BRIEF

Prototype is a well-established engineering concept to have thorough understanding, design evaluation and outcome inspection. Utilizing everything in recursive and optimized fashion, final Algorithm/Structure/Model emerges as the most practical candidate for actual/true implementation.

Software Prototyping (Simulation) is the most recent, highly effective and flexible with minimal cost & time benefits. Out of a known set of algorithms or new variants of existing algorithms that might have seemed potential enough must be tested/simulated to highlight their own advantages and limitations under various degrees of synthetic environment. They all have to be judged in all respects with actually implemented and proven algorithms to open up new directions!

Even the selection of a simulation language or a package is also as crucial as the algorithm. Features like availability, reliability, easy to use, user-friendly help, fast execution and the most important is its ability to provide directly or programmatically all complex and application specific constructs needed for the simulation of interest.

In case of SAR Imaging, a small portion of the illuminated ground patch at a given time with a resolution of interest is considered a Point Target. The key element for ground imaging is a point target because a given ground patch of illumination can be viewed as a two-dimensional grid of several point targets. An algorithm which works well for a point target has to work satisfactorily for a given ground patch and hence for an entire swath.

There are three major algorithms for Azimuth Processing (Correlation) to achieve desired Azimuth Resolution.

1 Time-Domain Azimuth Signal Processing (TASP)

2 Frequency-Domain Azimuth Signal Processing (FASP)

2.1 Time Weighted FASP (TW-FASP)

2.2 Frequency Weighted FASP (FW-FASP)

3 Spectral Analysis (SPECAN)

In this Section, the underlying core essence are tried to be presented…

1 MATLAB as a powerful simulation tool.

2 Importance of a point target in calibration of SAR processing algorithms.

3 End-to-end design understanding and verification of actually implemented Time-Domain algorithm with the help of MATLAB simulation.

4 An approach to a Frequency-Domain algorithm with two innovative ideas of Weighting in Time and Weighting in Frequency.

5 Results of Time-Domain & Frequency-Domain simulations and a comparative study of various outcomes and interpretations.

For both Time-Domain & Frequency-Domain Azimuth Signal Processing simulations in MATLAB, certain assumptions are followed to avoid unnecessary complexities.

· Point target geometry in context to Air-borne SAR in Slant Range.

· Ideal, stable radar platform with no spatial motion, straight- linear flight path of air-craft with constant velocity.

· Uniform illumination & scattering for the ground patch and symmetrical horizontal & vertical Beam-width of a Monostatic Antenna.

· No RCMC (Range Cell Migration Correction).

· No Radiometric and Geometric Correction.

Selected parameters for a given system and various formats of Azimuth Resolution & ISLR for both the simulations with ideal & noisy conditions are shown here as look ahead clues.

Requirements:

Azimuth Resolution: At least 6m or better.

ISLR (dB): Maximum (in absolute form) as possible.

System Parameters:

Antenna Length: 1.3 m, Antenna Width: 8 to 9 cm

Antenna Look Angle: » 60°

Air-craft Velocity: 120 m/s, Air-craft Altitude: 6000 m

Center Frequency/ Wavelength of Transmitted Chirp: 5.3GHz/ 5.6cm

Shortest Slant Range: 8000 m, Longest Slant Range: 32,000 m

Swath-width: 25000 m

Processing Bandwidth for given Resolution: 20Hz+ dbw tolerance = 26Hz to 31.25Hz

Various formats of Azimuth Resolution/ ISLR as End Results (Outcomes):

1 Time-Domain (TASP)

Without Weighting (No Noise): ________m, _______dB

Without Weighting (With Noise): ________m, _______dB TASP

With Weighting (No Noise): ________m, _______dB

With Weighting (With Noise): ________m, _______dB

2 Frequency-Domain (FASP)

Without Weighting (No Noise): ________m, _______dB TW-FASP

Without Weighting (No Noise): ________m, _______dB FW-FASP

With Weighting in Time (No Noise): ________m, _______dB

With Weighting in Time (With Noise): ________m, _______dB TW-FASP

With Weighting in Freq (No Noise): ________m, _______dB

With Weighting in Freq (With Noise): ________m, _______dB FW-FASP

CHAPTER 1: MATLAB - A VERSATILE SIMULATION TOOL

S2.C1.1 WHAT IS MATLAB?

