Fundamentals of Radar Signal Processing Some MATLAB Tutorials

Fundamentals of Radar Signal Processing 

© 2009 Mark A. Richards, All Rights Reserved 


Some MATLAB Tutorials 

Dr Dr. Mark AA. Richards 

School of Electrical & Computer Engineering 

Georgia g Institute of Technology gy 

Atlanta, Georgia 30332-0250 

mark.richards@ece.gatech.edu

LICENSE 

• Permission to use, copy, modify and 

distribute, including the right to grant others 

rights to distribute at any tier, this software 

and its documentation for any purpose and 

without fee or royalty is hereby granted, 

provided that the following copyright and 

attribution tt ib ti and d the th disclaimer di l i (see ( next t two t 

pages) are retained in ALL copies and 

derivative works of the software and 

documentation, including modifications that 

you y 

make for internal use or for distribution. 



2

COPYRIGHT AND ATTRIBUTION 

• Except as otherwise noted, this software was 

developed by Dr. Mark A. Richards and/or Gregory 

Heim of the Georgia Institute of Technology, and was 

provided by the Georgia Institute of Technology as 

part of the professional education course 

“Fundamentals of Radar Signal Processing”, 2006 

and subsequent offerings, or by Dr. Mark A. 

Richards to accompany the book Fundamentals of 

Radar Signal Processing (McGraw-Hill, New York, 

2005). 

• Copyright 2006-2009, Mark A. Richards and/or 

Gregory Heim. All Rights Reserved. 



3

DISCLAIMER 

• All software is provided "as is". It is intended for 

tutorial and demonstration use only and is provided 

as a convenience i and d courtesy t to t the th user. No N user 

support is available. 

• The developer, developer the Georgia Institute of Technology, 

Technology 

and the Distance Learning and Professional 

Education division of the Georgia Institute of 

Technology make absolutely no warranty of 

merchantability or fitness for any use for any 

particular purpose purpose, or that the use of the software 

will not infringe on any third party patents, 

copyrights, py g , trademarks, , or other rights. g 



4


(FRSP) Tutorial MATLAB Software - 1 

• Software is available … 

– On FRSP textbook support web site at www www.radarsp.com 

radarsp com 

– On CD-ROM for FRSP professional education course 

(“short course”) 

• Software is provided as a WinZip file titled 

FRSP_Demos.zip 

• Assumes MATLAB 6 and Signal Processing 

Toolbox 

– mainly for hamming, db functions, but may be 

others 

– Used with version 7.8 (R2009a) 



5


(FRSP) Tutorial MATLAB Software - 2 

• Software contains the following GUI-based MATLAB 

demonstrations: 

– RCS of Complex Targets 

– LFM Pulse Compression 

– Multi-PRF Blind Zone Calculation 

• … and the following non-GUI-based demonstrations 

– Pulse Doppler Processing 

– Detection Calculator 

– Doppler Beam Sharpening 

– Adaptive Beamformer 

• … and the following g student project p j assignments g 

– Pulse Doppler Processing (similar to above, in project form) 

– RCS (similar to above, in project form) 

– LFM waveform and matched filtering g( (similar to above, , in project p j form) ) 

– Threshold detection 



6

Software Installation 

• Unzip FRSP_Demos.zip in the directory of your 

choice 

• This will create a new directory called FRSP_Demos 

• Start MATLAB and choose the Set Path command 

under the File menu 

• Navigate to the FRSP FRSP_Demos Demos directory and click the 

Add with Subfolders button 

• Click the Save button, and then Close 

• All of the FRSP demo software should now be in 

your y MATLAB ppath 



7



GUI-Based Demos 

8

RCS: 

GUI-Based RCS of Complex Targets 

• Angle variation of RCS of “complex target” 

composed of “many” scatterers 

– With or without “dominant scatterer” 

• RReproduces d thi this experiment: i t 

– Can vary # of scatterers, box size, 

presence/absence of dominant scatterer and 

relative strength 

– CCompare tto various i pdfs df 

– Compute autocorrelation 

lengths 

• >> RCS 

– Select/change target 

characteristics, then 

click on 

‘New Scatterers’ 

– Select/change plot 

options, then click on 

‘Compute RCS 

and Plot Results’ 



