JOURNAL OF COMPUTERS (JCP)
ISSN : 1796-203X
Volume : 2    Issue : 6    Date : August 2007

Computation of the Normalized Detection Threshold for the FFT Filter Bank-Based Summation
CFAR Detector
Sichun Wang, François Patenaude, and Robert Inkol
Page(s): 35-48
Full Text:
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Abstract
The FFT lter 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.

Index Terms
Digital FFT flter bank, Detection and estimation, Constant false alarm rate (CFAR) detection.