. Fig. 5.2. shows the last received signal after compression.

## Fig. â€Ž5.2 Received signal after pulse compression

All of the compressed received signals were stored in a matrix form in order to make it suitable for the data processing stage. Fig. 5.3. presents the received signal in two dimensional signal memory as well as Fig. 5.4. is a zoomed version of Fig. 5.3. . From Fig. 5.3. and Fig. 5.4. , it can be seen that the received signal strength get its maximum value at the center of the aperture and it gets reducing when moving away from the center. This Phenomenon can be interpreted from the auto-correlation properties since it is known that the maximum auto-correlation value for any signal is at i.e. ; while the maximum auto-correlation value for any signal and a delayed version of that signal at . i.e. ; this case correspond to monostatic case, and the time delay for any received signal is related to the double of the slant range for the corresponding aperture position. The minimum slant range is at the center of the aperture and it is increased when moving far away from the centure . This interprets the bow-shaped curved line of the SAR raw data in Fig. 5.3. and Fig. 5.4.

Fig. â€Ž5.3 Received SAR data in two-dimensional signal memory

Fig. â€Ž5.4 Zoomed SAR Raw Data

The GBA was applied for the SAR raw data matrix in order to generate the final SAR image of an area of 400 pixels x400 pixels , the result is shown in Fig. 5.5. ; this figure is the main figure in the whole story since it represents the final SAR image coresponding to the point target. The resolution is the majer factor used in this work in order to compare the performance of different configurations, as previously mentioned there are two resolutions, azimuth resolution and range resolution. To measure the resolution the contour plots of the final SAR image is generated and presented in Fig. 5.6. for the levels , the resolution is determined by the and the lower levels represent the side lobes. Fig. 5.7. represent a zoomed version of Fig. 5.6. in order to clearly show the . It can be shown from Fig. 5.7. that the resolution in range direction is while in azimuth direction is .

Fig. â€Ž5.5 Final SAR Image of the Point Target

Fig. â€Ž5.6 The Contour Plots of the Point Target

Fig. â€Ž5.7 zoomed contour plots

An alternative method to mesure the resolution, is to extract two vectors in the middle of the SAR image in azimuth and range directions, the resolution is the distance between the two points at which the intensity is one half of the peak intensity. Fig. 5.8. and Fig. 5.9. present the two vectors extracted from the middle SAR image in the range and azimuth directions respectively. Fig. 5.8. shows the resolution in range direction is also it can be seen that there are no sidelobes and this due to the code charcterstics and the selected area is small. Fig. 5.9. shows the resolution in azimuth direction is . The SAR image spectrum in frequency domain correspond to this point target is produced and presented in Fig. 5.10.

Fig. â€Ž5.8 Middle SAR image Vector in Range Direction

Fig. â€Ž5.9 Middle SAR image Vector in Azimuth Direction

Fig. â€Ž5.10 Frequency Domain

The above discussions presented the results for monostatic case which will be used as basis of comaprison to the bi-static configuration. As previously metioned, the difference between the two configurations is the location of the reciever only. The bistatic case is presented in the following paragraphs.

## Bistatic Image Processing and Formation

This part describes the bi-static SAR image formation model. In this case, it is assumed that, the receiver is located on a tower somewhere above the ground looking down to the illuminated scene.

## System geometry

Fig. â€Ž5.11 Bi-static SAR geometry

Fig. 5.11. presents the Bi-Static SAR model, it can be seen that the only difference compared to monostatic is the location of the receiver. The same parameters summarized in Table 5.1. and Table 5.2. will be used, in addition , a new parameters that define the location of the receiver will be added and it is shown in Table 5.3 . The location of the receiver, in comparison to the target and SAR, is important and affecting the resolution. In this study, different locations have been considered and it will be clarified later on in this chapter.

Table 3. The receiver location

## Coordinate

## Value

X-axis

1035.5m

Y-axis

500 m

Z-axis

100 m

## Signals representations

Similar to the monostatic case, at each azimuth position, the transmitted signal is the C/A code modulated with QPSK modulation technique, then the received signal is a delayed version of the transmitted signal. However, in this case, the receiver receives two signals, the first one is the direct signal from the transmitter and the second one is the scatter from the target. The delay for each signal is related to the distance that is travelled by that signal, Hence, there exist two delays should be calculated at each azimuth position.

The delay for the direct signal is given by

where is time delay of position , is the distance between the transmitter and the receiver, and is the speed of light. is calculated using the following formula

where , and are the SAR transmitter coordinates at position , and , and are the receiver coordinates.

The delay for the signal reflected from the target is given by

where is time delay correspond to position , is the distance from the transmitter to the target and then to the receiver, and is the speed of light. is summation of two distances

is the distance from the transmitter to the target and is given by

where , and are the SAR coordinates at the position , and , and are the target coordinates.

is the fixed distance from the receiver to the target and is given by

where , and are the SAR receiver coordinates, and , and are the target coordinates.

