MATLAB Examples

Figure 42. SINR Loss as a function of Doppler filter sidelobe level, for Element Space post-Doppler STAP.

Contents

Coded by Ilias Konsoulas, 16 Dec. 2014. Code provided for educational purposes only. All rights reserved.

clc; clear; close all;

Radar System Operational Parameters

fo = 450e6;                   % Operating Frequency in Hz
Pt = 200e3;                   % Peak Transmit Power 200 kW
Gt = 22;                      % Transmit Gain in dB
Gr = 10;                      % Column Receive Gain in dB
B  = 4e6;                     % Receiver Instantaneous Bandwidth in Hz
Ls = 4;                       % System Losses in dB
fr = 300;                     % PRF in Hz
Tr = 1/fr;                    % PRI in sec.
M = 18;                       % Number of Pulses per CPI.
Tp = 200e-6;                  % Pulse Width in sec.
N = 18;                       % Number of Array Antenna Elements
Gel = 4;                      % Element Gain in dB
be = -30;                     % Element Backlobe Level in db
Nc = 360;                     % Number of clutter patches uniformly distributed in azimuth.
c   = 299792458;              % Speed of Light in m/sec.
lambda = c/fo;                % Operating wavelength in meters.
d = lambda/2;                 % Interelement Spacing

% Azimuth angle in degrees:
phi = -180:179;
Lphi = length(phi);
f = zeros(1,Lphi);
AF = zeros(1,Lphi);           % Array Factor pre-allocation.

% Platform Parameters:
beta = 1;                     % beta parameter.
ha = 9e3;                     % Platform altitude in meters.

Thermal Noise Power Computations

k = 1.3806488e-23;            % Boltzmann Constant in J/K.
To = 290;                     % Standard room Temperature in Kelvin.
F = 3;                        % Receiver Noise Figure in dB;
Te = To*(10^(F/10)-1);        % Effective Receiver Temperature in Kelvin.
Lr = 2.68;                    % System Losses on receive in dB.
Ts = 10^(Lr/10)*Te;           % Reception System Noise Temperature in Kelvin.
Nn = k*Ts;                    % Receiver Noise PSD in Watts/Hz.
Pn = Nn*B;                    % Receiver Noise Power in Watts
sigma2 = 1;                   % Normalized Noise Power in Watts.

Clutter Patch Geometry computations

Rcik = 130000;                % (clutter) range of interest in meters.
dphi = 2*pi/Nc;               % Azimuth angle increment in rad.
dR = c/2/B;                   % Radar Range Resolution in meters.
Re = 6370000;                 % Earth Radius in meters.
ae = 4/3*Re;                  % Effective Earth Radius in meters.
psi = asin(ha/Rcik);          % Grazing angle at the clutter patch in rad (flat earth model).
theta = psi;                  % Elevation (look-down angle) in rad. Flat earth assumption.
gamma = 10^(-3/10);           % Terrain-dependent reflectivity factor.
phia = 0;                     % Velocity Misalignment angle in degrees.

Clutter-to-Noise Ratio (CNR) Calculation

Calculate the Voltage Element Pattern:

for i =1:Lphi
    if abs(phi(i))<=90
        f(i) = cos(phi(i)*pi/180);
    else
        f(i) = 10^(be/10)*cos(phi(i)*pi/180);
    end
end

% Calculate the Array Factor (AF) (Voltage):
steering_angle = 0; % Angle of beam steering in degrees.
for k=1:Lphi
    AF(k) = sum(exp(-1i*2*pi/lambda*d*(0:N-1)*(sin(phi(k)*pi/180) ...
        - sin(steering_angle*pi/180))));
end

% Calculate the Full Array Transmit Power Gain:
Gtgain = 10^(Gt/10)*abs(AF).^2;

% Calculate the Element Receive Power Gain:
grgain = 10^(Gel/10)*abs(f).^2;

% Clutter Patch RCS Calculation:
PatchArea = Rcik*dphi*dR*sec(psi);
sigma0 = gamma*sin(psi);
sigma = sigma0*PatchArea;

% Calculate the Clutter to Noise Ratio (CNR) for each clutter patch:
ksi = Pt*Gtgain.*grgain*10^(Gr/10)*lambda^2*sigma/((4*pi)^3*Pn*10^(Ls/10)*Rcik^4);
Ksic = sigma2*diag(ksi);

Clutter Covariance Matrix Computations

Platform Velocity for beta parameter value:

va = round(beta*d*fr/2);
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:
a = zeros(N,Nc);
b = zeros(M,Nc);
Vc = zeros(M*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:M-1)); % Temporal Steering Vector
    Vc(:,k) = kron(b(:,k),a(:,k));           % Space-Time Steering Vector.
end

Rc = Vc*Ksic*Vc';                            % Eq. (64)

Rn = sigma2*eye(M*N);

Jamming Covariance Matrix Calculation

J = 2;                                                    % Number of Jammers.
thetaj = 0; phij = [-40 25];                              % Jammer elevation and azimuth angles in degrees.
R_j = [370 370]*1e3;
Sj = 1e-3;                                                % Jammer ERPD in Watts/Hz.
fspj = d/lambda*cos(thetaj*pi/180)*sin(phij*pi/180);      % Spatial frequency of the j-th jammer.
Lrj = 1.92;                                               % System Losses on Receive in dB.
Aj = zeros(N,J);
for j=1:J
    Aj(:,j) =  exp(1i*2*pi*fspj(j)*(0:N-1));              % Jammer Spatial Steering Vector.
end

indices= zeros(1,J);
for j=1:J
    indices(j) = find(phi == phij(j));
end
grgn = grgain(indices);
ksi_j = (Sj*grgn*lambda^2)./((4*pi)^2.*Nn*10^(Lrj/10).*R_j.^2);

