radar_target_generation_and_detection.m

clear all
close all;
clc;

%% Radar Specifications 
%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Frequency of operation = 77GHz
% Max Range = 200m
% Range Resolution = 1 m
% Max Velocity = 100 m/s
%%%%%%%%%%%%%%%%%%%%%%%%%%%

%speed of light = 3e8
%% User Defined Range and Velocity of target
% *%TODO* :
% define the target's initial position and velocity. Note : Velocity
% remains contant

target_velocity = -20;
initial_range = 110;
speed_of_light = 3e8;


%% FMCW Waveform Generation

% *%TODO* :
%Design the FMCW waveform by giving the specs of each of its parameters.
% Calculate the Bandwidth (B), Chirp Time (Tchirp) and Slope (slope) of the FMCW
% chirp using the requirements above.
max_range = 200;
Bsweep = speed_of_light / (2*1);
Tchirp= 5.5 * (2 * max_range / speed_of_light);
slope = Bsweep/Tchirp;

%Operating carrier frequency of Radar 
fc= 77e9;             %carrier freq

                                                          
%The number of chirps in one sequence. Its ideal to have 2^ value for the ease of running the FFT
%for Doppler Estimation. 
Nd=128;                   % #of doppler cells OR #of sent periods % number of chirps

%The number of samples on each chirp. 
Nr=1024;                  %for length of time OR # of range cells

% Timestamp for running the displacement scenario for every sample on each
% chirp
t=linspace(0,Nd*Tchirp,Nr*Nd); %total time for samples


%Creating the vectors for Tx, Rx and Mix based on the total samples input.
Tx=zeros(1,length(t)); %transmitted signal
Rx=zeros(1,length(t)); %received signal
Mix = zeros(1,length(t)); %beat signal

%Similar vectors for range_covered and time delay.
r_t=zeros(1,length(t));
td=zeros(1,length(t));


%% Signal generation and Moving Target simulation
% Running the radar scenario over the time. 

for i=1:length(t)         
    
    
    % *%TODO* :
    %For each time stamp update the Range of the Target for constant velocity. 
    r_t(i) = initial_range + target_velocity * t(i);
    td(i) = 2 * r_t(i) / speed_of_light;
    % *%TODO* :
    %For each time sample we need update the transmitted and
    %received signal. 
    Tx(i) = cos(2*pi*(fc*t(i) + slope*(t(i)^2)/2 ));
    delay = t(i) - td(i);
    Rx (i) = cos(2*pi*( fc*delay + slope * (delay^2)/2));
    
    % *%TODO* :
    %Now by mixing the Transmit and Receive generate the beat signal
    %This is done by element wise matrix multiplication of Transmit and
    %Receiver Signal
    Mix(i) = Tx(i)*Rx(i);
    
end

%% RANGE MEASUREMENT


 % *%TODO* :
%reshape the vector into Nr*Nd array. Nr and Nd here would also define the size of
%Range and Doppler FFT respectively.
Mix = reshape(Mix, [Nr, Nd]);
 % *%TODO* :
%run the FFT on the beat signal along the range bins dimension (Nr) and
%normalize.
signal_fft = fft(Mix, Nr); 
L = Tchirp * Bsweep;
 % *%TODO* :
% Take the absolute value of FFT output
signal_fft = abs(signal_fft/L);
 % *%TODO* :
% Output of FFT is double sided signal, but we are interested in only one side of the spectrum.
% Hence we throw out half of the samples.
signal_fft = signal_fft(1:L/2+1);

 % *%TODO* :
 % plot FFT output 
f = Bsweep*(0:(L/2))/L;
figure('Name','FFT Output')
plot(f,signal_fft)

R = (speed_of_light*Tchirp*f)/(2*Bsweep);
figure('Name','Range from First FFT')
plot(R,signal_fft) 
axis ([0 max_range 0 1]);



%% RANGE DOPPLER RESPONSE
% The 2D FFT implementation is already provided here. This will run a 2DFFT
% on the mixed signal (beat signal) output and generate a range doppler
% map.You will implement CFAR on the generated RDM


% Range Doppler Map Generation.