MATLAB is a high performance language for technical computing. It integrates computation, visualization, and programming in an easy to use environment where problems and solutions are expressed in familiar mathematical notations with high precision. Typical uses include:

· Math and computation

· Algorithm development

· Modeling, simulation and prototyping

· Data analysis, exploration and visualization

· Scientific and engineering graphics

· Application development including Graphical User Interface building

MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. This allows us to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of time otherwise it would take to write a huge program in a scalar, less-interactive languages such as C or Fortran. Inherent vectorization of large data can significantly reduce the program code structure and internal memory management of MATLAB frees user from a great overhead.

The name MATLAB stands for MATRIX LABORATORY. MATLAB was originally written to provide easy access to matrix software developed by LINPACK and EISPACK projects, which together represent the state-of the art in software for Matrix computation. MATLAB has evolved over a period of years with input from many users. In university environments, it is the standard instructional tool for introductory and advanced courses in Mathematics, Engineering and Sciences. In industry, MATLAB is the tool of choice for high productivity research, development and analysis.

MATLAB features a family of application-specific solutions called toolboxes. They are very important to the high end users who are involved in learning and applying specialized technology. Toolboxes are comprehensive collection of MATLAB functions that extend the power of MATLAB environment in solving particular classes of problems. Following is the list of a few representative toolboxes of an ever-expanding library of toolboxes: Signal Processing, Control Systems, Neural Networks, Fuzzy Logic, Image Processing, Wavelets, Statistics and many others.

S2.C1.2 MATLAB SYSTEM

The MATLAB System consists of five main parts:

2.1 The MATLAB Language : This is a high-level Matrix/Array language with control flow statements, functions, data structures, input/output, and object-oriented programming features. It allows both “Programming in the Small” to rapidly create quickly and dirty throwaway programs and “Programming in Large” to create complete large and complex application programs.

2.2 The MATLAB Working Environment : This is the set of tools and facilities that you work with as a user or programmer. It includes facilities for managing the variables in your workspace and importing and exporting. It also includes tools for developing, managing and profiling M-files, MATLAB’s applications.

2.3 Handle Graphics : This is the MATLAB graphics system. It includes high-level commands for two-dimensional and three-dimensional data visualization, image processing, and animation and presentation graphics. It also includes low-level commands that allow you to fully customize the appearance of graphics as well as to build complete Graphical User Interface on your MATLAB applications.

2.4 The MATLAB Mathematical Function Library : This is a vast collection of computational algorithms ranging from elementary functions like sum, sine, cosine, and complex arithmetic to more sophisticated functions like Matrix inverse, Matrix Eigen values, Bessel functions and Fast Fourier transforms.

2.5 The MATLAB Application Program Interface (API) : This is a library that allows you to write C and Fortran Programs that interact with MATLAB. It includes facilities for calling routines from MATLAB, calling MATLAB as a computational engine, and for reading and writing MATLAB- files.

S2.C1.3 OTHER MODULES

Simulink, a companion program to MATLAB, is an interactive system for simulating non-linear dynamic systems. It is a graphical mouse driven program that allows you to model a system by drawing a block diagram on the screen and manipulating it dynamically. It can work with linear, non-linear, continuous-time, discrete-time, multivariable and multi-rate systems. Block-sets are add-ins to Simulink that provide additional libraries of block for specialized applications like Communications, Signal Processing and Power Systems. Real-time Workshop is a program that allows you to generate C code from your block diagram and run it on a variety of Real-time systems.

