Doppler Map for a beginner pulsed radar

Question

I have been assigned to simulate a Pulsed radar with Chirps hitting a moving target and then analyzing the data to create a Doppler-Range map.

Im having trouble completing some of the "algorithm's" steps(listed below):

• When correlating the signals using xcor(code below) the output signal is greater then the Matrix column size. What portion of that information is needed?

• For some reason the DFT of a column results in mainly 0 frequency.. (Picture below)

• Also, after correlating, How do I construct the map?

Algorithm:

1. Lower signal to baseband
2. For the receiving part of the n'th PRI, store the data in the n'th row of a matrix.
3. For each row, Cross-correlate it with the transmitted signal
4. DFT each column
5. Plot the doppler map

code:

%parameters
PRI=5*10^-6; 
Pw=2*10^-6; %chirp time-width
CPI=0.5*10^-3 ;
B=100*10^6;
fc=40*10^9;
PRF=1/PRI; %pulses repetition freq

N=100;  %number of PRI total
Fs=10*B; %sampling freq
dt=1/Fs;
t=0:dt:(N*PRI-dt); %complete time axis

c=3*10^8; 
R_t=400+100*(t);  % moving object
tau=2*R_t/c;  %delay of signal

M_RX=zeros([N samples]);  %Matrix Of signal receiving (R_X)
chirp=@(t)    ((0<(t)) & (t<(Pw))).*exp(1i*pi*(t-0.5*Pw).^2*B/Pw).*exp(1i*2*pi*fc*t);

for n = 0:1:(N-1)
   
    recv_sig = h_t(t-n*PRI-tau) .* exp(-1i*2*pi*fc*(t-n*PRI-tau)); %downsample+delay
    
    
    lower_b=(Pw+n*PRI)/dt;
    upper_b=ceil((n+1)*PRI/dt-1);
    %since recv_sig spans the whole time line, take only the receiving time
    %window for the current PRI:
    M_RX(n+1,:)= recv_sig( lower_b : upper_b );  
    
    tmp2=chirp(t-n*PRI); % the original transmitted signal
    [x2, lags2]=xcorr( recv_sig, tmp2);
end

Edit: DFT of column and Doppler map

Thanks alot in advance!!

Answer 1

When correlating the signals using xcor(code below) the output signal is greater then the Matrix column size. What portion of that information is needed?

This is because the default parameters of xcorr give you the full cross-correlation, which includes both negative and positive lags. This is the same thing you see when doing a convolution. In a real system, we can only observe positive lags. Thus, half of the result is not usable to you and can be discarded.

In your case, simply take the positive lag values that accommodate your desired range interval (which is established by your PRI, sample rate, etc.).

Also, after correlating, How do I construct the map?

When you say "construct", I think of the processing needed to calculate the map. This involves performing the matched-filtering and taking the Doppler DFT. What you're asking is how to display the map, and the way you proposed is one way.

I personally use surf with the shading flat option and set it to a view using view(0, -90). I like this because I want to see the raw data values, without having to contend with the RGB and index related information produced by imagesc's figure. Typically for display you want to show the power values of your data using a logarithmic scale, so you would plot the 20*log10 values.