Currently I need to calculate detection probabilities (PD) from radar cross section (RCS) data. Beta distribution parameters for this RCS data are calculated and will be used in Swerling0 Equation. The idea is based on the Research article: "Detection Probabilities for Beta-Distributed Scattering Cross Sections 1984, by Robert L. Kulp" From beta distribution parameters we have to measure the detection probabilities. This will be done by making a Confluent Hypergeometric Function of a characteristic function and then taking the inverse LaPlace transform of that function and after that integrating this inverse LaPlace function on a certain interval from zero to threshold voltage. Specific values for Signal SNR, beta distribution parameters, Number of pulses, Probability of False alarm and Threshold voltage are provided in the article in tables1,2 and 3.

The problem is what could be the input of the Confluent Hypergeometric function and how to make a transfer function from it so that it can dealt with Inverse Laplace Transform. I would like to mention that it is Swerling0 case. Beta parameters (a and b) are integrated in the Swerling0 characteristic function and made a confluent hypergeometric function. No Fourier integral pair is used for this characteristic function. Confluent Hypergeom function is evaluated via asymptotic expansion and then its output is used to make the LaPlace transfer function. Any help about its implementation in MATLAB is appreciated.