Precise detection statistics by probability transform (PT) simulation, applied to a hard-limited radar receiver

Probability transform (PT) simulation is a new method of calculating the detection statistics of radar and communication receivers. PT numerically computes the output probability density function (PDF) of a receiver from its input PDF. The existing methods for performing this simulation are closed form, and Monte Carlo. PT is a numerical version of closed form simulation. In some applications, PT simulation produces results far more quickly and accurately than the existing methods. Results can be obtained numerically when closed form results are not tractable or closed form approximations inaccurate. The utility of PT simulation is demonstrated in this paper by applying it to a hard-limited radar receiver. Accurate closed form expressions do not exist for the output PDF of the hard-limiter due to its high nonlinearity. In this application, PT is far faster and more accurate than the traditional Monte Carlo approach. Detection statistics for all five Swerling cases have been calculated for the hard-limited receiver. PT simulation is made far more practical by several innovations presented in this paper. These include the two-dimensional convolution formula to simulate coherent integration, the use of two-dimensional FFT to speed the two-dimensional convolution, holding target phase constant without affecting the simulation results and reversing the order of the Swerling integration and noncoherent integration simulation steps to correctly simulate either Swerling cases 1 and 3 or 2 and 4. More general applications of PT simulation such as to receivers with a linear channel and linear detector are discussed