S2.C1.4 MATLAB & SIMULATIONS CARRIED OUT

The given tasks viz. Point Target Simulation and Azimuth Signal Processing of SAR return, in both Time-Domain and Frequency-Domain are explored with a versatile MATLAB. Lot of utilities helps to reduce the time without elaborate coding. It has been found that MATLAB with Signal Processing Toolbox is an ideal environment for simulation of a Point Target, a reliable reference for design parameters modeling, verification in a short time duration. It is also useful in strategic algorithm planning for Real-time implementation, which may be of long duration, quite complex, unforeseeable and sometimes unpredictable.

In the simulations carried out, only hand coding is used with M-files and functions instead of using Simulink. M-file gives complete control over the algorithm flow and reliable output judgment to the alterations of design parameters and offers good amount of flexibility and tractability.

Workspace concept has the wonderful advantage of preserving the past variables and automatic memory management and this feature relieves the task of handling File-I/O. Very easy plotting function with different color and style options is the key of effective waveform display and analysis. The biggest advantages are the complex multiplications, Squares, Square roots by vectorization in a single shot. Signal Processing Toolbox contains key utilities like FIR Filter design, Convolution, FFT, IFFT, Decimation, Interpolation, etc.

Because of availability of such utilities:

· More time was given for understanding highly mathematical and abstract SAR theory.

· It was possible to simulate and verify end-to-end TASP algorithm in short time duration.

· Innovative implementations of FASP algorithm were successfully carried out.

CHAPTER 2: POINT TARGET

S2.C2.1 RADAR TARGET CLASSIFICATION

Target classification requires that the radar measure with sufficient accuracy a set of target parameters that will permit it to be as a member of (or rejected as not belonging to) a class of objects the system is intended to detect, and to which it is intended to react. These classes may be broad or narrow, but will fall within those shown in Figure S2.C2.D1.

S2.C2.D1

Examples of Single or Multiple Targets are air-craft, helicopter, ballistic target, bird, man, corner reflector, ground vehicle and any distinct object with uniform scattering and probably having some shaped geometry of smaller or moderate dimensions. Clouds, aurora and large sea targets are the examples of Volume Targets. Water surface, bushes, forest and arable land fall in to Surface Target classification.

S2.C2.2 WHAT IS POINT TARGET AND WHY POINT TARGET ?

In high resolution SAR imaging, return signal is always a vector sum of scattering from various kinds of distributed targets with different properties within the illuminated ground patch. Any target (object) can be seen as or modeled as a Point Target or a set of Point Targets if it gives uniform scattering piecewise (part-wise) over the whole structure, or its dimensions (complete/part-wise) are comparable with the resolution of our interest. For the ground-mapping problem with SAR, the ground area (patch) illuminated by the narrow azimuth beam-width antenna is viewed as a 2-dimensional grid of several point targets as shown in Figure S2.C2.D2. In general even though the ground area consist of flat land, a rocky ridge, bushes, forest, sea-water, man made structures, animals, human or vehicles, has the validity of point target analysis, and any algorithm calibrated for a point target holds equally good in dealing with a massive data set associated with entire swath imaging case.

S2.C2.D2

S2.C2.3 POINT TARGET GEOMETRY FOR ASAR

In Figure S2.C2.D3 & in Figure S2.C2.D4 Point Target Geometry for ASAR in Azimuth-Slant Range plane (Top view) and in Range-Altitude plane (Elevation view) is depicted respectively. First Figure S2.C2.D3 tells about the Synthetic Aperture Length, Aperture Time for data collection and total Doppler Bandwidth from the parameters like

· The shortest Slant Range distance between air-craft and point target

· Velocity of air-craft, actual Antenna Length and Wavelength

· Horizontal (Azimuth) Antenna Beam-width q_H

Second Figure S2.C2.D4 tells about the Vertical (Range) Beam-width q_V of the antenna, Antenna Look Angle, distance of the swath from Nadir track and Swath-width.

