# MATLAB Simulations for Radar Systems Design

### Bassem Mahafza (view profile)

• 1 file
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11 Sep 2003 (Updated )

MATLAB Simulations for Radar Systems Design

clutter_rcs.m
```function [sigmaC,CNR] = clutter_rcs(sigma0, thetaE, thetaA, SL, range, hr, ht, pt, f0,...
b,  t0, f, l,ant_id)
% This function calculates the clutter RCS and the CNR for a ground based radar.
clight = 3.e8; % speed of light in meters per second
lambda = clight /f0;
thetaA_deg = thetaA;
thetaE_deg = thetaE;
thetaA = thetaA_deg * pi /180; % antenna azimuth beamwidth in radians
thetaE = thetaE_deg * pi /180.; % antenna elevation beamwidth in radians
re = 6371000; % earth radius in meter
rh = sqrt(8.0*hr*re/3.); % range to horizon in meters
SLv = 10.0^(SL/10); % radar rms sidelobes in volts
sigma0v = 10.0^(sigma0/10); % clutter backscatter coefficient
tau = 1/b; % pulse width
deltar = clight * tau / 2.; % range resolution for unmodulated pulse
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
range_m = 1000 .* range;  % range in meters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
thetar = asin(hr ./ range_m);
thetae = asin((ht-hr) ./ range_m);
propag_atten = 1. + ((range_m ./ rh).^4); % propagation attenuation due to round earth
Rg = range_m .* cos(thetar);
deltaRg = deltar .* cos(thetar);
theta_sum = thetae + thetar;
% use sinc^2 antenna pattern when ant_id=1
% use Gaussian antenna pattern when ant_id=2
if(ant_id ==1) % use sinc^2 antenna pattern
ant_arg = (2.78 * theta_sum ) ./ (pi*thetaE);
gain = (sinc(ant_arg)).^2;
else
gain = exp(-2.776 .*(theta_sum./thetaE).^2);
end
% compute sigmac
sigmac = (sigma0v .* Rg .* deltaRg) .* (pi * SLv * SLv + thetaA .* gain.^2) ./ propag_atten;
sigmaC = 10*log10(sigmac);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1)
plot(range, sigmaC)
grid
xlabel('Slant Range in Km')
ylabel('Clutter RCS in dBsm')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculate CNR
pt = pt * 1000;
g = 26000 / (thetaA_deg*thetaE_deg); % antenna gain
F = 10.^(f/10); % noise figure is 6 dB
Lt = 10.^(l/10); % total radar losses 13 dB
k = 1.38e-23; % Boltzmans constant
T0 = t0; % noise temperature 290K
argnumC = 10*log10(pt*g*g*lambda*lambda*tau .* sigmac);
argdem = 10*log10(((4*pi)^3)*k*T0*Lt*F .*(range_m).^4);
CNR = argnumC - argdem;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(2)
plot(range, CNR,'r')
grid
xlabel('Slant Range in Km')
ylabel('CNR in dB')```