% rho_r = c/(2*Fr)而不是rho_r = c/(2*Bw)
% Hsrcf exp函数里忘记乘pi了
clc
clear
close all参数设置
距离向参数设置
R_eta_c = 20e3;             % 景中心斜距
Tr = 2.5e-6;                % 发射脉冲时宽
Kr = 20e12;                 % 距离向调频率
alpha_os_r = 1.2;           % 距离过采样率
Nrg = 320;                  % 距离线采样数
距离向参数计算
Bw = abs(Kr)*Tr;            % 距离信号带宽
Fr = alpha_os_r*Bw;         % 距离向采样率
Nr = round(Fr*Tr);          % 距离采样点数（脉冲序列长度）
方位向参数设置
c = 3e8;                    % 光速
Vr = 150;                   % 等效雷达速度
Vs = Vr;                    % 卫星平台速度
Vg = Vr;                    % 波束扫描速度
f0 = 5.3e9;                 % 雷达工作频率
Delta_f_dop = 80;           % 多普勒带宽
alpha_os_a = 1.25;          % 方位过采样率
Naz = 256;                  % 距离线数
theta_r_c = 21.9;            % 波束斜视角
方位向参数计算
lambda = c/f0;              % 雷达工作波长
eta_c = -R_eta_c*sind(theta_r_c)/Vr;% 波束中心偏移时间
f_eta_c = 2*Vr*sind(theta_r_c)/lambda;% 多普勒中心频率
La = 0.886*2*Vs*cosd(theta_r_c)/Delta_f_dop;% 实际天线长度
Fa = alpha_os_a*Delta_f_dop;% 方位向采样率
Ta = 0.886*lambda*R_eta_c/(La*Vg*cosd(theta_r_c));% 目标照射时间
R0 = R_eta_c*cosd(theta_r_c);% 最短斜距
Ka = 2*Vr^2*cosd(theta_r_c)^3/(lambda*R0);% 方位向调频率
theta_bw = 0.886*lambda/La; % 方位向3dB波束宽度
theta_syn = Vs/Vg*theta_bw; % 合成角
Ls = R_eta_c*theta_syn;     % 合成孔径
其他参数计算
rho_r = c/2/Fr;             % 距离向分辨率 
rho_a = La/2;               % 方位向分辨率
Trg = Nrg/Fr;               % 发射脉冲宽度
Taz = Naz/Fa;               % 目标照射时间
d_t_tau = 1/Fr;             % 距离向采样时间间隔
d_t_eta = 1/Fa;             % 方位向采样时间间隔
d_f_tau = Fr/Nrg;           % 距离向采样频率间隔
d_f_eta = Fa/Naz;           % 方位向采样频率间隔目标设置
设置目标点距离景中心的距离
% A_r = -50;A_a = -50;
% B_r = -50;B_a = +50;
C_r = +50;C_a = +90;
坐标
% A_x = R0+A_r;A_y = A_a;
% B_x = R0+B_r;B_y = B_a;
C_x = R0+C_r;C_y = C_a;
N_position = [%A_x,A_y;B_x,B_y;C_x,C_y];
波束中心穿越时刻
N_target = 1;
Target_eta_c = zeros(1,N_target);
for i = 1:N_targetDelta_Y = N_position(i,2)-N_position(i,1)*tand(theta_r_c);Target_eta_c(i) = Delta_Y/Vs;
end
绝对零多普勒时刻
Target_eta_0 = zeros(1,N_target);
for i = 1:N_targetTarget_eta_0(i) = N_position(i,2)/Vs; 
end变量设置
时间变量：以景中心绝对零多普勒时刻作为方位向零点
t_tau = (-Trg/2:d_t_tau:Trg/2-d_t_tau)+2*R_eta_c/c;     % 距离时间变量
t_eta = (-Taz/2:d_t_eta:Taz/2-d_t_eta)+eta_c;           % 方位时间变量
r_tau = (t_tau*c/2)*cosd(theta_r_c);                    % 最近距离变量
频率变量
f_tau = fftshift(-Fr/2:d_f_tau:Fr/2-d_f_tau);           % 距离频率变量
f_tau = f_tau-round((f_tau-0)/Fr)*Fr;                   % 将频率折叠入(-Fr/2,Fr/2)，距离可观测频率变量