9 

Fluctuating Target Model 

Collection of Equal Size Scatterers 

1 

0.9 

0.8 

0.7 

0.6 

γ γ = 1 

0.5 

0.4 

Fluctuation model follows from 0.3 

Fluctuating Target Model 

Central Limit Theorem 

0.2 

0.1 

Collection of Scatterers with One Dominant Scatterer 

p(γ ) = 

Radar Signal Processing 

© 2005 Mark A. Richards 

1 

0 

Swerling Cases 1 and 2 

γ 

γ 

p(γ ) = e− , γ ≥ 0 

γ 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

γ 

• Exponential RCS pdf 

• chi-square with k=1 

• Sometimes called Rayleigh 

because corresponding voltage 



(not power) pdf is Rayleigh 

1 

0 


γ 

γ 

e− , γ ≥ 0 

γ 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

γ 

• Exponential RCS pdf 

• chi-square with k=1 

• Sometimes called Rayleigh 

because corresponding voltage 

(not power) pdf is Rayleigh 

p(γ ) = 4γ − 

e 

2 

γ 2γ 

0.8 

0.7 


γ 

p(γ ) = , γ ≥ 0 

0.6 

0.5 

0.4 

0.3 

0.2 

γ = 1 

• Chi-square with k=2 

0.1 

pdf for RCS 

0 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

γ 

4γ − 

e 

2 

γ 2γ 

0.8 

0.7 


γ 

, γ ≥ 0 

0.6 

0.5 

0.4 

0.3 

0.2 

γ = 1 

• Chi-square with k=2 

0.1 

pdf for RCS 

0 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 

γ 

p(γ) 



p(γ)

LFM: 

GUI-Based LFM Waveform Characteristics 

• Generates and analyzes LFM 

waveforms and corresponding 

matched filter outputs 

– Can vary pulse duration, 

bandwidth, sampling rate 

– Effects of windows 

– Two Two-scatterer scatterer resolution 

>> LFM 

– Select/change waveform, window, 

plot pot 

characteristics 

• Plots should update 

automatically 

– Click on 

‘View Additional Plots’ for 

two-scatterer and ambiguity plots 

• Caution: ambiguity function 

can be VERY slow and/or 

exhaust memory! 



10

BlindZone: 

GUI-Based Multi-PRF Blind Zone Calculator 

• Computes range-Doppler 

blind zones for multiple 

PRIs and “M-of-N” 

detection 

– Can vary # and value of 

PRIs, and the threshold (M) 

for M-of-N detection 

– Allows for clutter spectrum 

width, near-in clutter 

eclipsing 

>> BlindZone li d 

– Enter PRIs and detection 

threshold 

– Other parameters as desired 

– Click “Plot Blind Zones” 



2-of-5 example 

Single PRI Grayscale Display Mode 

11



Non-GUI-Based Demos 

12 

0 

-10 

-20 

-30 

-40 

-50 

-60 

-70 

-80 

7 

6 

range relative to CRP (km) ( 

5 

-1.5 

-1 

-0.5 

0 

0.5 

1 

1.5 

2 

4 

range (km) 

After Range Compression, Before Cross-Range Compression 

-15 -10 -5 0 5 10 15 

aperture position (m) 

RANGE-DOPPLER PLOT OF UNPROCESSED DATA 

3 

2 

1 

-80 

-60 

-40 40 

-20 

0 

20 

velocity (m/s) 

40 

60 

80

Detection Calculator Pd_calc 

• DDetection t ti calculator l l t that th t computes t Pd for non-coherent square-law 

integration of Swerling target models in Gaussian I/Q noise with a 

square-law detector 

– Implements equations in the appendix of Radar Target Detection- Detection 

Handbook of Theory and Practice by Daniel P. Meyer and Herbert A. 

Mayer, (Academic Press, 1973) (“M&M”) 

– Computes the threshold and probability of detection for the four 

standard t d d SSwerling li cases and d the th nonfluctuating fl t ti case 

– Also included is the Albersheim approximation to the nonfluctuating 

case. 

• To use: write a main program to call Pd Pd.m m 

– See examples on next two slides 

• Based on meyerfun.m, version 1.2 (by Douglas Dougherty, 

NSWC DD Code T45, T45 4/14/99) 

– meyerfun.m and a controlling GUI, meyer.m, available on MathWorks’ 

MATLAB Central file exchange, 

http://www.mathworks.com/matlabcentral/fileexchange/1569 

• Modified significantly 

– Additional cases, vectorization, numerical issues 



13

Example Calling Program #1: 

Pd_as_a_function_of_N.m 

_ _ _ _ _ 

% M file for computing a figure to illustrate the effect of 

% noncoherent integration on Pd vs. SNR for Swerling 0, 

% for Pfa = 1e-8, SNR from -2 to+15 dB, and N=1 to 100. 

