模糊函数

clc
clear
close all
%cw
tp = 100e-6;
fc = 10e9;
N = 90;
[t, fd] = meshgrid(linspace(-1, 1, N), linspace(-10, 10, 2*N));
A = abs(sin(pi*fd/tp*tp.*(1-abs(t*tp)/tp))/pi./fd/tp/tp./(1-abs(t*tp)/tp)).*(1-abs(t*tp)/tp);
A_norm = A/max(max(A));
% figure;surf(t, fd, A_norm, 'EdgeColor', 'none');
figure;
mesh(t, fd, A_norm);
colormap jet;
colorbar;
title('CW signal');
xlabel({'Delay(Second)'});
ylabel({'Doppler Shift(Hertz)'});
zlabel('Amplitude');

figure;
imagesc(A_norm);
colormap jet;
colorbar;
set(gca, 'XTick', [1 N/2 N]);
set(gca, 'XTickLabel', {-1 0 1});
set(gca, 'YTick', [1 N N*2]);
set(gca, 'YTickLabel', {-10 0 10});
title('CW signal');
xlabel('Delay(Second)');
ylabel('Doppler Shift(Hertz)');

figure;
contour(t, fd, A_norm);
grid on
colormap jet;
colorbar;
title('CW signal');
xlabel('Delay(Second)');
ylabel('Doppler Shift(Hertz)');

[row, col] = size(A_norm);
range_ambiguity = A_norm(row/2, :);
velocity_ambiguity = A_norm(:, col/2);

figure;
plot(t, range_ambiguity, 'b');
grid on;
title('Range Ambiguity');
xlabel('Delay');
ylabel('|\chi(\tau,0)|');

figure;
plot(fd, velocity_ambiguity, 'b');
grid on;
title('Velocity Ambiguity');
xlabel('Doppler Shift');
ylabel('|\chi(0,f_d)|');

　　

%% 线性调频信号
clc
clear 
close all

tp = 10e-6;
B = 1e6;
fc = 10e6;
k = B/tp;
N = 90;
[t, fd] = meshgrid(linspace(-1, 1,N), linspace(-20, 20, 2*N));
A = (1-abs(t*tp)/tp).*abs(sin(pi*(fd/tp*tp+B*t*tp).*(1-abs(t*tp)/tp))/pi./(fd/tp*tp+B*t*tp)./(1-abs(t*tp)/tp));
A_norm = A/max(max(A));

figure;
mesh(t, fd, A_norm);
colormap jet;
grid on
colorbar;
title('LFM');
xlabel({'Delay'});
ylabel({'Doppler Shift'});
zlabel('Amplitude');

figure;
imagesc(A_norm);
colormap jet;
colorbar;
grid on
set(gca, 'XTick', [1 N/2 N]);
set(gca, 'XTickLabel', {-1 0 1});
set(gca, 'YTick', [1 N N*2]);
set(gca, 'YTickLabel', {-20 0 20});
title('LFM');
xlabel('Delay');
ylabel('Doppler Shift');
	
figure;
contour(t, fd, A_norm);
colormap jet;
title('LFM');
xlabel('Delay');
ylabel('Doppler Shift');
colorbar;
grid on
	
[row, col] = size(A_norm);
range_ambiguity = A_norm(row/2, :);
velocity_ambiguity = A_norm(:, col/2);
figure;plot(t, range_ambiguity, 'b');grid on;
title('Range Ambiguity');
xlabel('Delay');
ylabel('|\chi(\tau,0)|');

figure;
plot(fd, velocity_ambiguity, 'b');
grid on;
title('Velocity Ambiguity');
xlabel('Doppler Shift');
ylabel('|\chi(0,f_d)|');

　　

 

%% 伪随机码（PRN）/最大长度序列（MLS）码
%Compute the ambiguity function utilizing the FFT
%through combining multiple range cuts.
clc
clear
close all
clear u ambig
N = 31;	%15, 31

switch N
	case 15
		PRN = [1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1];
	case 31
		PRN = [1 -1 -1 -1 -1 1 -1 1 -1 1 1 1 -1 1 1 ...
				-1 -1 -1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 -1];
	otherwise
		disp 'There doesn''t exist such PRN code.';
	return;
end
tau = N;
samp_num = N*10;
nfft = 2^ceil(log(samp_num)/log(2));
u(1:nfft) = 0;
j = 0;

for index = 1:10:samp_num
	j = j+1;
	u(index:index+10-1) = PRN(j);
end

if 1
	delay = linspace(0, 10*tau, nfft);
else
	delay = linspace(-tau, tau, nfft);
end
	freq_del = 8/tau/100;
	j = 0;
	vfft = fft(u, nfft);
for freq = -4/tau:freq_del:4/tau
	j = j+1;
	exf = exp(1i*2*pi*freq*delay);
	u_times_exf = u.*exf;
	ufft = fft(u_times_exf, nfft);
	prod = ufft.*conj(vfft);
	ambig(:, j) = fftshift(abs(ifft(prod))');
end
freq = -4/tau:freq_del:4/tau;
delay = linspace(-N, N, nfft);

figure;
mesh(freq, delay, ambig/max(max(ambig)));
colormap jet;
grid on
colorbar;
axis tight;
title('31-bit M sequence code');
xlabel('Doppler Shift');
ylabel('Delay');
zlabel('Amplitude');
% 		xlabel('frequency');
% 		ylabel('delay');
% 		zlabel('ambiguity function a PRN code');

figure;
contour(freq, delay, ambig/max(max(ambig)));
colormap jet;
colorbar;
grid on
title('31-bit M sequence code');
xlabel('Doppler Shift');
ylabel('Delay');
% 		xlabel('frequency');
% 		ylabel('delay');

[row, col] = size(ambig);
range_ambiguity = ambig(:, ceil(col/2));
velocity_ambiguity = ambig(ceil(row/2), :);

figure;
plot(delay, range_ambiguity/max(max(ambig)), 'b');
axis tight;
grid on;
title('Range Ambiguity');
xlabel('Delay');
ylabel('|\chi(\tau,0)|');
% 		xlabel('delay');
% 		ylabel('normalized amibiguity cut for f=0');

figure;
plot(freq, velocity_ambiguity/max(max(ambig)), 'b');
grid on;
axis tight;
title('Velocity Ambiguity');
xlabel('Doppler Shift');
ylabel('|\chi(0,f_d)|');