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Hi. I am a Masters Student who requires this as a first step to start my Thesis, and I am new to matlab signal processing. I have theoretical knowledge but I just started Matlab implementation of the same. Also I am completely new to the FMCW tool chain. I have to create an FMCW signal, transmit, receive and mix them to get the IF signal, and inturn get the radar 2D matrix for post processing. But I my 2nd FFT doesnt give the correct value of velocity. I set the chirp parameters and thus obtain the Vmax and Rmax values.

There are 2 IF signals created : one the theoretical, obtained from equation, and the other is obtained from mixing the received and transmitted signals and applying a Lowpass Filter. The goal is to create a radar 2D matrix (No. of samples x No. of chirps) so that I can try post processing to get the Range and velocity. I am able to get the correct range value, but the velocity is always wrong. I am unable to figure out what's wrong. I have posted the code below. Any help would be greatly appreciated.

Thanks in advance.

close all;

clear all;

clc;

%% Params

c=3e8;

%%% Transmit side params

f0 = 10e9;

% dR = 15e-2;

% Rmax = 7.5e3;

% dV = 0.94;

% Vmax = 7.5;

B = 1e9;

T = 1e-5;

Ns = 2048;

L = 64;

% fdmax=1/(1*T);

%%% Receive side params

R1 = 70;

v1 = 50; % Corresponds to 43.2kmph

%% Derived Params

%----------------

% If Vmax, Rmax, dR, dV specified

% T = c/(4*Vmax*f0);

% B=c/(2*dR);

% Ns = (4*B*Rmax)/c;

% L = ceil(c/(2*f0*dV*T)) ; % No.of Chirps

%-------------------------------

%If B, T, Ns, L are specified

Vmax = c/(4*T*f0);

dR=c/(2*B);

m = B/T;

Rmax = Ns*c/(4*B);

dV = c/(2*f0*L*T);

%-------------------------------

% n=ceil(log10(Vmax));

% factor = roundn(Vmax,n)

% v1 = factor-v1;

%-------------------------------

t0 = 2*R1/c;

phi0 = 2*pi*f0*t0 - pi*m*(t0^2);

fb = 2*R1*m/c;

fd = -2*v1*f0/c;

% fif_val1 = fb + fd; % For comparison purpose

% fif_val2 = m*t0 +f0*2*v/c;

% v1=v1-T*1e8/2;

fif_val= fb + fd;

Ts = T/Ns;

Fs = 1/Ts;

%Therefore

t=0:Ts:T-Ts;

%

%% Big time scale

time_scale = zeros(1,L*Ns);

time_scale(1:length(t)) = t(1:end);

%% For No.of chirps = L

for i=1:L-1

time_scale((i*length(t))+1:(i+1)*length(t)) = t + (T*i);

end

% time_scale=0:Ts:T*L-Ts;

% td=1e-6;

td=2*(R1+v1.*t)/c;

% R= c*td/2

f_t = f0 + m*t;

% f_r = f0 + m*(t-td)/2;

%% For L chirps

t=time_scale;

td=2*(R1+v1.*t)/c;

f_t = repmat(f_t,1,L);

% New -----------

f_r = zeros(size(f_t));

n = ceil(t0/Ts);

f_r(n+1:end) = f_t(1:end-n);

f_r = f_r + fd;

%----------

% f_r = repmat(f_r,1,L);

f_if = f_t-f_r;

% f_if(1:n) = 0;

st = cos(2*pi.*f_t.*t);

rt = cos(2*pi.*f_r.*t);

% rt = cos(2*pi.*f_r.*(t+td)); %%%%%%%%

% rt = cos(2*pi*(f0(t-td) + m*((t-td)^2)/2));

% t = time_scale;

% st = repmat(st,1,L);

% rt = repmat(rt,1,L);

% f_t = repmat(f_t,1,L);

% f_r = repmat(f_r,1,L);

fif = rt.*st;

fif_lpf = lowpass(fif,max(f_if),2*B,'Steepness',0.8);

%% Final IF signal

fif_the = 0.5*cos(phi0 + 2*pi*fif_val.*t);

% fif_the = 0.5*cos(phi0 + 2*pi.*f_if.*t);

%% Plots

% xlimit = 2*T;

xlimit = T/2;

%-------Fig 3 For Big time scale----------%

figure(3)

subplot(511)

plot(t,st);

xlim([0 xlimit])

title("Received signal as st = cos(2*pi.*f_t.*t);")

subplot(512)

plot(t,rt);

xlim([0 xlimit])

title("Received signal as rt = cos(2*pi.*f_r.*t);")

subplot(513)

plot(t,fif);

xlim([0 xlimit])

title("IF after Mixing")

subplot(514)

plot(t,fif_lpf);

xlim([0 xlimit])

title("IF after LPF")

subplot(515)

plot(t,fif_the);

xlim([0 xlimit])

title("IF from fif_the = 0.5*cos(phi0 + 2*pi*fif_val.*t);")

figure(5)

subplot(211)

plot(t,f_t);

% xlim([0 T/10])

hold on;

grid on;

plot(t,f_r);

ylim([f0-B f0+(2*B)]);

xlim([0 T*5])

legend('f_t','f_r')

subplot(212)

plot(t,f_if);

grid on;

xlim([0 T*5])

%% Post processing

% radar_mat = reshape(fif_the,Ns,L); %% Using the Theoretical IF Signal

radar_mat = reshape(fif_lpf,Ns,L); %% Using the Mixed and LPF IF Signal

%% Window function

window_1D = hann(size(radar_mat,1));

window_2D = hann(size(radar_mat,2));

%% FFT

rfft = (fft(radar_mat.*window_1D,[],1));

rfft = rfft./max(max(rfft)); %Normalization

rfft = rfft(1:size(rfft)/2,:);

% zeroPadding = zeros(size(rfft));

% rfft = vertcat(rfft,zeroPadding);

vfft = fft(rfft.*window_2D',[],2);

%% Normalization

% normalize = vfft./max(max(vfft));

%vfft = fftshift(vfft,2)

vfft = vfft./max(max(vfft));

%% Range and Velocity vectors

R = 0:dR:Rmax-dR;

V = linspace(-Vmax, Vmax, L);

figure(4);

h=imagesc(V,R,20*log10(abs(fftshift(vfft,2))),[-60 0]);

cb = colorbar;

set(gca,'YDir','normal')

xlabel('Velocity (m/s)');

ylabel('Range (m)');

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