Upper and Lower Bounds for the Threshold of the FFT Filter Bank-Based Summation CFAR Detector

The reliable computation of detection threshold T given a desired probability of false alarm P_fa a is an important issue in the design of the FFT filter bank-based summation CFAR (constant false alarm rate) detector. The computation of detection threshold T is based on numerical procedures such as the Newton-Ralphson algorithm and a priori knowledge of lower and upper bounds for T for a given P_fa. Current approaches used in the initialization stage of the computation of threshold T are largely ad hoc as there are no theoretical upper and lower bounds for T reported in the literature. In this article, several theoretical upper and lower bounds for T for overlapped and non-overlapped signal data are derived. These results enable a proper design of the FFT filter bank-based summation CFAR detector