# 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

pd_swerling2 (nfa, np, snrbar)
```function pd = pd_swerling2 (nfa, np, snrbar)
% This function is used to calculate the probability of detection
% for Swerling 2 targets.
format long
snrbar = 10.0^(snrbar/10.);
eps = 0.00000001;
delmax = .00001;
delta =10000.;
% Calculate the threshold Vt
pfa =  np * log(2) / nfa;
sqrtpfa = sqrt(-log10(pfa));
sqrtnp = sqrt(np);
vt0 = np - sqrtnp + 2.3 * sqrtpfa * (sqrtpfa + sqrtnp - 1.0);
vt = vt0;
while (abs(delta) >= vt0)
igf = incomplete_gamma(vt0,np);
num = 0.5^(np/nfa) - igf;
temp = (np-1) * log(vt0+eps) - vt0 - factor(np-1);
deno = exp(temp);
vt = vt0 + (num / (deno+eps));
delta = abs(vt - vt0) * 10000.0;
vt0 = vt;
end
if (np <= 50)
temp = vt / (1.0 + snrbar);
pd = 1.0 - incomplete_gamma(temp,np);
return
else
temp1 = snrbar + 1.0;
omegabar = sqrt(np) * temp1;
c3 = -1.0 / sqrt(9.0 * np);
c4 = 0.25 / np;
c6 = c3 * c3 /2.0;
V = (vt - np * temp1) / omegabar;
Vsqr = V *V;
val1 = exp(-Vsqr / 2.0) / sqrt( 2.0 * pi);
val2 = c3 * (V^2 -1.0) + c4 * V * (3.0 - V^2) - ...
c6 * V * (V^4 - 10. * V^2 + 15.0);
q = 0.5 * erfc (V/sqrt(2.0));
pd =  q - val1 * val2;
end

```