radar detecting the target

Problem Statement: Use the MATLAB code for MATLAB Assignment-4. Use the SNR for target #1 and plot the probability of detecting the target during its full flight from t=0 seconds to t=60 seconds (i.e. make a plot of PD vs. Time) for the following three cases (plot all 3 curves on the same plot):

1. 1-detection in 1 dwell (trial),
2. 2-detections out of 4 dwells (trials),
3. 5-detections out of 8 dwells (trials)

Also, give the resulting PFA for each of the three cases above. Assumptions:

• Target rcs = 60 m2
• Target fluctuation type is SW-1
• Initial required 1-dwell PFA = 10-5.

Assignment-4 code:

%% Radar Parameters

clear all;clf

clc;

%

% Now we will calculate maximum unambiguous range, Ru

c = 3e8; % Speed of light (m/s)

fo = 5e9; % Radar center frequency (Hz)

lam = c/fo; % Radar wavelength (m)

to = 0; % Starting time

tf = 60; % Ending time (sec)

scan_rpm = 120; % Antenna scanning rate (rev/min)

scan_rps = scan_rpm/60; % Antenna scannning rate (rev/sec) or (360/sec)

scan_period = 1/scan_rps % Time to complete one rev (sec/rev) or (sec/360)

time_for_deg = scan_period/360 % Time for the antenna to turn ONE deg

t = to:time_for_deg:tf; % The time domain for the simulation

tot_incs = length(t)

%

%% Initial Targets Parameters for THREE Targets

% POSITION VECTORS

x_init = [12000 -14000 15000]; % Initial target location x-coordinates

y_init = [6000 9000 11000]; % Initial target location y-coordinates

z_init = [6000 7000 8000]; % Initial target location z-coordinates

Pos_vectors_init = [x_init(1) y_init(1) z_init(1); x_init(2) ...

y_init(2) z_init(2); x_init(3) y_init(3) z_init(3)];

% VELOCITY VECTORS

vx = [-300 250 -275]; % velocity vector x-component (m/s)

vy = [200 150 250]; % No velocity componennt in y-axis

vz = [0 0 0]; % No velocity componennt in z-axis

Vel_vectors_init = [vx(1) vy(1) vz(1); vx(2) vy(2) vz(2); vx(3) vy(3) vz(3)];

%

%% Creating Target Parameter Vectors for Full Flight Duration

% Initiating target locations, and angles

no_targets = length(x_init);

Pos_vectors = zeros(no_targets, 3, tot_incs); % position vectors for all time increments

Pos_vectors(:,:,1) = Pos_vectors_init;

Vel_vectors = zeros(no_targets, 3, tot_incs); % Range to targets (m)

Vel_vectors(:,:,1) = Vel_vectors_init;

R = zeros(no_targets,tot_incs); % Range to targets (m)

vr = zeros(no_targets,tot_incs); % Radial velocity (m/s)

fD = zeros(no_targets,tot_incs); % Doppler frequency vector (Hz)

%

%% Now inserting the initial parameters into the target vectors

for tgt = 1:no_targets

R(tgt,1) = norm(Pos_vectors(tgt,:,1));

vr(tgt,1) = Vel_vectors(tgt,:,1)*Pos_vectors(tgt,:,1)'/norm(Pos_vectors(tgt,:,1));

fD(tgt,1) = -2*vr(tgt,1)/lam;

end

%

%% Now Incrementing the time by one degree rotation and updating the calculations

%

for i= 2:tot_incs

for tgt = 1:no_targets

Pos_vectors(tgt,:,i) = Pos_vectors(tgt,:,i-1) + Vel_vectors(tgt,:,i-1)*time_for_deg;

R(tgt,i) = norm(Pos_vectors(tgt,:,i));

Vel_vectors(tgt,:,i) = Vel_vectors(tgt,:,i-1);

vr(tgt,i) = Vel_vectors(tgt,:,i)*Pos_vectors(tgt,:,i)'/norm(Pos_vectors(tgt,:,i));

fD(tgt,i) = -2*vr(tgt,i)/lam;

end

end

%

%% Plotting results

clf(1)

figure(1)

hold on

grid on

for tgt = 1:3

plot(R(tgt,:),fD(tgt,:),'LineWidth',1)

end

hold off

%% SNR Calculations (Using the Radar Rannge Equation)

k = 1.38e-23;

To = 290;

snr = zeros(no_targets,tot_incs); % SNR for all time increments

snr_db = zeros(no_targets,tot_incs); % SNR for all time increments

% Radar parameters

Gt = 1000;

Gr = Gt;

Pt = 4e3;

np = 40;

NF = 20;

B = 2e6;

Ls = 200;

% Target parameters (3 targets)

Sig = [60 140 200];

%%

clf(2)

figure(2)

hold on

grid on

for tgt = 1:3

snr(tgt,:) = Pt*Gt*Gr*lam^2*Sig(tgt)*np./((4*pi)^3.*R(tgt,:).^4 ...

* k*To*NF*B*Ls);

snr_db(tgt,:) = 10*log10(snr(tgt,:));

plot(t,snr_db(tgt,:),'LineWidth',1)

end

plot(t,15+zeros(size(t)),'--')

hold off