f_eta = fftshift(-Fa/2:d_f_eta:Fa/2-d_f_eta);           % 方位频率变量
f_eta = f_eta-round((f_eta-f_eta_c)/Fa)*Fa;             % 将频率折叠入f_eta_c附近(-Fa/2,Fa/2)范围，方位可观测频率变量
坐标设置
[t_tauX,t_etaY] = meshgrid(t_tau,t_eta);                % 距离时间X轴，方位时间Y轴
[f_tauX,f_etaY] = meshgrid(f_tau,f_eta);                % 距离频域X轴，方位频域Y轴
[r_tauX,f_eta_Y] = meshgrid(r_tau,f_eta);               % 距离长度X轴，方位频域Y轴信号设置，原始回波生成
tic                                                     % 计时，与toc搭配使用
wait_title = waitbar(0,'开始生成回波数据 ...'); 
pause(1);
st_tt = zeros(Naz,Nrg);
for i = 1:N_targetR_eta = sqrt(N_position(i,1)^2+Vs^2*(t_etaY-Target_eta_0(i)).^2);% 瞬时斜距，还有近似公式可以尝试A0 = [1,1,1,1]*exp(+1j*0);                          % 后向散射系数wr = (abs(t_tauX-2*R_eta/c)<=Tr/2);                 % 距离向包络wa = sinc(0.886*atan(Vs*(t_etaY-Target_eta_c(i))/N_position(i,1))/theta_bw).^2;% 方位向包络，用波束穿越时刻
%     wa = sinc(0.886*(atan(Vs*(t_etaY-Target_eta_0(i))/N_position(i,1))+theta_r_c)/theta_bw).^2;st_tt_target = A0(i)*wr.*wa.*exp(-1j*4*pi*f0*R_eta/c)....*exp(1j*pi*Kr*(t_tauX-2*R_eta/c).^2);st_tt = st_tt+st_tt_target;pause(0.001);time = toc;Display_Data = num2str(roundn(i/N_target*100,-1));Display_Str  = ['Computation Progress',Display_Data,'%',' --- ',...'Using Time: ',num2str(time)];waitbar(i/N_target,wait_title,Display_Str);         % 三参数：进度，句柄，展示的话
end
pause(1);
close(wait_title);
tocH = figure();
set(H,'position',[100,100,600,600]);
subplot(221)
imagesc(real(st_tt))
xlabel('距离时间(采样点)'),ylabel('方位时间(采样点)'),title('(a)实部')
subplot(222)
imagesc(imag(st_tt))
xlabel('距离时间(采样点)'),ylabel('方位时间(采样点)'),title('(b)虚部')
subplot(223)
imagesc(abs(st_tt))
xlabel('距离时间(采样点)'),ylabel('方位时间(采样点)'),title('(c)幅度')
subplot(224)
imagesc(angle(st_tt))
xlabel('距离时间(采样点)'),ylabel('方位时间(采样点)'),title('(d)相位')一次距离压缩
方式三：根据脉冲频谱特性直接在频域生成频域匹配滤波器
window = kaiser(Nrg,2.5)';              % 时域窗
Window = fftshift(window);              % 频域窗
% 计算滤波器
Hrf = (abs(f_tauX)<=Bw/2).*Window.*exp(+1j*pi*f_tauX.^2/Kr);
Sf_ft = fft(st_tt,Nrg,2);
Srf_ft = Sf_ft.*Hrf;
srt_tt = ifft(Srf_ft,Nrg,2);figure('Name','一次距离压缩'),subplot(121)
imagesc(real(srt_tt))
xlabel('距离时间(采样点)'),ylabel('方位时间(采样点)'),title('(a)实部')
subplot(122)
imagesc(abs(srt_tt))
xlabel('距离时间(采样点)'),ylabel('方位时间(采样点)'),title('(b)虚部')% 方位向FFT
% Saf_tf = fft(srt_tt,Naz,1);
% 
% figure('Name','方位FFT'),subplot(121)
% imagesc(real(Saf_tf)),set(gca,'YDir','normal')
% xlabel('距离时间(采样点)'),ylabel('方位时间(采样点)'),title('(a)实部')
% subplot(122)
% imagesc(abs(Saf_tf)),set(gca,'YDir','normal')