S2.C2.D3

R1 - Minimum Near Slant Range = 8000 m

R2 - Maximum Far Slant Range » 32000 m

q1,q2 – Incidence Angles, q1 » 41.40°, q2 » 78.79°

qv – 3dB Vertical Beam-width, Range Beam-width » 37.38°

qL – Look Angle » 60°

Ws – Swath-width » 25 kms

h – Altitude » 6000 m

xd » 5.29 m

S2.C2.D4

S2.C2.4 DATA COLLECTION, STORAGE & PROCESSING

As such there is no need to have data collection and storage for a point target simulation. LFM (Chirp) data (samples) are generated in MATLAB, which are analogous to a data set (some single column) for a given Range Gate, of actually mapped 2-D data gathered during the observation time. Figure S2.C2.D5 illustratively clears the whole picture of 2-D data organization. Every PRF (Pulse Repetition Frequency) return is stored row wise from near-to-far range and each element (data) in that row corresponds to a single resolution cell in the range direction. The collection of such several PRF returns stacked together forms equal numbers of columns as the number of range gates or range cells in Range direction. Near Range column has a smaller dimension compared to a Far Range column because of different Aperture Time and different Synthetic Aperture Length for different Range Gates. Intersections of all rows and columns give formation of 2D cells, any one of that is identified as i^th range gate in j^th PRF return. Interestingly the data set, a sampled version of a return signal in both range and azimuth directions carry the LFM (Chirp) nature. Of course LFM shape row-wise is obvious, as the transmitted signal is LFM only and there is only a point target to interact with it, but because of Doppler effect the same constant transmitted frequency for all cells in a given column (Range Gate) takes the LFM shape when viewed as a return. This phenomenon called Doppler effect is the result of relative motion between a steady point target on the ground and a moving radar platform on the air-craft.

Now with the clear idea about 2-D data organization, processing is the implementation of various algorithms on a selected data set. Out of two basic types of signal processing (correlation) required for high-resolution ground imaging,

1 Range processing &

2 Azimuth processing, it is assumed to have Range processed data available for further Azimuth processing.

Here the row wise data in 2-D space are assumed to be Range compressed (processed). Azimuth processing is done to improve the Azimuth Resolution of the ground image. Time-Domain (TASP) and Frequency-Domain (FASP) are the two fundamental approaches with different implementation requirements, trade-offs, advantages and limitations generally used for Azimuth Signal Processing. Both approaches for a given point target rely on a same data set (i^th column of n 1-D samples) which is generated by LFM equation in MATLAB workspace.

S2.C2.D5

S2.C2.5 END RESULTS

After processing a given data set having LFM shape turns to be a sharp long peak with several side lobes. The amplitude of the peak is mapped with some intensity level to a corresponding pixel on the display monitor representing the characteristic of a point target. Quality of image and ground feature extraction depends on the following two End Results (outcomes) that can be derived from finally processed data set (registered data) having a distinct peak and side lobe nature.

1 Azimuth Resolution

2 ISLR (Integrated Side Lobe Ratio)

Registered data set is quite small in dimension due to moderately small Azimuth Resolution and multi-look processing necessity in practical situations. As shown in Figure S2.C2.D6, to estimate the End Results in effective manner, registered data is interpolated by some suitable factor, and from the magnitude response of the interpolated data, number of samples within 3-dB threshold are calculated. These samples are the spatial 3-dB resolution samples.

Azimuth Resolution is directly proportional to the number of 3-dB resolution samples. Formulation of exact equation for Azimuth Resolution depends on the approach used for processing. It tells about smallest possible ground feature extraction.

ISLR (dB) is the ratio of energy contained in significant side lobes around the peak and the energy within 3-dB of a peak response. ISLR tells about an image quality in terms of inter pixel interference, blurring or the sharpness of extracted features.

ISLR = Energy of the Shaded Area

Energy of the non Shaded Area

ra = Number of 3dB resolution samples

S2.C2.D6
CHAPTER 3: PARAMETERS & EQUATIONS

For a point target simulation certain system dependant parameters are involved, that characterize the real SAR system. Such standard parameters are listed with their values for both simulation approaches.

