Range Doppler Plot Radar

Dear all,

I have written a code in MATLAB to determine the range and doppler response of a single target for FMCW Radar.

I am able to determine the accurate range of target after performing the first FFT. However, as I determine the 2nd FFT to get the Doppler response, the velocity is accurately determined. However, when I plot the contour map from the 2nd FFT, the range is doubled as compared to the initial user defined range.

I think I am making some mistake in plotting the values in the final figure. I presume that there shouldn't be any fault until the end of first FFT (because range calculation after first FFT is fine). But plot after 2nd FFT shows double range.

clear all
clc;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% User Defined Range and Velocity of target
R=150; %initial distance of the target
v=50; %speed of the target (give some value between 0 and 10)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

R_max = 200;
c=3e8; %speed of light
Swp_Tm = 5.5*range2time(R_max,c);

Fs=150e6;
fc=77e9; %carrier freq
BW=150e6; %sweep freq
Slope=BW/Swp_Tm; %sweep rate

D=128; % #of doppler cells OR #of sent periods           % number of chirps
N=2^10; %for length of time
t=linspace(0,D*Swp_Tm,D*N); %total time

n=0;
Dcells_T=length(t)/D; %length of one period
Tx=zeros(1,length(t)); %transmitted signal
Rx=zeros(1,length(t)); %received signal
r_t=zeros(1,length(t));
td=zeros(1,length(t));

for i=1:length(t)
    r_t(i)=R+(v*t(i)); % range of the target in terms of its velocity and initial range
    td(i)= 2*r_t(i)/c; % delay for received signal
    if i>n*Dcells_T && i<=(n+1)*Dcells_T % doing this for D of periods (nt length of pulse)
        Tx(i)=sin(2*pi*(fc*t(i)+.5*Slope*t(i)^2-Slope*t(i)*n*Swp_Tm)); %transmitted signal
        Rx(i)=sin(2*pi*(fc*(t(i)-td(i))+.5*Slope*(t(i)-td(i))^2-Slope*(t(i)-td(i))*n*Swp_Tm)); %received signal
    else
        n=n+1;
        Tx(i)=sin(2*pi*(fc*t(i)+.5*Slope*t(i)^2-Slope*t(i)*n*Swp_Tm)); %transmitted signal
        Rx(i)=sin(2*pi*(fc*(t(i)-td(i))+.5*Slope*(t(i)-td(i))^2-Slope*(t(i)-td(i))*n*Swp_Tm)); %received signal
    end
end

figure ('Name','Transmitted, Received and Beat Signals');
subplot(3,2,1);
plot(t,Tx);
subplot(3,2,2);
spectrogram(Tx,256,250,256,Fs,'yaxis');
subplot(3,2,3);
plot(t,Rx);
subplot(3,2,4);
spectrogram(Rx,256,250,256,Fs,'yaxis');

mixer=(Tx.*Rx);  % IF
subplot(3,2,5);
spectrogram(mixer,256,250,256,Fs,'yaxis');

mix1=reshape(mixer,[length(mixer)/D,D]);   
% Row showing range info for one period
% Each column showing number of periods
[My,Ny]=size(mix1');
nfft = 2^nextpow2(Ny);
%Hann_Wnd = mix1.*hamming(Ny);  
Hann_Wnd=conj(mix1).*(hamming(Ny)*ones(1,My));         % sidelobe reduction

R_FFT = fft(Hann_Wnd,nfft)/Ny;
Range_FFT2 = abs(R_FFT);
Range_FFT = Range_FFT2 (1:nfft/2+1);
Range_FFT (2:end-1) = 2* Range_FFT(2:end-1);

range = periodogram(Hann_Wnd, hamming(length(Hann_Wnd)));
figure ('Name','Range from First FFT')
subplot(2,1,1)
plot(range);
title ('Range From Periodogram')
axis tight;
subplot(2,1,2)
plot(15*Range_FFT);
axis ([0 500 0 5]); %Zoom in
title('Range with Hann Wnd from First FFT');
xlabel('Range');
ylabel('|Amplitude|');

%DOPPLER FROM 2ND FFT
Dop=fftshift(fft(R_FFT',1024));         %Second FFT for Doppler information
[My,Ny]=size(Dop);
Range=linspace(-N,N,Ny);
doppler=linspace(-D,D,My);
figure ('Name','Range and Doppler after 2nd FFT');
subplot(3,1,1)
plot(abs(Dop),doppler);
axis tight;
subplot(3,1,2)
plot(Range,abs(Dop));
axis tight;
subplot(3,1,3);
contour(Range,doppler,abs(Dop));
axis tight;
% xlim ([0 300])
% ylim ([-200 0])
grid on;
xlabel('Range');
ylabel('Doppler')
grid minor;

[Michele Woodland]

I am trying to write a similar code where we analyze a signal collected from a radar system. We are having trouble plotting the range in meters. How would you go from the number of doppler cells (or some multiple of it) to meters so I can tell how far the object is from the radar system?

[MULLAPUDI GIRI VASU]

how to find doppler frequency?? from plot

Answer 1

[Tony Azar]

once you have your DeChirped signal, you can use the "phased.RangeDopplerResponse" from the Phased Array Toolbox and the corresponding display function. See

https://www.mathworks.com/help/phased/ref/phased.rangedopplerresponse-system-object.html?searchHighlight=phased.RangeDopplerResponse&s_tid=srchtitle_phased.RangeDopplerResponse_1

and the example "Range-Doppler Response of FMCW Signal" on the same page

For a more detailed example see the "For ... Loop" and beyond in example "Increasing Angular Resolution with Virtual Arrays" at

https://www.mathworks.com/help/phased/ug/increasing-angular-resolution-with-mimo-radars.html