MATLAB Examples

Figure 48.1. Adapted Pattern for PRI-staggered post-Doppler STAP for K=2.

Contents

Coded by Ilias Konsoulas, 16 Sept. 2018. Code provided for educational purposes only. All rights reserved.

clc; clear; close all;

Radar System Operational Parameters

radar_oper_params;

Thermal Noise Power Computation

thermal_noise_power;

Thermal Noise Covariance Matrix

Rn = sigma2*eye(M*N);

Clutter Patch RCS Computation

clutter_patch_rcs;

Calculate the Array Transmit and Element Receive Power Gains

Tx_Rx_power_gains;

Calculate the Clutter to Noise Ratio (CNR) for each azimuth angle

ksi = Pt*Gtgain.*Grec*lambda^2*sigma/((4*pi)^3*Pn*10^(Ls/10)*Rcik^4);   % Eq. (58)

Clutter Covariance Matrix Computations

beta = 1;   % beta parameter.
phia = 0;   % Velocity Misalignment Angle.

Rc = clutt_cov(ksi,beta);

Jamming Covariance Matrix Calculation

jamm_cov;

Total Interference Covariance Matrix

Ru = Rc + Rj + Rn;                                                      % Eq. (98)
InvRu = inv(Ru);

Target Space-Time Steering Vector

phit = 0; thetat = 0;                 % Target azimuth and elevation angles in degrees.
fdt = 100;                            % Target Doppler Frequency.
fspt = d/lambda*cos(thetat*pi/180)*sin(phit*pi/180);
omegat = fdt/fr;
bt = exp(-1i*2*pi*omegat*(0:M-1)).';  % Target Doppler Steering Vector.
at = exp(-1i*2*pi*fspt*(0:N-1)).';    % Target Spatial Steering Vector.
ta = chebwin(N,30);                   % 30 dB Chebychev Spatial Tapper.
gt = kron(bt,ta.*at);

Doppler Filter Bank Creation:

dopplerfilterbank = linspace(-150,150,M+1);
omegadopplerbank = dopplerfilterbank/fr;

Doppler Filter Matrix Construction for PRI-Staggered Post-Doppler method:

K = 2;
M1= M - K +1;

U1 = zeros(M1,M);
for m=1:M
    U1(:,m) =  1/sqrt(M)*exp(-1i*2*pi*omegadopplerbank(m)*(0:M1-1)); % Doppler Filter Steering Vector
end

td0   = ones(M1,1);
td30 = chebwin(M1,30);                                               % 30-dB Chebyshev Doppler Taper.
td60 = chebwin(M1,60);                                               % 60-dB Chebyshev Doppler Taper.
td90 = chebwin(M1,90);                                               % 90-dB Chebyshev Doppler Taper.

F0   = diag(td0)*U1;                                                 % Eq. 227.
F30 = diag(td30)*U1;
F60 = diag(td60)*U1;
F90 = diag(td90)*U1;

Create Doppler Filter Bank in Fm Matrix for PRI-Staggered Post-Doppler method

Fm0   = zeros(M,K,M);
Fm30 = zeros(M,K,M);
Fm60 = zeros(M,K,M);
Fm90 = zeros(M,K,M);
for m=1:M
    Fm0(:,:,m)  = toeplitz([F0(:,m);  zeros(K-1,1)],[F0(1,m)  zeros(1,K-1)]);  % Eq. 229.
    Fm30(:,:,m) = toeplitz([F30(:,m); zeros(K-1,1)],[F30(1,m) zeros(1,K-1)]);
    Fm60(:,:,m) = toeplitz([F60(:,m); zeros(K-1,1)],[F60(1,m) zeros(1,K-1)]);
    Fm90(:,:,m) = toeplitz([F90(:,m); zeros(K-1,1)],[F90(1,m) zeros(1,K-1)]);
end


m = 16;      % This is the Target's Doppler Bin.

PRI-Staggered Computations

f0m   = Fm0(:,:,m);
f30m = Fm30(:,:,m);
f60m = Fm60(:,:,m);
f90m = Fm90(:,:,m);

R0um   = kron(f0m,eye(N))'*Ru*kron(f0m,eye(N));
R30um = kron(f30m,eye(N))'*Ru*kron(f30m,eye(N));
R60um = kron(f60m,eye(N))'*Ru*kron(f60m,eye(N));
R90um = kron(f90m,eye(N))'*Ru*kron(f90m,eye(N));

gt0m   =  kron(f0m,eye(N))'*gt;
gt30m =  kron(f30m,eye(N))'*gt;
gt60m =  kron(f60m,eye(N))'*gt;
gt90m =  kron(f90m,eye(N))'*gt;

w0m   = R0um\gt0m;    % Calculate K*N X 1 Adaptive Weight for m-th Doppler Bin.
w30m = R30um\gt30m;
w60m = R60um\gt60m;
w90m = R90um\gt90m;

w0   = kron(f0m,eye(N))*w0m;
w30 = kron(f30m,eye(N))*w30m;
w60 = kron(f60m,eye(N))*w60m;
w90 = kron(f90m,eye(N))*w90m;

