FMCW Radar Processing for SAR

I have written some code to simulate a FMCW radar that is flying past. I have two targets in my scene which are found in the center of the aperture. I am working with a dechirped system hence, the radar equation is simplified. Although I am supposed to have two targets in the scene, when I perfrom the range FFT I only see a single target. I am not sure what I could be doing wrong. Any suggestion would be helpful. Thank you!

% FMCW Radar Simulation with Point Targets
clear;clc; close all;

% Constants
c = 3e8;                % Speed of light (m/s)

Fc = 10e9;              % Carrier frequency (Hz)
B = 500e6;              % Chirp bandwidth (Hz)
PRF = 1e3;              % Pulse Repetition Frequency 
Tp = 1e-3;              % Pulse length
H = 100;                % Height of radar  
Ys = 200;               % Y center to scene center
radarVel = 10;          % Radar Velocity

Y0 = 80; % ground range swath
Xs = 0;  % X centers
Rs = sqrt(Ys^2+H^2); % Slant Range to scene Center

pa = 0.5;% azimuth res
pr = c/2/B;% range res

% Derieved Parameters
lamC = c/Fc;
delTh = (lamC)/(2*pa);
L = Rs*delTh/sin(deg2rad(90)); % Synthetic Aperture Length (2.21)
Ta = L/radarVel; % Synthetic Aperture time (2.22)
Naz = round(PRF * Ta /2) * 2; % Number of Azimuth samples (matter of convenience)

PRI = 1/PRF; % Pulse Repetition Interval
Cr=B/PRI; % Chirprate
Rmin = sqrt((Ys-Y0/2)^2 + H^2);
Rmax = sqrt((Ys+Y0/2)^2 + H^2);
Fs = (Cr*2*(Rmax-Rmin)/c) * 2; % Sampling frequency (Hz)
ts = 1/Fs;
Nrg=ceil(2*(Rmax)/c/ts - 2*(Rmin)/c/ts); % reuturns a 1   
Nrg = 1024; % hardcoded value
ts=(2*Rmax/c-2*Rmin/c)/Nrg;     
Fs=1/ts; % new Fs

t = linspace(-Nrg/2, Nrg/2, Nrg)*ts; %demodulated fast time

% Setting up the scene geometry
sceneCenter = [0, Ys, 0];
radarPosc = [0,0,H];% Radar Coords at Aperture center along the path
tSeq = [0:Naz] * PRI;
radarPoss = radarPosc - [radarVel, 0 ,0] * ceil(Naz/2) * PRI; % Radar's Starting Position

radarSeq = zeros(3,length(tSeq)); % x y z positions of radar 
radarSeq(1,:) = radarPoss(1) + tSeq * radarVel(1);
radarSeq(2,:) = radarPoss(2) + tSeq * 0;
radarSeq(3,:) = radarPoss(3) + tSeq * 0;

radarSeq = radarSeq';

% Generation of signal
raw = zeros(Naz,Nrg);

ntargets = 2;
targets = [[0,sqrt(Rs^2-H^2)+20,0];[0,sqrt(Rs^2-H^2)-20,0]];

% Loop over each target
for i = 1:Naz
    for k = 1:ntargets
        % Calculate target range and delay
        target_range = norm(radarSeq(i,:)-targets(k,:)); % Target range
        tau = 2*target_range/c; % Target delay
        % Add received signal to total received signal
        raw(i, :) = raw(i, :) + exp(1j*2*pi*(Fc*tau + Cr*tau*t - 0.5*Cr*tau*tau));
    end
end

figure;imagesc(abs(fftshift(fft(raw,[],2)))); % Range FFT -> range

[silvia cano]

hi can you explain me . your code ? i want to made a imege from FMCW radar

Answer 1

[Abhimenyu]

Hi Hariharan,

I understand that you are unable to see two targets after performing the range FFT. The code provided by you is correct and detects two objects, but the range resolution must be increased to view them using FFT. To improve range resolution in the above code, you can decrease the pulse length “Tp” or increase the chirp bandwidth “B”. Both parameters affect the range resolution of the radar system.

You can use the following values to see the two targets,

B=5000e8; 
Tp=0.1e-3; 

However, you can experiment with the above values to get desired FFT response.

I hope this helps!

Thank you,

Abhimenyu.