spiral antenna monofilar

Does anyone work with this type of antenna (monofilar spiral microstrip a.k.a single-arm spiral on microstrip). I post here a paper in which the author designed this antenna with 50 ohm input impedance (real part). But when I simulated it in CST I don't get the same results as in the paper (fig.5 b, c, d). Anyone know how to calculate the real part of the input impedance of this antenna? as the paper it is said to be depended on the microstrip spiral width and the distance from it to the gnd but what is the exact formulas.
Does anyone has any suggest or experiences with this antenna.
Thanks in advance.