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: PDF (596 KB)

**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.

ISSN : 1796-203X

Volume : 2 Issue : 6 Date : August 2007

CFAR Detector

Page(s): 35-48

Full Text: PDF (596 KB)

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.