Adapted Patterns

phi = -90:90; Lphi = length(phi);
fd = -150:150;   Lfd = length(fd);
fsp = d/lambda*cos(theta*pi/180)*sin(phi*pi/180);
omega = fd/fr;
Pw0 = zeros(Lfd,Lphi);
Pw30 = zeros(Lfd,Lphi);
Pw60 = zeros(Lfd,Lphi);
Pw90 = zeros(Lfd,Lphi);
for m1=1:Lphi
    for n=1:Lfd
        a = exp(-1i*2*pi*fsp(m1)*(0:N-1));           % Dummy Spatial Steering Vector.
        b = exp(-1i*2*pi*omega(n)*(0:M-1));     % Dummy Doppler Steering Vector
        v = kron(b,a).';
        Pw0(n,m1)   = abs(w0'*v)^2;
        Pw30(n,m1) = abs(w30'*v)^2;
        Pw60(n,m1) = abs(w60'*v)^2;
        Pw90(n,m1) = abs(w90'*v)^2;
    end
end

Normalisation

max_value0   = max(max(Pw0));
max_value30 = max(max(Pw30));
max_value60 = max(max(Pw60));
max_value90 = max(max(Pw90));

Pw0 = Pw0/max_value0;
Pw30 = Pw30/max_value30;
Pw60 = Pw60/max_value60;
Pw90 = Pw90/max_value90;

[rows0 cols0] = find(10*log10(abs(Pw0))<-150);
for i=1:length(rows0)
    Pw0(rows0(i),cols0(i)) = 10^(-150/10);
end

[rows30 cols30] = find(10*log10(abs(Pw30))<-150);
for i=1:length(rows30)
    Pw30(rows30(i),cols30(i)) = 10^(-150/10);
end

[rows60 cols60] = find(10*log10(abs(Pw60))<-150);
for i=1:length(rows60)
    Pw60(rows60(i),cols60(i)) = 10^(-150/10);
end

[rows90 cols90] = find(10*log10(abs(Pw90))<-150);
for i=1:length(rows90)
    Pw90(rows90(i),cols90(i)) = 10^(-150/10);
end

Plot the Adapted Pattern

figure('NumberTitle', 'off','Name', ...
       ['Figure 48.1. Adapted Patterns for PRI-Staggered post-Doppler STAP for K= ', ...
      num2str(K), ' and Doppler bin ', num2str(m)],...
      'Position',[1 1 1200 1000]);
subplot(2,2,1);
[Az Doppler] = meshgrid(sin(phi*pi/180),fd);
colormap jet;
pcolor(Az, Doppler, 10*log10(abs(Pw0)));
shading interp;
xlim([-1 1])
ylim([-150 150]);
%xlabel('sin(Azimuth)');
ylabel('Doppler Frequency (Hz)');
h = colorbar;
% set(get(h,'YLabel'),'String','Relative Power (dB)');
title('Doppler Filters Untapered');

subplot(2,2,2);
pcolor(Az, Doppler, 10*log10(abs(Pw30)));
shading interp;
xlim([-1 1])
ylim([-150 150]);
%xlabel('sin(Azimuth)');
% ylabel('Doppler Frequency (Hz)');
title('Chebychev 30 dB Doppler Taper');
h = colorbar;
set(get(h,'YLabel'),'String','Relative Power (dB)');

subplot(2,2,3);
pcolor(Az, Doppler, 10*log10(abs(Pw60)));
shading interp;
xlim([-1 1])
ylim([-150 150]);
xlabel('sin(Azimuth)');
ylabel('Doppler Frequency (Hz)');
title('Chebychev 60 dB Doppler Taper');
h = colorbar;
% set(get(h,'YLabel'),'String','Relative Power (dB)');

subplot(2,2,4);
pcolor(Az, Doppler, 10*log10(abs(Pw90)));
shading interp;
xlim([-1 1])
ylim([-150 150]);
xlabel('sin(Azimuth)');
% ylabel('Doppler Frequency (Hz)');
title('Chebychev 90 dB Doppler Taper');
h = colorbar;
set(get(h,'YLabel'),'String','Relative Power (dB)');

%tightfig;