% 

% Mark Richards 

% July 2002 

SNR_dB = linspace(0,15); 

Pfa = 1e-8*ones(size(SNR 1e 8 ones(size(SNR_dB)); dB)); 

% Step through the cases: 

Pd0 = Pd(1*ones(size(SNR_dB)),Pfa,SNR_dB,0); 


Pd(2* ( i (SNR dB)) Pf SNR dB 0) 




% OK, now draw the results 

plot(SNR_dB,[Pd0; Pd1; Pd2; Pd3; Pd4]) 

axis([0,15,0,1]); 

xlabel('SNR xlabel(SNR (dB)'); (dB) ); ylabel('Pd'); ylabel(Pd); grid; 

legend('N=1','N=2','N=5','N=10','N=20','Location','SouthEast'); 



Pd 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

N=1 

N=2 

N=5 

01 0.1 

NN=10 10 

N=20 

0 

0 5 10 15 

SNR (dB) 

14

Example Calling Program #1: 

Swerling_compare.m 

_ 

% M file for computing a figure to compare the 5 swerling cases + Albersheim 

% for N=10 pulses, Pfa = 1e-8, and SNR from -2 to+15 dB 

% 

% Mark Richards 

% July 2002 

1 

SNR_dB = linspace(-2,15); 

Pfa = 1e-8*ones(size(SNR_dB)); 

0.8 

N = 10*ones(size(SNR_dB)); ( ( _ )); 

0.7 

% Step through the cases: 

Pd0 = Pd(N,Pfa,SNR_dB,0); % nonfluctuating; also 

called Swerling 0 or 5 in some cases 

Pd1 = Pd(N,Pfa,SNR_dB,1); 

Pd(N Pfa SNR dB 1); 




Pd6 d6 = Pd(N,Pfa,SNR d( , a,S _d dB,6); ,6); % Albersheim's be s e s equation equat o 

% OK, now draw the results 

plot(SNR_dB,[Pd0; Pd1; Pd2; Pd3; Pd4]; Pd6) 

axis([-2,15,0,1]); 

xlabel('SNR (dB)'); ylabel('Pd'); grid; 

legend('Nonfluctuating','Swerling 1','Swerling 2','Swerling 3', ... 

'Swerling 4','Albersheim','Location','Southeast'); 



Pd 

15 

0.9 

0.6 

0.5 

0.4 

0.3 Nonfluctuating 

Swerling 1 

0.2 

Swerling 2 

Swerling 3 

0.1 

Swerling 4 

0 

-2 0 2 4 6 

SNR (dB) 

8 10 

Albersheim 

12 14

Pulse Doppler Processing Demonstration 

• Formation of a fast-time/slow-time (range/pulse #) 

data matrix for moving targets in noise and clutter 

– LFM chirp hi waveform f 

• Pulse Doppler processing for target detection; and 

range, velocity, and relative RCS estimation 

– Formation of range-Doppler matrix 

– Pulse compression 

– MTI filter compensation 

– R4 correction 

– Threshold detection 

– Peak interpolation 



16

Pulse Doppler Processing Procedure 

• Two stages 

– makePDdata creates a fast-time/slow-time data matrix that will 

support the desired scenario 

– procPDdata performs the processing 

• Stage 1: Data Creation 

– >> edit dit makePDdata k PDd t 

• Set all simulation parameters by editing input section of 

makePDdata.m 

– >> makePDdata 

• To create data set for processing 

• Output in file.mat 

– Where file is the “root file name” you y specify p y 

– Parameters logged in file.lis 

• Stage 2: Processing 

– >> procPDdata 



17

Pulse Doppler Processing Inputs 

makePDdata user input section: 

% User Input Section ############################### 

% ############################################### 

% Get root file name for saving results 

file=input('Enter root file name for data and listing files: ','s'); 