% xlabel('距离时间(采样点)'),ylabel('方位时间(采样点)'),title('(b)幅度')
二次距离压缩
D0 = sqrt(1-lambda^2*f_eta_c^2/(4*Vr^2));
Kscr = 2*Vr^2*f0^3*D0^3/(c*R0*f_eta_c^2);
Hsrcf = exp(-1j*pi*f_tauX.^2/Kscr);Srf_ff = fft(Srf_ft,Naz,1);
% Srf_tf = ifft(Srf_ff,Nrg,2);
% figure,imagesc(abs(Srf_tf)),title('方位向FFT'),set(gca,'YDir','normal')% S_ff = fft(Saf_tf,Nrg,2);
S_ff_scr = Srf_ff.*Hsrcf;
S_tf_scr = ifft(S_ff_scr,[],2);
s_tt_scr = ifft2(S_ff_scr);figure,imagesc(abs(S_tf_scr)),set(gca,'YDir','normal'),title('SRC')% figure
% subplot(121),imagesc(abs(Srf_tf)),set(gca,'YDir','normal')
% subplot(122),imagesc(abs(S_tf_scr)),set(gca,'YDir','normal')% S_ff_1 = fft(Srf_tf,Naz,1);
% S_ff_scr_1 = S_ff_1.*Hsrcf;
% S_tf_scr = ifft(S_ff_scr_1,[],2);
%  绘图
H5 = figure('Name','二次距离压缩后');
set(H5,'position',[100,100,600,300]); 
subplot(121),imagesc(real(s_tt_scr))
%  axis([0 Naz,0 Nrg])
xlabel('距离时间(采样点)→'),ylabel('←方位时间(采样点)'),title('(a)实部')
subplot(122),imagesc( abs(s_tt_scr))
%  axis([0 Naz,0 Nrg])
xlabel('距离时间(采样点)→'),ylabel('←方位时间(采样点)'),title('(b)幅度')距离徙动校正——8点插值
% RCM = lambda^2*r_tauX.*f_etaY.^2/(8*Vr^2);
% RCM = R0+RCM-R_eta_c;                       % 将距离徙动量转换到原图坐标系下
D = sqrt(1-lambda^2*f_etaY.^2/(4*Vr^2));              % 距离多普勒域中的徙动因子
RCM = r_tauX./D-r_tauX;
RCM = R0+RCM-R_eta_c;                       % 将距离徙动量转换到原图坐标系下
offset = RCM/rho_r;                         % 将距离徙动量转换为距离单元偏移量
计算插值表
x_tmp = repmat(-4:3,[16,1]);                % 插值长度
x_tmp = x_tmp+repmat(((1:16)/16).',[1,8]);   % 量化位移
% figure,imagesc(repmat(((1:16)/16)',[1,8])),colorbar
% figure,imagesc(repmat(-4:3,[16,1])),colorbar
% figure,imagesc(repmat(((1:16)/16)',[1,8])+repmat(-4:3,[16,1])),colorbar
hx = sinc(x_tmp);                           % 生成插值核
% % figure,imagesc(hx)
hx = kaiser(8,2.5)'.*hx;
hx = hx./sum(hx,2);                         % 归一化
插值表校正
Srcmf_tf_8 = zeros(Naz,Nrg);
for a_tmp = 1:Nazfor r_tmp = 1:Nrgoffset_ceil = ceil(offset(a_tmp,r_tmp));offset_frac = round((offset_ceil-offset(a_tmp,r_tmp))*16);if offset_frac == 0Srcmf_tf_8(a_tmp,r_tmp) = S_tf_scr(a_tmp,ceil(mod(r_tmp+offset_ceil-0.1,Nrg)));elseSrcmf_tf_8(a_tmp,r_tmp) = S_tf_scr(a_tmp,ceil(mod((r_tmp+offset_ceil-4:r_tmp+offset_ceil+3)-0.1,Nrg)))*hx(offset_frac,:).';endend
endfigure('Name','8点距离徙动校正'),subplot(121)
imagesc(real(Srcmf_tf_8)),set(gca,'YDir','normal')
xlabel('距离时间(采样点)'),ylabel('方位频率(采样点)'),title('(a)实部')
subplot(122)
imagesc(abs(Srcmf_tf_8)),set(gca,'YDir','normal')
