inv_erfc.m

A wireless channel implemenatation in MATLAB

function x = inv_erfc(y)
% inverse of complementary error function
% y = erfc(x) --> x = inv_erfc(y)

z = y;
if (y > 1) 
    z = 2 - y;
end
w = 0.916461398268964 - log(z);
u = sqrt(w);
s = (log(u) + 0.488826640273108) / w;
t = 1 / (u + 0.231729200323405);
x = u * (1 - s * (s * 0.124610454613712 + 0.5)) - ...
    ((((-0.0728846765585675 * t + 0.269999308670029) * t + ...
    0.150689047360223) * t + 0.116065025341614) * t + ...
    0.499999303439796) * t;
t = 3.97886080735226 / (x + 3.97886080735226);
u = t - 0.5;
s = (((((((((0.00112648096188977922 * u + ...
    1.05739299623423047e-4) * u - 0.00351287146129100025) * u - ...
    7.71708358954120939e-4) * u + 0.00685649426074558612) * u + ...
    0.00339721910367775861) * u - 0.011274916933250487) * u - ...
    0.0118598117047771104) * u + 0.0142961988697898018) * u + ...
    0.0346494207789099922) * u + 0.00220995927012179067;
s = ((((((((((((s * u - 0.0743424357241784861) * u - ...
    0.105872177941595488) * u + 0.0147297938331485121) * u + ...
    0.316847638520135944) * u + 0.713657635868730364) * u + ...
    1.05375024970847138) * u + 1.21448730779995237) * u + ...
    1.16374581931560831) * u + 0.956464974744799006) * u + ...
    0.686265948274097816) * u + 0.434397492331430115) * u + ...
    0.244044510593190935) * t - ...
    z * exp(x * x - 0.120782237635245222);
x = x + s * (x * s + 1);
if (y > 1)
    x = -x;
end

return