T = 10e-6; 10e 6 % ppulse lse length length, seconds 

W = 10e6; % chirp bandwidth, Hz 

fs = 12e6; % chirp sampling rate, Hz; oversample by a little 

Np = 20; % # of pulses 

jkl = 0:(Np-1); % pulse index array 

PRF = 25.0e3; % PRF in Hz 

PRI = (1/PRF); % PRI in sec 

T_0 = PRI*jkl; % relative start times of pulses, in sec 

g = ones(1,Np); % gains of pulses 

T_out = [12 38]*1e-6; % start and end times of range window 

in sec 

T_ref = 0; % system reference time in usec 

fc = 10e9; % RF frequency in Hz; 10 GHz is X-band 



18 

% Compute unambiguous Doppler interval in m/sec 

% Compute unambiguous range interval in meters 

vua = 3e8*PRF/(2*fc); 

rmin = 3e8*T_out(1)/2; 

rmax = 3e8*T_out(2)/2; 

rua = rmax-rmin; 

% Define number of targets, then range, amplitude, and 

% radial velocity of each 

Ntargets = 44; 

del_R = (3e8/2)*( 1/fs )/1e3; % in km 

ranges = [2.3 2.7 3.1 3.5]*1e3; % in km 

SNR = [10 20 15 20]; % dB 

vels = [-0.3 -0.15 +0.1 +0.25]*vua; % in m/sec 

% End User Input Section ######################### 

% ############################################

power 

40 

35 

30 

25 

20 

Pulse Doppler Processing Outputs - 1 

NONCOHERENTLY INTEGRATED RANGE TRACE 

15 

1.5 2 2.5 3 3.5 4 4.5 5 

-30 

5.5 6 

range bin 

-40 



0 

-10 

-20 

-50 

-60 

-70 

-80 80 

6 

5 

4 

range (km) 

3 

RANGE-DOPPLER PLOT OF UNPROCESSED DATA 

2 

1 

-200 

-150 

19 

-100 

-50 

0 


rangee 

(km) 

5.5 

5 

50 

4.5 

4 

3.5 

3 

2.5 

2 

100 

150 

RANGE-DOPPLER CONTOUR PLOT OF UNPROCESSED DATA 

200 

-150 -100 -50 0 


50 100 150

0 

-10 

-20 20 

-30 

-40 

-50 

-60 

-70 

-80 

-90 

6 


5 

4 

range (km) 

RANGE-DOPPLER PLOT OF CLUTTER-CANCELLED DATA RANGE-DOPPLER CONTOUR PLOT OF CLUTTER-CANCELLED DATA 

-200 



3 

2 

1 

-150 

-100 

-50 

0 

50 


100 

150 

200 

20 

range (km) 

5.5 

5 

45 4.5 

4 

3.5 

3 

2.5 

2 

-150 -100 -50 0 


50 100 150

ange (km) 

5.5 

5 

4.5 

4 

3.5 

3 

2.5 

2 


RANGE-DOPPLER CONTOUR PLOT OF CLUTTER-CANCELLED DATA 

range (km) 

4 

3.5 

3 

2.5 

2 

RANGE-DOPPLER CONTOUR PLOT OF FULLY-PROCESSED DATA 

-150 -100 -50 0 50 100 150 

-150 -100 -50 0 50 100 150 

velocity (m/s) velocity (m/s) 



power (dB) 

0 

-20 

-40 

-60 

-80 

-100 

MAXIMUM DOPPLER RESPONSE VS. RANGE 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 

-120 

range (km) 

21 

1.5 

1 

0.5

Doppler Beam Sharpening Imaging - 1 

• Closely related to the pulse Doppler demonstration and project 

• Imaging of a user-specified array of point scatterers 

• TTwo stages t 

– makeSARdata_DBS creates a fast-time/slow-time data matrix that 

will support the desired scenario 

– procSARdata procSARdata_DBS DBS performs the DBS imaging algorithm 

• Stage 1: Data Creation 

>> edit makeSARdata makeSARdata_DBS DBS 

– Set all simulation parameters by editing input section of 

makeSARdata_DBS.m 

>> makeSARdata_DBS 

– To create data set for processing 

– Output in file.mat 

• Where file is the “root file name” you specify 

• Parameters logged in file.lis 



22

Doppler Beam Sharpening Imaging - 2 

• Stage 2: Image Formation 

>> edit procSARdata_DBS 

– Set image formation option switches by editing input 

section of procSARdata_DBS.m _ 

>> procSARdata_DBS to generate DBS image 

– Range Range-compressed compressed only in Fig Fig. 1 window 

– Fully-formed image in Fig. 2 window 

– If geometric corrections selected, then 

• CCross-range resampled l d iimage iin Fi Fig. 3 window i d 

• Range curvature-corrected image in Fig. 4 window 



23

DBS Demonstration: makesardata_DBS 

% User input section ################################# 

% need a file name to store data, e.g. 'myfile' or 'temp' or 'sardata'. 