Ksi_j = sigma2*diag(ksi_j);
Phi_j = Aj*Ksi_j*Aj';                                     % Eq. (47)
% Jamming Covariance Matrix:
Rj = kron(eye(M),Phi_j);                                  % Eq. (45)

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 in Hz.
fspt = d/lambda*cos(thetat*pi/180)*sin(phit*pi/180);
omegat = fdt/fr;
at = exp(1i*2*pi*fspt*(0:N-1)).';                         % Target Spatial Steering Vector.
ta = chebwin(N,30);                                       % 30 dB Chebychev Spatial Tapper.
gt = ta.*at;

Doppler Filter Matrix Construction

dopplerfilterbank = linspace(0,300,M+1);
omegadopplerbank = dopplerfilterbank/fr;
U = zeros(M,M);
fd = 0:.5:300;   Lfd = length(fd);
omegad = fd/fr;
SNRo = M*N;

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

F40  = diag(chebwin(M,40))*conj(U);  % Doppler Filter Bank Matrix with 40-dB Chebyshev Doppler Taper applied.
F60  = diag(chebwin(M,60))*conj(U);  % Doppler Filter Bank Matrix with 60-dB Chebyshev Doppler Taper applied.
F80  = diag(chebwin(M,80))*conj(U);  % Doppler Filter Bank Matrix with 80-dB Chebyshev Doppler Taper applied.
F100 = diag(chebwin(M,100))*conj(U); % Doppler Filter Bank Matrix with 100-dB Chebyshev Doppler Taper applied.

LSINR Computation for Optimum Fully Adaptive Case

LSINRopt = zeros(1,Lfd);
for n=1:Lfd
    bt = exp(1i*2*pi*omegad(n)*(0:M-1)).'; % Target Doppler Steering Vector
    vt = kron(bt,at);
    w = InvRu*vt; %#ok<MINV>
    LSINRopt(n) = real(w'*vt)/SNRo;
end

LSINR Computations for 40, 60, 80 and 100 dB SLL.

SINR40_mat   = zeros(M,Lfd);
SINR60_mat   = zeros(M,Lfd);
SINR80_mat   = zeros(M,Lfd);
SINR100_mat = zeros(M,Lfd);

for m=1:M % for every Doppler Bin ...

    f40m = F40(:,m);
    f60m = F60(:,m);
    f80m = F80(:,m);
    f100m = F100(:,m);

    R40um = kron(f40m,eye(N))'*Ru*kron(f40m,eye(N));
    R60um = kron(f60m,eye(N))'*Ru*kron(f60m,eye(N));
    R80um = kron(f80m,eye(N))'*Ru*kron(f80m,eye(N));
    R100um = kron(f100m,eye(N))'*Ru*kron(f100m,eye(N));

    w40m = R40um\gt;
    w60m = R60um\gt;
    w80m = R80um\gt;
    w100m = R100um\gt;

    w40 = kron(f40m,w40m);
    w60 = kron(f60m,w60m);
    w80 = kron(f80m,w80m);
    w100 = kron(f100m,w100m);

    for n=1:Lfd
        bt = exp(1i*2*pi*omegad(n)*(0:M-1)).'; % Dummy Target Doppler Steering Vector
        vt = kron(bt,at);
        SINR40_mat(m,n) = abs(w40'*vt)^2/real(w40'*Ru*w40);
        SINR60_mat(m,n) = abs(w60'*vt)^2/real(w60'*Ru*w60);
        SINR80_mat(m,n) = abs(w80'*vt)^2/real(w80'*Ru*w80);
        SINR100_mat(m,n) = abs(w100'*vt)^2/real(w100'*Ru*w100);
    end

end

SINR40   = max(abs(SINR40_mat));
SINR60   = max(abs(SINR60_mat));
SINR80   = max(abs(SINR80_mat));
SINR100  = max(abs(SINR100_mat));
LSINR40  = SINR40/SNRo;
LSINR60  = SINR60/SNRo;
LSINR80  = SINR80/SNRo;
LSINR100 = SINR100/SNRo;

Plot the SINR Losses

figure('NumberTitle', 'off','Name', ...
       'Figure 42. SINR loss as a function of Doppler filter sidelobe level',...
       'Position', [1 1 700 500]);
plot(fd,10*log10(LSINRopt),'LineWidth',1.5)
hold on;
plot(fd,10*log10(LSINR40),'r','LineWidth',1.5)
plot(fd,10*log10(LSINR60),'g','LineWidth',1.5)
plot(fd,10*log10(LSINR80),'m','LineWidth',1.5)
plot(fd,10*log10(LSINR100),'c','LineWidth',1.5)
grid on;

ylabel('SINR Loss (dB)');
xlabel('Target Doppler Frequency (Hz)');
ylim([-40 1]);
xlim([-5 305]);
legend('Optimum', '40 dB Doppler SLL', '60 dB Doppler SLL', '80 dB Doppler SLL', '100 dB Doppler SLL',...
       'Location','Best');
grid on;