There are some flexible variables or parameters, some are common to both approaches others are algorithm selective. As an example Slant Range R is a common variable and has been by default taken as 8000 m.

Very important equations related to SAR signal processing used in both the approaches are also listed below.

S2.C3.1 FIXED- STANDARD PARAMETERS

· Antenna Length: l = 1.3 m, Antenna Width: w = 8 to 9 cm

· Transmitted Signal Wavelength: l = 0.056 m, Frequency: f = 5.3 GHz

· Speed of Air-craft: v =120 m/s

· Pulse Repetition Frequency: PRF = 500 Hz, Antenna Look Angle: q_L » 60°

· Minimum Slant Range: R1 = 8000 m, Maximum Slant Range: R2 = 32000 m

· Air-craft Altitude: h = 6000 m

· Swath-width: Ws = 25000 m

S2.C3.2 IMPORTANT EQUATIONS

· Horizontal Beam-width q_H = l/l, Vertical Beam-width q_V = l/w

· Total Doppler Bandwidth TB = 2.v/l, TB = k. AP_time

· Chirp Rate k = 2.v²/l.R

· Synthetic Length L= l.R/l, L = v.Ts

· Aperture Time AP_time = l.R/l.v = L/v

· Number of Samples Nsamp = AP_time.prf

· Bandwidth selected for required Azimuth Resolution bw, bw = k.t, t = time

· Range Resolution (Slant) dRs = c.t/2, t = Compressed pulse width

· Range Resolution (Ground) dRg = c.t/(2.sinqi), qi = Incident angle

· Azimuth Resolution dAz = v/bw

CHAPTER 4: TIME - DOMAIN APPROACH (TASP)

S2.C4.1 ALGORITHM

Basic block diagram and algorithm flow for Time-Domain approach is shown in Figure S2.C4.B1. Also an acronym guide and program flow supplement is attached in tabular form in Figure S2.C4.T1. The sequence of MATLAB m-files/ Functions is shown in Figure S2.C4.D1. All these three figures are very crucial for further enhancement, modifications and development. Time-Domain approach can be simulated through simulate.m as shown in Figure S2.C4.D1.

The entire processing is in digital domain, hence anywhere the term signal means samples only, even though for better presentation it can be plotted in continuous form in MATLAB figures at several stages during simulation.

	S2.C4.D1

S2.C4.B1

Acronym and Program Flow Supplement for Time-Domain Approach

Block Acronym	Block Name	Description	Input to the Block	Output of the Block
LFM	Linear Frequency Modulation	Generates an Ideal Input Chirp Signal	Runtime? R	yo
GN	Gaussian Noise	Generates White Gaussian Noise of Specified Power	Runtime? Noise pset	g_noise1 or g_noise
A	Addition	Adds Ideal Input Chirp with White Gaussian Noise	yo g_noise 1 or g_noise	y
PF	Pre-Filter	Selects the required bw from total Doppler bw based on number of Looks	y	c
CD5	Decimate by 5	Decimates the Pre-filtered signal by 5	c	cd
LF/LFi	Look Filtering	Separates desired number of Looks by filtering Pre-filtered & decimated signal	cd--cd1,cd2	lki
DC3i	Decimate by 3	Each look signal is again decimated by 3	lki	lkdi
MFi	Match Filtering	Look filtered & decimated i/p signals are convoluted with Reference Function	lkdi	mfoi
Di	Detection	Peak responses after match filtering are converted to magnitude responses without phase information	mfoi	dmfoi
RG	Registration	Registers or integrates the detected peaks at different times by non-coherent averaging	dmfoi	rg
EST3dB	3dB Estimation	Estimates number of samples with in 3-dB of maximum Registered output Peak.	rg	ra
Outcome1	Outcome 1	Presents Azimuth Resolution as the First Image Quality Predictor	ra	Azres
Outcome2	Outcome 2	Presents ISLR as the Second Image Quality Predictor	ra	ISLR

S2.C4.T1

S2.C4.2 BLOCKWISE DESCRIPTION

2.1. Block LFM represents the simulated version of received return in azimuth direction for a given range over a defined Aperture Time with LFM/Chirp equation as below

yo = exp (j.p.k.t²) .....................................................….(2.4.1)

Here yo is an ideal Chirp without any noise effect.

