Computation of the Normalized Detection Threshold for the FFT Filter Bank-Based Summation CFAR Detector

Abstract

The FFT filter bank-based summation CFAR detector is widely used for the detection of narrowband signals embedded in wideband noise. The simulation and implementation of this detector involves some problems concerning the reliable computation of the normalized detection threshold for a given probability of false alarm. This paper presents a comprehensive theoretical treatment of major aspects of the numerical computation of the normalized detection threshold for an AWGN channel model. Equations are derived for the probability of false alarm, Pfa, for both non-overlapped and overlapped input data and then used to compute theoretical upper and lower bounds for the detection threshold T. A very useful transformation is introduced that guarantees the global quadratic convergence of the Newton-Ralphson algorithm in the computation of T for overlapped data with an overlap ratio not exceeding 50%. It is shown that if the product of the number of FFT bins assigned to a channel for signal power estimation and the number of input data blocks is relatively small, e.g., less than 60, the theoretical normalized detection threshold can be accurately computed without numerical problems. To handle other cases, good approximations are derived.