% The output of the 2D FFT is an image that has reponse in the range and
% doppler FFT bins. So, it is important to convert the axis from bin sizes
% to range and doppler based on their Max values.

Mix=reshape(Mix,[Nr,Nd]);

% 2D FFT using the FFT size for both dimensions.
sig_fft2 = fft2(Mix,Nr,Nd);

% Taking just one side of signal from Range dimension.
sig_fft2 = sig_fft2(1:Nr/2,1:Nd);
sig_fft2 = fftshift (sig_fft2);
RDM = abs(sig_fft2);
RDM = 10*log10(RDM) ;

%use the surf function to plot the output of 2DFFT and to show axis in both
%dimensions
doppler_axis = linspace(-100,100,Nd);
range_axis = linspace(-200,200,Nr/2)*((Nr/2)/400);
figure,surf(doppler_axis,range_axis,RDM);

%% CFAR implementation

%Slide Window through the complete Range Doppler Map

% *%TODO* :
%Select the number of Training Cells in both the dimensions.
Tr = 14;
Td = 6;

% *%TODO* :
%Select the number of Guard Cells in both dimensions around the Cell under 
%test (CUT) for accurate estimation
Gr = 6;
Gd = 3;

% *%TODO* :
% offset the threshold by SNR value in dB
offset = 6;

% *%TODO* :
%Create a vector to store noise_level for each iteration on training cells
noise_level = zeros(1,1);


% *%TODO* :
%design a loop such that it slides the CUT across range doppler map by
%giving margins at the edges for Training and Guard Cells.
%For every iteration sum the signal level within all the training
%cells. To sum convert the value from logarithmic to linear using db2pow
%function. Average the summed values for all of the training
%cells used. After averaging convert it back to logarithimic using pow2db.
%Further add the offset to it to determine the threshold. Next, compare the
%signal under CUT with this threshold. If the CUT level > threshold assign
%it a value of 1, else equate it to 0.
number_of_cells = (2 * Tr + 2 * Gr + 1) * (2 * Td + 2 * Gd + 1) - (2 * Gr + 1) * (2 * Gd + 1);
cfar_output = zeros(Nr /2 , Nd);

   % Use RDM[x,y] as the matrix from the output of 2D FFT for implementing
   % CFAR
for i = 1:(Nr/2 - (2 * Gr + 2 * Tr))
    for j = 1:(Nd - (2 * Gd + 2 * Td))
        s1 = sum(db2pow(RDM(i : i + 2*Tr+2*Gr, j : j + 2*Td+2*Gd)) , "all");
        s2 = sum(db2pow(RDM(i+Tr : i+Tr+2*Gr, j+Td : j + Td+2*Gd)) , "all");
        
        noise_level = s1 - s2;
        
        cfar_threshold = noise_level / number_of_cells;
        cfar_threshold = pow2db(cfar_threshold) + offset;
        cfar_threshold = db2pow(cfar_threshold);
        
        cut_level = db2pow(RDM(i + Tr + Gr, j + Td + Gd));
        
        if (cut_level <= cfar_threshold)
            cut_level = 0;
        else 
            cut_level = 1;
        end
        
        cfar_output(i + Tr + Gr, j + Td + Gd) = cut_level;
        
    end
end




% *%TODO* :
% The process above will generate a thresholded block, which is smaller 
%than the Range Doppler Map as the CUT cannot be located at the edges of
%matrix. Hence,few cells will not be thresholded. To keep the map size same
% set those values to 0. 
 








% *%TODO* :
%display the CFAR output using the Surf function like we did for Range
%Doppler Response output.
figure,surf(doppler_axis,range_axis,cfar_output);
colorbar;