2.2. Block GN generates Additive White Gaussian Noise. It is possible to generate Real as well Complex noise with desired power level of 0.5, 1, 2 or 5 times the complex input signal power yo, which has a unit complex power, obvious from equation 2.4.1. Real noise is denoted by g_noise1 and Complex noise is by g_noise.

2.3. Block A presents the point-to-point addition of input Chirp yo and Gaussian noise g_noise1 or g_noise. It makes an ideal Chirp noisy and offers a better model of truly received return as

y = yo+0 or y = yo+g_noise1 or y = yo+g_noise...........(2.4.2)

If the inserted noise power is zero then y has the same power as yo because the power of y is an addition of power of yo (i.e. 1) and power of Gaussian noise.

2.4. Block PF represents a Pre-filter. The spectrum of input Chirp y is quite large and has a total Doppler bandwidth

TB = 2.v/l ...............................................…………….…(2.4.3)

For any moderate Azimuth Resolution we need only a small portion of this total Doppler bandwith as per

dAz = v/bw Þ bw = v/dAz...............................………………..(2.4.4)

But the inherent problem of multiplicative speckle noise associated with Active Microwave Remote Sensing forces to go for multi-look processing overhead. Hence minimum bandwidth for multi-look processing is number of look times the bandwidth (bw) calculated in equation 2.4.4. The job of Pre-filter is to separate out the required bandwidth portion of the whole Doppler spectrum for multi-look processing.

There are various ways of Pre-filter design. In this application Pre-filter is designed as a Low Pass FIR Filter with different windowing option, and with Actual and Custom Tap Lengths. Parameters needed for a low pass FIR filter design are passband and stopband cutoff frequencies, amount of allowable ripple and a sampling rate. The stringent requirement of minimum side lobe levels with less broadening for a given custom tap length finally ends up with a choice of Kaiser window. End Results of the algorithm implementation or Image quality predictors depend on the tightness or the looseness of a Pre-filter. Implementation of a Pre-filter in Time-Domain is the convolution of input Chirp y and selected window co-efficients, results in a filtered signal c for further processing.

2.5. Block DC5 decimates a Pre-filtered signal c by an integer factor 5 to simulate the need of data reduction for Real-time processing without much adverse effect on the quality of final image. Decimated signal cd is, now with a data size and sampling frequency reduced by an amount equal to the same integer factor (i.e. 5 here).

2.6 Block LE/LEi means Look Extraction or Look Filtering. The decimated signal contains a bandwidth more than the required for a single look. Look Filtering helps in segregation of several looks for independent and simultaneous processing, and speckle reduction. There are two ways for Look Filtering,

1 Design a Low Pass Filter with a fixed spectrum, and shift the input signal spectrum as required by exponential multiplication in time.

2 Transformation of LPF to BPF, shifting of spectral response of BPF as required and keeping input signal spectrum stationary.

The first method is explored here in view to adopt the same design methodology of Pre-filter with only changes in supplied parameters for Look Filter. Analogous to shifting of input spectrum in frequency is multiplication in time by an exponential factor. Depending on look bandwidth and number of multi-looks, it is at least marginally convenient to go for first method. Here the tightness or the looseness of the filter contributes a lot to the computation as a result of precise bandwidth extraction for each look. Amount of variations in shifting of input signal spectrum is also a significant factor.

