radar_target_generation_and_detection.m

clear all;
close all;
clc;

%Radar Specifications
%%%%%%%%%%%%%%%%%%%%%%%%%%%
Frequency_of_operation = 77e9;
Max_Range = 200;
Range_Resolution = 1;
Max_Velocity = 100;
%%%%%%%%%%%%%%%%%%%%%%%%%%%

speed_of_light = 3e8;

%User Defined Range and Velocity of target
%TODO : define the target's initial position and velocity. Note : Velocity remains contant
R = 110; % Target Initial Range
v = 50; % Target velocity
%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.


%Operating carrier frequency of Radar 
fc= 77e9;             %carrier freq
sweep_time_factor = 5.5;

B      = speed_of_light / (2 * Range_Resolution); % Bandwidth of the FMCW, Bsweep
Tchirp = (sweep_time_factor*2*Max_Range)/speed_of_light; % Chirp Time of the FMCW
slope = B/Tchirp; %slope of the FMCW                                                        
%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) = R + (v*t(i)); % range_covered
    td(i) = (2*r_t(i)) / speed_of_light; % time delay
    % *%TODO* :
    %For each time sample we need update the transmitted and
    %received signal. 
    Tx(i) = cos(2*pi*(fc*(t(i)) + (0.5 * slope * t(i)^2)));
    Rx (i)  = cos( 2*pi*( fc*(t(i)-td(i)) + (0.5 * slope * (t(i)-td(i))^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.
sig_fft = fft(Mix,Nr);  
sig_fft = sig_fft./Nr;

% *%TODO* :
% Take the absolute value of FFT output
sig_fft = abs(sig_fft);  

 % *%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.
single_side_sig_fft = sig_fft(1:Nr/2);


%plotting the range
figure ('Name','Range from First FFT')
subplot(2,1,1)

% *%TODO* :
% plot FFT output 
plot(single_side_sig_fft); 

 
axis ([0 200 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 = 10;
Td = 8;

% *%TODO* :
%Select the number of Guard Cells in both dimensions around the Cell under 
%test (CUT) for accurate estimation
Gr = 4;
Gd = 4;
% *%TODO* :
% offset the threshold by SNR value in dB
offset = 1.4;

% *%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.


   % Use RDM[x,y] as the matrix from the output of 2D FFT for implementing
   % CFAR

RDM = RDM/max(max(RDM));
for i = Tr+Gr+1:(Nr/2)-(Gr+Tr)
    for j = Td+Gd+1:Nd-(Gd+Td)
        noise_level = zeros(1,1);
        % calculate the noise SUM in the area around CUT 
        for p = i-(Tr+Gr):i+(Tr+Gr)
            for q = j-(Td+Gd):j+(Td+Gd)
                if (abs(i-p) > Gr || abs(j-q) > Gd)
                    noise_level = noise_level + 10.^(RDM(p,q)/10); %db2pow(RDM(p,q));
                end
            end
        end
        % Calculate threshold from noise average then add the offset
        % threshold = pow2db(noise_level/(2*(Td+Gd+1)*2*(Tr+Gr+1)-(Gr*Gd)-1));
        threshold = 10*log10(noise_level/(2*(Td+Gd+1)*2*(Tr+Gr+1)-(Gr*Gd)-1));
        threshold = threshold + offset;
        CUT = RDM(i,j);
        
        if (CUT < threshold)
            RDM(i,j) = 0;
        else
            RDM(i,j) = 1;
        end
    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. 
RDM(union(1:(Tr+Gr),end-(Tr+Gr-1):end),:) = 0;  % Rows
RDM(:,union(1:(Td+Gd),end-(Td+Gd-1):end)) = 0;  % Columns  








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