脉冲压缩及MATLAB仿真

function [y] = matched_filter(nscat,taup,b,rrec,scat_range,scat_rcs,winid)
eps = 1.0e-16;      % 定义了一个很小的常量，用于处理数值计算中的舍入误差，此变量未用到
% time bandwidth product
time_B_product = b * taup;      % 计算时间带宽乘积
if(time_B_product < 5 )
    fprintf('************ Time Bandwidth product is TOO SMALL ***************')
    fprintf('\n Change b and or taup')
  return
end
% speed of light
c = 3.e8; 
% number of samples
% 在匹配滤波器的应用中，时间带宽积和采样点数之间存在一定的关系。通常情况下，为了准确地捕捉信号的特征并避免信息的丢失，采样点数应该足够多，以确保在时间域内有足够的采样点来表示信号的特征。一般而言，采样点数应该大于等于时间带宽积，以确保恢复出精确的信号特征。
n = fix(5 * taup * b);  % 乘以5的目的是为了提供一定的冗余，以防止信号特征在时间域上的模糊化。
% initialize input, output and replica vectors
x(nscat,1:n) = 0.;
y(1:n) = 0.;
replica(1:n) = 0.;
% determine proper window
if( winid == 0.)
   win(1:n) = 1.;
end
if(winid == 1.);
    win = hamming(n)';
end
if( winid == 2.)
    win = kaiser(n,pi)';
end
if(winid == 3.)
    win = chebwin(n,60)';
end
% check to ensure that scatterers are within recieve window
index = find(scat_range > rrec);
if (index ~= 0)
    'Error. Receive window is too large; or scatterers fall outside window'
  return
end
% calculate sampling interval
t = linspace(-taup/2,taup/2,n);
replica = exp(i * pi * (b/taup) .* t.^2);
figure(1)
subplot(2,1,1)
plot(t,real(replica))
ylabel('Real (part) of replica')
xlabel('time in seconds')
grid
subplot(2,1,2)
sampling_interval = taup / n;       % 采样间隔
freqlimit = 0.5/ sampling_interval; % 通过将0.5除以采样间隔，可以计算出信号的最高频率，在这个频率以下的信号可以被准确地表示和恢复。
freq = linspace(-freqlimit,freqlimit,n);
plot(freq,fftshift(abs(fft(replica))));
ylabel('Spectrum of replica')
xlabel('Frequency in Hz')
grid
% 对于每个散射体，计算其距离range对应的散射信号，并将其与输出向量y相加。
 for j = 1:1:nscat
    range = scat_range(j) ;
    x(j,:) = scat_rcs(j) .* exp(i * pi * (b/taup) .* (t +(2*range/c)).^2) ; % 回波信号
    y = x(j,:)  + y;    % 回波信号相加
end
figure(2) 
y = y .* win;
plot(t,real(y),'k')
xlabel ('Relative delay - seconds')
ylabel ('Uncompressed echo')
grid
out =xcorr(replica, y);     % 计算发射信号和回波信号的相关性
out = out ./ n;             % 归一化
s = taup * c /2;            % 计算脉冲宽度taup对应的距离步长s
Npoints = ceil(rrec * n /s);	% LFM 的距离步长为 s 对应 n 个点，则 rrec 对应的点数
dist =linspace(0, rrec, Npoints);   % 基于接收窗口的范围rrec计算距离向量dist
delr = c/2/b;
figure(3)
plot(dist,abs(out(n:n+Npoints-1)),'k')
xlabel ('Target relative position in meters')
ylabel ('Compressed echo')
grid

% use this program to reproduce Fig. 5.2 of text
clear all
close all
nscat = 2; %two point scatterers
taup = 10e-6; % 10 microsecond uncompressed pulse
b = 50.0e6; % 50 MHz bandwdith
rrec = 50 ; % 50 meter processing window
scat_range = [15 25] ; % scattterers are 15 and 25 meters into window
scat_rcs = [1 2]; % RCS 1 m^2 and 2m^2
winid = 0; %no window used
[y] = matched_filter(nscat,taup,b,rrec,scat_range,scat_rcs,winid);