Original input- decimated signal cd and its exponential multiplied versions cdi (equation 2.4.5) as an input to Look Filter produce look filtered output signals lki by the same convolution approach.

cdi= cd. exp( ± j.2.p.f0.t).........…………....................….(2.4.5)

2.7 Block DC3i again represents decimation of Look Filtered signal lki by 3; picking up every third sample of the sequence only. Output signals after DC3i are lkdi.

2.8 Block MFi is a Match Filter bank. Corresponding to each Look Filtered signal there is one Match Filter. Match Filter represents a pre-determined Reference Function similar to input Chirp but smaller in length. Match Filtering is the process of correlation between Reference Function and Look Filtered signals lkdi. It gives sharp peak response mfoi at different time indices for different looks.

2.9 Block Di is a Detection process. Peak responses after Match Filtering are complex valued. Detection means conversion of such complex valued signals to their magnitude (absolute) form, suitable for an image display. Information about phase is lost at this point. Detected outputs are dmfoi.

2.10 Block RG models Registration/Integration process of all detected looks, means the absolute peak responses at different time indices are non-coherently added and averaged. It reduces speckle noise and gives better image quality. Registered output is rg.

2.11 Outcomes: Determination of End Results/Outcomes is subsequent to the registration process. Registered output rg is small in size due to decimation by a factor of 15 during the whole process and hence it is interpolated at least by a factor of 15 for better 3-dB resolution samples estimation. Higher interpolation factors give stable estimate. With the help of 3-dB resolution samples estimate, sharpness of a registered peak response is judged in terms of Azimuth Resolution and side lobe levels & spread in terms of ISLR.

Outcome1: Azimuth Resolution : It is the first End Result after a long, complex and very involved processing chain. It should be as minimum as possible for the extraction of very minute ground features with due clarity. Azimuth Resolution in Time-Domain approach is summarized as...

Azimuth Resolution (dAz) µ v v: Velocity of Air-craft

µ 1/PRF PRF: Pulse Repetition Frequency

Outcome2: ISLR( Integrated Side Lobe Ratio) : It is the second End Result, It should be as high as possible in ( - dB scale). It can be summarized as...

ISLR = Total Energy content out of 3-dB Main Lobe & in all significant Side Lobes

Energy within 3-dB Main Lobe

S2.C4.3 RESULTS

At the end, for Time-Domain Azimuth Signal Processing Approach (TASP), several important design/simulation parameter selections, effect of parameter variations and effect of noise on the End Results are shown below as a representative set.

· System Parameters : ( Side Looking Stripmap SAR)

Velocity of Air-craft- 120 m/s

Actual Antenna Length- 1.3 m, Antenna Width- 8 to9 cm

Air-craft Altitude- 6000 m

Center Wavelength- 0.056 m

· Simulation case study :

Slant Range(R) = 8000 m, Chirp Rate (k) = 63.60 Hz/s,

Aperture Time (AP_time) =2.9028 sec

Number of Samples of i/p Chirp (No_samp) = 1451,

Synthetic Aperture Length (L) = 348.33 m,

Reference Function Length (Ref_len) = 13.62

Signal Power = 1, Noise Power (Real/Complex)= Variable (0,0.5,1,2...100)