## Data Acquisition And Processing

At each azimuth position, the received signal is compressed by correlating the two received signals; the result is stored as a row in a matrix. After repeating this operation for all azimuth positions, the SAR raw data matrix (two dimensional) is generated. A row in the matrix corresponds to a particular pulse while a column corresponds to a particular target range.

After data acquisition and generating the SAR raw data, similar to the monostati case but taking into account that two time delays will be calculated, the global back-projection algorithm is applied for this data in order to generate the final SAR image for a selected area of size (400 pixels x 400 pixels) considering that the point target in the middle of this area.

## Results And Analysis

Following the above descriptions, the systems were simulated in Matlab. The simulation results for case presented in Fig. 5.11 .i.e. the receiver is located in the position are discussed below.

Fig. 5.12. shows the last received signal after compression while Fig. 5.13. and Fig. 5.14. present the received signals in two dimensional memory and zoomed version of this signal respectively. In this case the cross-correlation is performed for a two delayed signals and of the transmitted signal . Here the maximum cross-correlation value at the difference i.e. . In other words, ; This interprets the results obtained, comparing Fig. 5.12. for bi-static with Fig. 5.2. for monostatic, it can be seen that the maximum value of Fig. 5.12. is more close to zero and this because it depends on the time difference which is small value compared with the value in monostatic case. This time differce controls the shape of the raw data matrix so various shapes can be obtained depends on the location of the reciever, not like monostatic case since in monostatic case there only the bow-shaped curved line of the SAR raw data.

Fig. â€Ž5.12 Received signal after pulse compression

Fig. â€Ž5.13 Received SAR data in two-dimensional signal memory

Fig. â€Ž5.14 Zoomed SAR Raw Data

The GBA is applied for the SAR raw data matrix in order to generate the final SAR image of an area of 400 pixels x400 pixels and the result is shown in Fig. 5.14. . As previously mentioned, the resolution is the most important factor of comparison considered in this work. Same procedures as in monostatic case will be used here.

Fig. â€Ž5.15 Final SAR Image of the Point Target

The contour plots of the final SAR image is generated and presented in Fig. 5.15. for the levels , as usual, the resolution is determined by the and the lower levels represent the side lobes. Fig. 5.16. represent a zoomed version of Fig. 5.15. in order to clearly show the . It can be shown from Fig. 5.16. that the resolution in range direction is while in azimuth direction is .

Fig. â€Ž5.16 The Contour Plots of the Point Target

Fig. â€Ž5.17 zoomed countour plot

Also the resolution can be measured using the alternative method. Fig. 5.17. and Fig. 5.18. present the two vectors extracted from the middle SAR image in the range and azimuth directions respectively. Fig. 5.17. shows the resolution in range direction is also it can be seen that there are no sidelobes and this due to the code charcterstics and the selected area is small. Fig. 5.18. shows the resolution in azimuth direction is . The SAR image spectrum in frequency domain correspond to this point target is produced and presented in Fig. 5.19.

Fig. â€Ž5.18 Middle SAR image Vector in Range Direction

Fig. â€Ž5.19 Middle SAR image Vector in Azimuth Direction

Fig. â€Ž5.20 Frequency domain

## Based on the obtained results, the monostatic configuration outperforms the bistatic configuration in azimuth direction, while for this specfic configuration, the bistatic configuration outperforms the monostatic configuration in range direction since the receiver location has a great effect on the range resolution. Table 5.4. summerize the resolution obtained from the results of the two configurations.

Table 4 resolution

## Configuration

## Range resolution [m]

## Azimuth resolution [m]

## Monostatic

## 100

## 12

## Bi-static

## 92

## 22

## The range resolution strongly depends on the receiver location in comparison to the transmitter and target locations. To prove this, various receiver location has been considered, the results are discussed in the following sections.

## Different receiver locations

This section discusses three study cases for different receiver locations to show the effect of the position on the resolution.

## Case Study No (1)

In this case, the receiver location coordinates are given in Table 5.5. and the system geometry is presented if Fig. 5.20.

Table 5. Receiver location for the case study no (1)

## Coordinate

## Value

X-axis

1035.5m

Y-axis

2000 m

Z-axis

100 m

Fig. â€Ž5.21 case 1

The reults for case study are presented in Fig. 5.21 . it depicts four figures . Fig. 5.21 (a) shows the received signals in two dimensional memory, it can be seen that the signal strength is almost the same for all azimuth positions. Fig. 5.21 (b) depicts the resulting final SAR image for the area of (400 pixels x 400 pixels). Fig. 5.21 (c) presents the contour plots of the final SAR image, it shows the levels , as before, the resolution is determined by the and the lower levels represent the side lobes. Fig. 5.21 (d) represents the SAR image spectrum in frequency domain correspond to the point target.

