LFM_radar.rar_Matched Filtering_lfm radar

% ========================================================================= % model of LFM pulse radar % ========================================================================= clear all; close all; T=10e-6; % pulse duration 10us B=30e6; % pulse bandwidth 30MHz Rmin=10000; Rmax=15000; % range of interest Rwid=Rmax-Rmin; R=[11000, 14000]; % positions of ideal point targets C=3e8; % propagation speed K=B/T; % chirp slope Twid=2*Rwid/C; % receive window in second Fs=8*B; Ts=1/Fs; % 8X sampling frequency SNR=15; % in dB scale Nwid=ceil(Twid/Ts); % receive window in sample % Gnerate the echos t=linspace(2*Rmin/C,2*Rmax/C,Nwid); % observe window % start at t=2*Rmin/C % end at t=2*Rmax/C M=length(R); % number of targets td=ones(M,1)*t-2*R'/C*ones(1,Nwid); Srt=[1 1]*(exp(j*pi*K*td.^2).*(abs(td)<T/2)); % radar echos % without noise Nchirp=ceil(T/Ts); % samples in one pulse Nfft=2^nextpow2(Nwid+Nchirp-1); Srw=fft(Srt,Nfft); t0=linspace(-T/2,T/2,Nchirp); St=exp(j*pi*K*t0.^2); Sw=fft(St,Nfft); Sot=fftshift(ifft(Srw.*conj(Sw))); % matched filtering N0=Nfft/2-Nchirp/2; Z=abs(Sot(N0:N0+Nwid-1)); Z=Z/max(Z); Z=20*log10(Z+1e-6); figure(1); subplot(211); plot(t*1e6,real(Srt)); axis tight; xlabel('Time (us)'); ylabel('Amplitude'); title('Echos without Pulse Compression'); subplot(212); plot(t*C/2,Z); axis([10000,15000,-60,0]); xlabel('Range in meters'); ylabel('Amplitude (dB)'); title('Echos with Pulse Compression'); wid=hamming(Nchirp); % windowing wSt=wid'.*St; wSw=fft(wSt,Nfft); wSot=fftshift(ifft(Srw.*conj(wSw))); % matched filtering N0=Nfft/2-Nchirp/2; wZ=abs(wSot(N0:N0+Nwid-1)); wZ=wZ/max(wZ); wZ=20*log10(wZ+1e-6); figure(2); subplot(211); plot(t*1e6,real(Srt)); axis tight; xlabel('Time (us)'); ylabel('Amplitude'); title('Echos without Pulse Compression'); subplot(212); plot(t*C/2,wZ); axis([10000,15000,-60,0]); xlabel('Range in meters'); ylabel('Amplitude (dB)'); title('Echos with Pulse Compression'); % with noise nSrt=Srt+sqrt(0.5*(1/(10^(SNR/10)))).*(randn(1,Nwid)+j*randn(1,Nwid)); nSrw=fft(nSrt,Nfft); nSot=fftshift(ifft(nSrw.*conj(Sw))); % matched filtering nZ=abs(nSot(N0:N0+Nwid-1)); nZ=nZ/max(nZ); nZ=20*log10(nZ+1e-6); figure(3); subplot(211); plot(t*1e6,real(nSrt)); axis tight; xlabel('Time (us)'); ylabel('Amplitude'); title('Echos without Pulse Compression'); subplot(212); plot(t*C/2,nZ); axis([10000,15000,-60,0]); xlabel('Range in meters'); ylabel('Amplitude (dB)'); title('Echos with Pulse Compression'); wnSot=fftshift(ifft(nSrw.*conj(wSw))); % matched filtering wnZ=abs(wnSot(N0:N0+Nwid-1)); wnZ=wnZ/max(wnZ); wnZ=20*log10(wnZ+1e-6); figure(4); subplot(211); plot(t*1e6,real(nSrt)); axis tight; xlabel('Time (us)'); ylabel('Amplitude'); title('Echos without Pulse Compression'); subplot(212); plot(t*C/2,wnZ); axis([10000,15000,-60,0]); xlabel('Range in meters'); ylabel('Amplitude (dB)'); title('Echos with Pulse Compression');