# Figures 35 and 36. K = 2 element-space pre-Doppler STAP.

## Contents

```clc; clear; close all;
```

```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)
Ksic = sigma2*diag(ksi);
```

## Clutter Covariance Matrix Computations

```K = 2;
beta = 1;   % beta parameter.
phia = 0;   % Velocity Misalignment Angle.
Ita = d/lambda*cos(theta);

% Calculate Spatial and Doppler Frequencies for k-th clutter patch.
% Spatial frequency of the k-th clutter patch:
fsp = Ita*sin(phi*pi/180);
% Normalized Doppler Frequency of the k-th clutter patch:
omegac = beta*Ita*sin(phi*pi/180 + phia*pi/180);

% Clutter Steering Vector Pre-allocation for sub-CPI of size K:
a = zeros(N,Nc);
b = zeros(K,Nc);
Vc = zeros(K*N,Nc);

for k=1:Nc
a(:,k) = exp(1i*2*pi*fsp(k)*(0:N-1));       % Spatial Steering Vector.
b(:,k) = exp(1i*2*pi*omegac(k)*(0:K-1));    % Temporal Steering Vector
Vc(:,k) = kron(b(:,k),a(:,k));              % Space-Time Steering Vector.
end

Rcsub = Vc*Ksic*Vc';
Rnsub = sigma2*eye(K*N);
```

## Jammer Covariance Matrix Calculation

```jamm_cov;

Rjsub = kron(eye(K),Phi_j);
```

## Analytic Interference Covariance Matrix for first sub-CPI

```Rusub = Rcsub + Rjsub + Rnsub;
```

## 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);    % Target Spatial Frequency
at = exp(1i*2*pi*fspt*(0:N-1)).';                       % Target Spatial Steering Vector.
ta = chebwin(N,30);                                     % 30 dB Chebychev Spatial Tapper.
if K==2
bt = [1; -1];                                        % K-pulse Temporal Target Steering Vector
tb = [1;  1];                                        % (K x 1) Binomial Taper for K = 2.
elseif K==3
bt = [1; -1; 1];                                     % K-pulse Temporal Target Steering Vector
tb = [1;  2; 1];                                     % (K x 1) Binomial Taper for K = 3.
elseif K==4
bt = [1; -1; 1; -1;];                                % K-pulse Temporal Target Steering Vector
tb = [1;  3; 3;  1;];                                % (K x 1) Binomial Taper for K = 4.
end

gt = kron(tb.*bt,ta.*at);                               % sub-CPI desired response.
```

## Tapered, Element-Space STAP Solution

```wsub = Rusub\gt;
wsub = wsub/max(abs(wsub));  % Weight Normalization.
```

```phi = -90:.5:90; Lphi = length(phi);
fd = -150:.5:150;   Lfd = length(fd);
fsp = d/lambda*cos(theta*pi/180)*sin(phi*pi/180);
omega = fd/fr;
Pw1 = zeros(Lfd,Lphi);
for m=1:Lphi
for n=1:Lfd
a = exp(1i*2*pi*fsp(m)*(0:N-1));    % Dummy Spatial Steering Vector.
b = exp(1i*2*pi*omega(n)*(0:K-1));  % Dummy Doppler Steering Vector
v = kron(b,a).';
Pw1(n,m) = abs(wsub'*v)^2;
end
end
```

## Normalisation

```max_value = max(max(Pw1));
Pw = Pw1/max_value;
[rows cols] = find(10*log10(abs(Pw))<-80);
for i=1:length(rows)
Pw(rows(i),cols(i)) = 10^(-80/10);
end
```

```figure('NumberTitle', 'off','Name', ...
'Figure 35. K = 2 element-space pre-Doppler STAP. (a) Sub-CPI adapted patter',...
'Position', [1 1 700 600]);
[Az Doppler] = meshgrid(sin(phi*pi/180),fd);
colormap jet;
pcolor(Az, Doppler, 10*log10(abs(Pw)));
xlim([-1 1])
ylim([-150 150]);
xlabel('sin(Azimuth)');
ylabel('Doppler Frequency (Hz)');
h = colorbar;
set(get(h,'YLabel'),'String','Relative Power (dB)');
``` ## Plot the Principal Cuts

```figure('NumberTitle', 'off','Name', ...
'Figure 35. K = 2 element-space pre-Doppler STAP. (b) Principal Cuts at Target Azimuth and Doppler',...
'Position', [1 1 700 600]);
% a. Cut of the Adapted Pattern at Doppler = 150 Hz.
subplot(2,1,1);
plot(sin(phi*pi/180), 10*log10(abs(Pw(fd == 150,:))));
ylim([-80 0.5]); xlim([-1  1]);
ylabel('Relative Power (dB)');
xlabel('sin(Azimuth)');
title('Doppler Frequency = 150 Hz');
grid on;

% b. Cut of the Adapted Pattern at Target Azimuth = 0 degrees.
subplot(2,1,2);
plot(fd, 10*log10(abs(Pw(:,phi == phit))));
ylim([-80 0.5]); xlim([-150 150]);
ylabel('Relatuve Power (dB)');
xlabel('Target Doppler Frequency (Hz)');
title('Azimuth = 0 deg');
grid on;
``` ## Figure 36. Sub-CPI weight vector decomposed into spatial beamformer components, illustrating the DPCA effect

```figure('NumberTitle', 'off','Name', ...
'Figure 36. Sub-CPI weight vector decomposed into spatial beamformer components, illustrating the DPCA effect.',...
'Position', [1 1 700 600]);
plot(0:N-1,abs(wsub(1:N)),'b*-');
hold on;
plot(0:N-1,abs(wsub(N+1:end)),'r+-');
xlim([0 18]);
ylim([0 1.025]);
grid on;
legend('PRI 1','PRI 2');
``` 