% Data will then be in 'myfile.dat', y , etc. 


DCR = 20; % cross-range resolution, m 

DR = 20; % range resolution, m 

Rcrp = 40000; % range to swath center 

v = 150; % platform velocity, m/s 

fc = 10e9; % RF frequency in Hz 

lambda = c/fc; % wavelength, m 

tau = 5e-6; % pulse length, seconds (bandwidth set by 

resolution) 

Daz = 0.2; % antenna azimuth size, m 

thetaaz = lambda/Daz; % azimuth beamwidth, radians 

BWdopp = 2*v/lambda*thetaaz; % slow time Doppler bandwidth, Hz 

Ls = 3000; % swath depth, m 

oversample oversample_st st = 2; % slow time oversample factor; higher makes 

% prettier pictures but larger data sets 

oversample_ft = 2; % fast time oversample factor, similar to slow 

time 



24 

% Define target locations, one row of (x,R) coordinates per 

target 

% Ranges are relative to the CRP range (Rcrp) above. 

% coords = [0,0]; % a single point target at the CRP 

coords = ... % a grid of 9 point targets 

[-1000,-1000; 

-1000,0; , ; 

-1000,+1000; 

0,-1000; 

0,0; 

0,+1000; 

+1000,-1000; 1000, 1000; 

+1000,0; 

+1000,+1000]; 

% End user input section 

##################################### 

% ###################################################

Sample Makesardata_DBS Output 

faast 

time (sec) 

2.6 

265 2.65 

2.7 

2.75 

2.8 

x 10 -4 



Real Part of Data Matrix 

100 200 300 

pulse number 

400 500 600 

25

DBS Demonstration: procsardata_DBS 

• %####################################################### 

• % User input section ################################### 

• % algorithm control parameters 

• dechirp = false; % use azimuth dechirp step or not 

• oversample_freq l f = 2 2; % oversampling li iin DDoppler; l bi bigger makes k bbetter tt 

• % picture but needs more memory and time 

• fix_geometry = false; % perform geometric corrections or not 

• % Get data file name 

• file=input('Enter root file name for data file: ','s'); 

• % End user input section ############################### 

• % ###################################################### 



26

angee 

relative to CRP (km) 

-1.5 

-1 

-0.5 

0 

0.5 

1 

1.5 

2 

Sample Makesardata_DBS Output, 

No Geometric Corrections 

After Range Compression, Before Cross-Range Compression 

range relativve 

to CRP (km) 

-1.5 

-1 

-0.5 

0 

05 0.5 

-15 -10 -5 0 

aperture position (m) 

5 10 15 



1 

15 1.5 

2 

Fully y Compressed p Image g 

-6 -4 -2 0 

cross-range g ( (km) ) 

2 4 

27

Sample Makesardata_DBS Output 

with Geometric Corrections 

range rellative 

to CRP (km) 

-1.5 

-1 

-0.5 

0 

0.5 

1 

1.5 



2 

Resampled and Range-Shifted Image 

-6 -4 -2 0 

cross cross-range range (km) 

2 4 6 

28

Sample procSARdata_DBS Images, 

with t aand d without t out Azimuth ut Dechirp ec p 

ΔCR ≥ λR 

• Azimuth dechirp not needed if 

• Consider R = 40 km, λ = 3 cm, ΔCR = rm 

– Violates limit limit, which is about 17 m in this case 

• Generate new data with ΔCR = 5 m, etc. 

