MATLAB Examples

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

## Contents

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

```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; ```