xlabel('距离时间(采样点)'),ylabel('方位频率(采样点)'),title('(b)幅度')方位压缩
Ka = 2*Vr^2*cosd(theta_r_c)^3./(lambda*r_tauX);
Haf = exp(-1j*pi*f_etaY.^2./Ka);                    % 匹配滤波器
Haf_offset = exp(-1j*2*pi*f_etaY*eta_c);            % 时间补偿项
Soutf_tf = Srcmf_tf_8.*Haf.*Haf_offset;
soutt_tt = ifft(Soutf_tf,Naz,1);绘图
H1 = figure();
set(H1,'position',[100,100,600,300]); 
subplot(121),imagesc(real(soutt_tt))
xlabel('距离时间(采样点)→'),ylabel('←方位时间(采样点)'),title('(a)实部')
subplot(122),imagesc( abs(soutt_tt)),colorbar
xlabel('距离时间(采样点)→'),ylabel('←方位时间(采样点)'),title('(b)幅度')点目标分析
len = 16;
cut = -len/2:len/2-1;
% sout_tt_C = soutt_tt(round(Naz/2+1+N_position(3,2)/Vr*Fa)+cut, ...
%                     round(Nrg/2+1+2*(N_position(3,1)-R0)/c*Fr)+cut);
sout_tt_C = soutt_tt(226+cut, 181+cut);
figure,imagesc(abs(sout_tt_C)),title('切片')Sout_ff_C = fft2(sout_tt_C);
figure,imagesc(abs(Sout_ff_C)),set(gca,'YDir','normal')len = 48;
cut = -len/2:len/2-1;
% sout_tt_C = soutt_tt(round(Naz/2+1+N_position(3,2)/Vr*Fa)+cut, ...
%                     round(Nrg/2+1+2*(N_position(3,1)-R0)/c*Fr)+cut);
sout_tt_C_1 = soutt_tt(226+cut, 181+cut);
figure,imagesc(abs(sout_tt_C_1)),title('切片')Sout_ff_C_1 = fft2(sout_tt_C_1);
figure,imagesc(abs(Sout_ff_C_1)),set(gca,'YDir','normal')Start_ff_1 = Sout_ff_C;% 高频补零
Start_buling_1 = zeros(len,16*len);
Start_buling_2 = zeros(16*len,16*len);
% 行补零
for i = 1:len[~,I] = min(Start_ff_1(i,:));Start_buling_1(i,1:I) = Start_ff_1(i,1:I);Start_buling_1(i,16*len-(len-I)+1:16*len) = Start_ff_1(i,I+1:end);
end
% 列补零
for i = 1:16*len[~,I] = min(Start_buling_1(:,i));Start_buling_2(1:I,i) = Start_buling_1(1:I,i);Start_buling_2(16*len-(len-I)+1:16*len,i) = Start_buling_1(I+1:end,i);
endstart_tf_1 = ifft(Start_buling_2,[],2);
start_tt_2 = ifft(start_tf_1,[],1);
% Start_ff_2 = fft2(start_tt_2);
% figure,imagesc(abs(fftshift(Start_ff_2))),set(gca,'YDir','normal')figure('Name','高频补零'),imagesc(abs(start_tt_2))
contour(abs(start_tt_2),15)% p为行索引，q为列索引
[aa,p] = max(start_tt_2);
[bb,q] = max(max(start_tt_2));% 距离切片
start_r = abs(start_tt_2(p(q),:));
start_r = db(start_r/max(start_r));
figure,plot(start_r),ylim([-35,0])% 方位切片
start_a = abs(start_tt_2(:,q));
start_a = db(start_a/max(start_a));
figure,plot(start_a),ylim([-35,0])% 距离向相位
start_r_p = rad2deg(angle(start_tt_2(p(q),:)));
figure,plot(start_r_p),xlim([0,16*len])% 方位向相位
start_a_p = rad2deg(angle(start_tt_2(:,q)));
figure,plot(start_a_p),xlim([0,16*len])