– Process with requency oversample = 4 for good mainlobe definition 

range relative to CRP (kmm) 

-1.04 

-1.02 

-1 

-0.98 

-0.96 

-0.94 

-0.92 

Fully Compressed Image 

-1.15 -1.1 -1.05 -1 -0.95 -0.9 -0.85 

cross-range (km) 

NNo AAzimuth i th DDechirp: hi 

Cross-Range Smearing 



29 

range relative to CRP (kmm) 

-1.04 

-1.02 

-1 

-0.98 

-0.96 

-0.94 094 

-0.92 

2 

FFully ll CCompressed d IImage 

-1.1 -1.05 -1 

cross-range (km) 

-0.95 -0.9 

With Azimuth Dechirp: 

Cross-Range Resolution Goal Met

Adaptive Beamformer 

• Simple demonstration of four different beamformer patterns in 

an environment with two jammers 

– NNon-adaptive d ti (fixed) (fi d) beamformer 

b f 

– fully-adaptive beamformer using weights 

– “distortionless” beamformer 

– PPost-DFT t DFT (beamspace) (b ) beamformer 

b f 

>> edit beamform 

-1 * 

h=SI t 

– Set all parameters by editing input section of beamform.m 

– RF, jammer AOAs, powers 

– Array parameters 

– Use -30 dB Taylor weighting (or not) 

>> beamform 

– Four different patterns in four figure windows 



30

Adaptive Beamformer beamform 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

% User Input Section 

lambda = 0.03; % wavelength g 

d = lambda/2; % element spacing 

dl = d/lambda; 

N = 16; % # of array elements 

aoa_max = asin(1/2/dl); % maximum "real space" AOA (radians) 

window_on i d = ffalse; l % true t or false f l 

Nangle = 1000; % # of angles for evaluating beam pattern 

Nm1 = Nangle-1; 

t_aoa = pi/180*(0); % target AOA (radians) 

j_aoa1 = pi/180*(18); % jammer #1 AOA (radians) 

j_aoa2 = pi/180*(-33); % jammer #2 AOA (radians) 

SNR = 0; % signal to noise ratio (dB) 

JSR1 = +50; % jammer #1 to noise ratio (dB) 

JSR2 = +30; % jammer #2 to noise ratio (dB) 

% End user input section 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 



31

Outputs from beamform, Both Jammers 

in the Sidelobes, Sidelobes No Weighting 

Normalized Array Response (dBB) 

Response (dB) 

Normalized Array 

0 

-10 

-20 

-30 

-40 

-50 

-60 

0 

-10 

-20 

-30 

-40 

-50 

-60 

Unadapted Array Pattern 

-80 -60 -40 -20 0 20 40 60 80 

Angle of Arrival (degrees) 

Di Distortionless t ti l BBeamformer f AArray PPattern tt 

-80 80 -60 60 -40 40 -20 20 0 20 40 60 80 




32 

Normalized Array Response (dBB) 

Response (dB) 

Normalized Array 

0 

-10 

-20 

-30 

-40 

-50 

-60 

0 

-10 

-20 

-30 30 

-40 

-50 

-60 

Fully Adaptive Array Pattern 

-80 -60 -40 -20 0 20 40 60 80 


Post-DFT (Beamspace) Array Pattern 

-80 80 -60 60 -40 40 -20 20 0 20 40 60 80 

Angle of Arrival (degrees)

Outputs from beamform, One Jammer in 

the Mainlobe , No Weighting 

Normalized Array Response (dB) ) 

Normalized Arrayy 

Response (dB) 

0 

-10 

-20 

-30 

-40 

-50 50 

-60 

0 

-10 

-20 

-30 30 

-40 

-50 

-60 

Unadapted Array Pattern 

-80 -60 -40 -20 0 20 40 60 80 


Normalized Array Response (dB) ) 

0 

-10 

-20 

-30 

-40 

-50 50 

-60 

Fully Adaptive Array Pattern 

-80 -60 -40 -20 0 20 40 60 80 


Di Distortionless t ti l BBeamformer f AArray PPattern tt PPost-DFT t DFT (Beamspace) (B ) Array A Pattern P tt 

0 

-80 80 -60 60 -400 -200 0 200 400 60 80 




33 

Normalized Arrayy 

Response (dB) 

-10 

-20 

-30 30 

-40 

-50 

-60 

-80 80 -60 60 -400 -200 0 200 400 60 80 

Angle of Arrival (degrees)

elative probabilitty 

poower 

3 

x 10-3 

2.5 

2 

1.5 

1 

0.5 

60 

50 

40 

30 

20 

10 

PDF of RCS vs. Aspect, Large Dominant+Many Case 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

radar cross section (m 2 ) 

0 

0 50 100 150 200 250 300 350 400 



Student Projects 

34 

amplitudee 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

01 0.1 

0 

sample -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 

normalized frequency (cycles) 