In order to determine the resolution, a zoomed version of Fig. 5.21 (c) is shown in Fig. 5.22. it clearly show the . It can be shown that the resolution in range direction is while in azimuth direction is .

Fig. â€Ž5.22 case 1

Fig. â€Ž5.23 zoomed contour plot

## Case Study No (2)

In this case, the receiver location coordinates are given in Table 5.6. and the system geometry is presented if Fig. 5.23.

Table 6. Receiver location for the case study no (2)

## Coordinate

## Value

X-axis

535.5m

Y-axis

500 m

Z-axis

100 m

Fig. â€Ž5.24 case 2

Similar to the case study no (1) results, the reults for this case study are presented in Fig. 5.24 . that is, Fig. 5.24 (a) shows the received signals in two dimensional memory, it can be seen that the SAR raw data shape is different compared to the previous bi-static cases Fig. 5.14 and Fig. 5.21 (a). The Fig. 5.24 (b) depicts the resulting final SAR image for the area of (400 pixels x 400 pixels). Fig. 5.24 (c) presents the contour plots of the final SAR image, it shows the levels , as before, the resolution is determined by the and the lower levels represent the side lobes. Fig. 5.24 (d) represents the SAR image spectrum in frequency domain correspond to the point target.

Fig. â€Ž5.25 case 2

In order to determine the resolution, a zoomed version of Fig. 5.24 (c) is shown in Fig. 5.25. it clearly show the . It can be shown that the resolution in range direction is while in azimuth direction is .

Fig. â€Ž5.26 zoomed contour plot

## Case Study No (3)

In this case, the receiver location coordinates are given in Table 5.7. and the system geometry is presented if Fig. 5.26.

Table 7. Receiver location for the case study no (3)

## Coordinate

## Value

X-axis

1535.5m

Y-axis

500 m

Z-axis

100 m

Fig. â€Ž5.27 case 3

Similar to previous cases, the reults for this case study are presented in Fig. 5.27 . that is, Fig. 5.27 (a) shows the received signals in two dimensional memory, also it can be seen that the SAR raw data shape is different compared to the previous bi-static cases. The Fig. 5.27 (b) presents the resulting final SAR image for the area of (400 pixels x 400 pixels). Fig. 5.27 (c) presents the contour plots of the final SAR image, it shows the levels , as before, the resolution is determined by the and the lower levels represent the side lobes. Fig. 5.27(d) represents the SAR image spectrum in frequency domain correspond to the point target.

Fig. â€Ž5.28 case 3

In order to determine the resolution, a zoomed version of Fig. 5.27 (c) is shown in Fig. 5.28. it clearly show the . It can be shown that the resolution in range direction is while in azimuth direction is .

Fig. â€Ž0.29 zoomed contour plot

By considering the three study cases as well as the first bi-static case, it can be shown that, different shapes for the SAR raw data for different reciver location can be obtained; also the resolution of the final image strongly depends on the position of the receiver I comparison to the transmitter and the point target , the results show that, the best resolution in the case when the reciever is in between the transmitter and the point target, while the worst resolution in the case when the point target is in between the transmitter and the reciever. The position in the left or the right doesnot affect the resolution but it affects the shape of the SAR raw data. Table 5.8. summerizes the resolution obtained in the three study cases.

Table 6 resolution obtained in the three study cases

## Case Study No

## Range resolution [m]

## Azimuth resolution [m]

## 1

## 340

## 22

## 2

## 96

## 22

## 3

## 96

## 22

CHAPTER 6: Conclusions and Recommendations

## Conclusions

The goal of this thesis work is to investigate the fixed receiver Bi-Static SAR image formation using C/A code and Global back-projection algorithm. The C/A code signals are already used in the GPS satellites.

Originally this work is oriented towards using the GPS as transmitter, however, due to time constrain and for simplicity, simplified parameters were used such as lower carrier frequency, low flying height and suitable speed. This work is considered as the first attempt for generation of SAR image using this SAR configuration (bistatic SAR, C/A code and GBA). The C/A code transmitter can be built and mounted on an aircraft instead of the satellite and it can use a low carrier frequency compared that one use GPS.

From the results it can be concluded that the Bi-Static SAR has high resolution especially in azimuth direction. The signal bandwidth plays the important role in the range resolution while the carrier frequency and the integration angle mainly affect the azimuth resolution. Also, the Bi-Static SAR resolution strongly depends on the receiver location. In order to get the best resolution the SAR receiver should be located somewhere in between the SAR transmitter and the target under focus. Also the results show that the shape of the SAR raw data depends on the SAR receiver in comparison to target and the transmitter. Various shapes can be obtained depending on the geometry.

## Recommendations

The research on the fixed receiver Bi-static SAR is still on its early stages. Thus, all fields in this area are possible candidates for future works.

The highly recommended feasible future work is to continue and optimize this work by investigating the real parameters, implementing the frequency down converter, as well as imaging more than one object.