function [y] = stretch(nscat,taup,f0,b,rrec,scat_range,scat_rcs,winid)
eps = 1.0e-16;              % 未用到
htau = taup / 2.;           % 未用到
c = 3.e8;
trec = 2. * rrec / c;       % 接收窗时间大小 
n = fix(2. * trec * b);     % 所要求的最小样本数，足以完全描述时宽为接收窗大小，带宽为 b 的 LFM 波形
m = power_integer_2(n);     % 计算一个大于等于 n 的最小的 2 的整数幂。
nfft = 2.^m;                % 接收窗 FFT 的长度
x(nscat,1:n) = 0.;
y(1:n) = 0.;
if( winid == 0.)
   win(1:n) = 1.;
   win =win';
else
   if(winid == 1.)
      win = hamming(n);
   else
      if( winid == 2.)
         win = kaiser(n,pi);
      else
         if(winid == 3.)
            win = chebwin(n,60);
         end
      end
   end
end
deltar = c / 2. / b;            % 每个带宽单位内的传播时间
max_rrec = deltar * nfft / 2.;  % 最大可接收的传播距离
maxr = max(scat_range);
if(rrec > max_rrec | maxr >= rrec ) % 判断接收窗口的大小是否合理
   'Error. Receive window is too large; or scatterers fall outside window'
   return
end
t = linspace(0,taup,n);
% 通过循环计算每个散射体对应的压缩回波信号。首先，根据散射体的距离 range 计算相位 psi1 和 psi2，然后使用指数函数计算每个散射体对应的回波信号，并将其累加到 y 中。
for j = 1:1:nscat                       
    range = scat_range(j);% + rmin;     % 目标距离
   psi1 = 4. * pi * range * f0 / c - ...
      4. * pi * b * range * range / c / c/ taup;
   psi2 = (2*4. * pi * b * range / c / taup) .* t;
   x(j,:) = scat_rcs(j) .* exp(i * psi1 + i .* psi2);
   y = y + x(j,:);
end
figure(1)
plot(t,real(y),'k')
xlabel ('Relative delay - seconds')
ylabel ('Uncompressed echo')
grid
ywin = y .* win';
yfft = fft(y,n) ./ n;
out= fftshift(abs(yfft));
figure(2)
delinc = rrec/ n;
%dist = linspace(-delinc-rrec/2,rrec/2,n);
dist = linspace((-rrec/2), rrec/2,n);
plot(dist,out,'k')
xlabel ('Relative range in meters')
ylabel ('Compressed echo')
axis auto
grid

clear all
close all
nscat = 3;      % three point scatterers
taup = 1e-2;    % 10 millisecond uncompressed pulse
f0 = 5.6e9;     % 5.6 GHz
b = 1e9;        % 1 GHz bandwdith
rrec = 30;      % 30 meter processing window
scat_range = [2 5 10] ; % scattterers are 2 and 5 and 10 meters into window
scat_rcs = [1 1 2]; % RCS 1 m^2 and 1m^2 and 2m^2
winid = 2; % kaiser window
[y] = stretch(nscat,taup,f0,b,rrec,scat_range,scat_rcs,winid);

% use this program to reproduce Fig. 5.14 of text
clear all
eps = 1.5e-5;
t = 0:0.001:.5;                 
y = chirp(t,0,.25,20);
figure(1)
plot(t,y);
yfft = fft(y,512) ;
ycomp = fftshift(abs(ifft(yfft .* conj(yfft))));
maxval = max (ycomp);
ycomp = eps + ycomp ./ maxval; 
figure(1)
del = .5 /512.;
tt = 0:del:.5-eps;
plot (tt,ycomp,'k')
axis tight
xlabel ('Relative delay - seconds');
ylabel('Normalized compressed pulse')
grid
%change center frequency
y1 = chirp (t,0,.25,21);
y1fft = fft(y1,512);
y1comp = fftshift(abs(ifft(y1fft .* conj(yfft))));
maxval = max (y1comp);
y1comp = eps + y1comp ./ maxval; 
figure(2)
plot (tt,y1comp,'k')
axis tight
xlabel ('Relative delay - seconds');
ylabel('Normalized compressed pulse')
grid
%change pulse width
t = 0:0.001:.45;                 
y2 = chirp (t,0,.225,20);
y2fft = fft(y2,512);
y2comp = fftshift(abs(ifft(y2fft .* conj(yfft))));
maxval = max (y2comp);
y2comp = eps + y2comp ./ maxval; 
figure(3)
plot (tt,y2comp,'k')
axis tight
xlabel ('Relative delay - seconds');
ylabel('Normalized compressed pulse')
grid