SOCA-CFAR Processor in A Homogeneous Erlang-Distributed Clutter: Exact Closed-Form Expression for the Pfa

In this work, we have derived a closed-form expression for the probability of false alarm (PFA) of the smallest-of cell-averaging constant false alarm rate (SOCA-CFAR) processor which operates in a homogeneous Erlang-distributed clutter environment.This expression indicates that the PFA is independent of the rate parameter of the Erlang clutter.Moreover, as an intermediate step, we have derived accurate formulations for the probability density function (PDF) for the sum and the minimum sum of independent and identically distributed (i.i.d) Erlang random variates.The numerical simulations stipulate an enhancement in the SOCA-CFAR's PFA as the shape parameter of the Erlang clutter increases.The accuracy of the analytical outcomes presented in this work is corroborated through Monte Carlo simulations.