0.2 0.3 0.4 0.5

Student Projects - 1 

• “Student projects” are simulation projects intended to illustrate 

radar signal behavior and/or teach students to implement 

simple signal processing algorithms 

• Included are four project topics 

– RCS statistics 

– Linear FM waveform properties and matched filtering 

– Pulse Doppler processing and detection 

– CFAR detection 

• For each project, p j the following g are provided: p 

– Example problem assignment in Microsoft Word format 

– Example problem solution consisting of 

• Sample MATLAB code 

• Microsoft Word document describing the solution 



35


• Document note for all projects: Equations in the 

problem assignment and solution documents were 

created in MathType. MathType is an upgrade to 

Microsoft’s Equation Editor. It can edit equations 

created in Equation Editor, however, the converse is 

not true. In addition, MathType may use some fonts or 

characters not available on machines on which it is not 

installed installed. Consequently, Consequently it is recommended that the 

user install MathType if it is desired to work with the 

student project assignment and solution documents. 

MathType is available at 

www.dessci.com/en/products/mathtype/. 



36


• All projects are self-contained and self-explanatory 

using the problem assignment document, except for 

the pulse Doppler project 

• Th The pulse l Doppler D l project j t requires i that th t data d t be b 

generated by the instructor, to be analyzed by the 

students. 

• The following charts provide some additional detail 

on creating ti data d t for f the th pulse l Doppler D l project j t and d 

then using that data in the sample solution. 



37

MTI + Pulse Doppler Processing 

• Place all files in the Pulse Doppler directory in the MATLAB 

work directory 

– Or anywhere on the MATLAB path 

>> edit makedata 

– Set all parameters by editing input section of makedata.m 

– Includes noise, clutter, moving targets, and R4 • RRadar d parameters: RF RF, PRF PRF, range window i d 

• Target SNR, ranges, velocities, #of targets 

• CNR 

>> makedata 

– To create data set for processing 

– Output data in file.mat 

• Where file is the “root file name” you specify 

• PParameters t logged l d iin 

file.lis 

>> procdata 

– To perform MTI + pulse Doppler processing, generate displays 

• Input is in same file file.mat mat specified in makedata 

• Program pauses at every graph; hit any key to continue 



38

Create PD Data: makedata 

% User Input Section #################################### 

% #################################################### 

% Get root file name for saving results 


T = 10e-6; % pulse length, seconds 

W = 10e6; % chirp bandwidth, Hz 

fs = 12e6; % chirp sampling rate, Hz; oversample by a little 

Np = 20; % # of pulses 

jkl = 0:(Np 0:(Np-1); 1); % pulse index array 

PRF = 25.0e3; % PRF in Hz 

PRI = (1/PRF); % PRI in sec 

T_0 = PRI*jkl; % relative start times of pulses, in sec 

g = ones(1,Np); ( p) % gains g of pulses p 

T_out = [12 38]*1e-6; % start and end times of range window in 

sec 

T_ref = 0; % system reference time in usec 

fc = 10e9; % RF frequency in Hz; 10 GHz is X-band 



39 

% Compute unambiguous Doppler interval in m/sec 

% Compute unambiguous range interval in meters 

vua = 3e8*PRF/(2*fc); 

rmin = 3e8*T_out(1)/2; 

rmax = 3e8*T_out(2)/2; 

rua = rmax-rmin; 

% Define number of targets, then range, amplitude, and 

% radial velocity of each 

Ntargets = 4; 

del del_R R = (3e8/2)*( 1/fs )/1e3; % in km 

ranges = [2.3 2.7 3.1 3.5]*1e3; % in km 

SNR = [10 20 15 20]; % dB 

vels = [-0.3 -0.15 +0.1 +0.25]*vua; % in m/sec 

% End User Input Section ############################### 

% #############################################

amplitude (dBB) 

30 

20 

10 

-10 

Final Output from makedata 

0 

-20 

-30 30 



-40 

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 

distance (km) 

40

Process PD Data: procdata 

• No parameters to set 

• Some sample figures: 



power (dB) 

0 

-10 

-20 

-30 

-40 40 

-50 

-60 

-70 

-80 

-90 

41 

MAXIMUM DOPPLER RESPONSE VS VS. RANGE 

-100 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 

range (km)



Missing Pieces? 

• Contact Mark Richards by ee-mail, mail, 

mark.richards@ece.gatech.edu 

42

Fundamentals of Radar Signal Processing Some MATLAB Tutorials

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