Interpolation Factor = 15

3.1 Comprehensive summary of selected Parameter variations for a Point Target at different Slant Range (Near®Far)

S2.C4.T3.1

Parameters ¯		Slant Range R (m) from 6000m Altitude
		8000	10,000	15,000	20,000	25,000	30,000	32,000
AP_time(sec)		2.9028	3.6284	5.4427	7.2569	9.0711	10.8853	11.6110
L(m)		348.33	435.41	653.12	870.82	1088.50	1306.20	1393.30
No_samp		1451	1815	2712	3629	4537	5443	5807
K(Hz/sec)		63.60	50.88	33.92	25.44	20.35	16.96	15.90
Rf_len		13.62	17.03	25.55	34.06	42.58	51.10	54.50
Det_size		121	149	218	286	357	425	454
Det_pos	Aft	47	57	84	109	136	162	173
	Center	61	75	109	143	179	213	227
	Fore	74	92	135	177	221	264	282
Det_mag	Aft	10.58	11.12	19.60	27.15	33.21	33.47	44.25
	Center	11.12	12.93	21.38	31.31	38.72	41.31	41.74
	Fore	9.88	11.71	20.17	26.76	30.55	38.20	44.25
Rg_size		153	189	274	360	447	533	568
Rg_pos		74	92	135	177	221	264	282
Rg_mag(NW)		10.53	11.92	20.38	28.41	34.16	37.66	43.41
Rg_mag(HW)		7.53	8.89	14.72	20.27	25.02	28.14	31.57
ISLR (dB) (NW)		-9.87	-11.05	-10.32	-9.93	-10.85	-13.24	-11.31
Azres (m) (NW)		4.80	5.52	4.80	4.56	4.80	5.28	5.04
ISLR (dB) (HW)		-17.80	-17.30	-18.17	-18.54	-18.57	-18.97	-19.48
Azres (m) (HW)		6.00	5.52	5.76	5.52	5.76	5.52	5.76

3.2 Actual Tap Length of Low Pass FIR Filter with 3 different windows

S2.C4.T3.2.1 Pre-filter

fpb	fsb	Passband/stopband Ripple rp/rs (dB)	fs	Actual Tap Length
				Boxcar Nbcar	Hamming Nham	Kaiser Nkais
39	61	40	500	21	79	53
39	50	40	500	42	158	103
39	45	40	500	77	290	187
39	40	40	500	460	1735	1117
39	61	20	500	21	79	21
39	61	30	500	21	79	37
39	61	50	500	21	79	69
39	61	60	500	21	79	85

S2.C4.T3.2.2 Look Filter

fpb	fsb	Passband/Stopband Ripple rp/rs (dB)	fs	Actual Tap Length
				Boxcar Nbcar	Hamming Nham	Kaiser Nkais
13	20.33	40	100	13	48	33
13	20	40	100	14	50	33
13	15	40	100	47	174	113
13	14	40	100	92	347	225
13	20.33	30	100	13	48	23
13	20.33	50	100	13	48	41
13	20.33	60	100	13	48	51

fpb: Passband cutoff frequency rp: Passband Ripple in dB

fsb: Stopband cutoff frequency rs: Stopband Ripple in dB

fs: Sampling Rate

Nbcar: Boxcar Window Tap Length

Nham: Hamming Window Tap Length

Nkais: Kaiser Window Tap Length

3.3 Effect of different window weighting without noise

S2.C4.T3.3.1 Custom Tap Length Filtering

S2.C4.T3.3.1.1

LPF type	Fpb	Fsb	Stopband Ripple Attenuation(dB)	Fs	Window Type	Tap Length
Pre-Filter	39	61	40	500	Kaiser	31
Look Filter	13	20.33	40	100	Kaiser	31

S2.C4.T3.3.1.2 Noise Power: 0

Reference Function Weighting	3-dB resolution samples (ra)	Azimuth Resolution (Azres) m	ISLR (dB)
Boxcar	20	4.80	-9.87
Hamming	25	6.00	-17.80
Hanning	27	6.48	-21.65
Blackman	33	7.92	-20.20
Dolf-Chebyshev	28	6.72	-21.07
Kaiser	27	6.48	-21.66

S2.C4.T3.3.2 Actual Tap Length Filtering

S2.C4.T3.3.2.1

LPF type	Fpb	Fsb	Stopband Ripple Attenuation(dB)	Fs	Window Type	Tap Length
Pre-Filter	39	61	40	500	Kaiser	Actual
Look Filter	13	20.33	40	100	Kaiser	Actual

S2.C4.T3.3.2.2 Noise Power: 0

Reference Function Weighting	3-dB resolution samples (ra)	Azimuth Resolution (Azres) m	ISLR (dB)
Boxcar	21	5.04	-10.35
Hamming	25	6.00	-18.09
Hanning	27	6.48