Comparison of Gaussian and Pearson approximations to the normalized detection threshold for the FFT filter bank-based summation CFAR detector

The simulation and practical implementation of the widely used FFT summation CFAR (constant false alarm rate) detector are both dependent on the accurate computation of the normalized detection threshold, T_n. This is generally computed using numerical procedures. However, unless the number of FFT bins assigned to each channel and the number of input data blocks used for the channel power estimation are both relatively small, numerical problems are likely to be encountered. Consequently, approximations that are both accurate and reliable are of practical interest. This paper shows that the recently proposed Pearson approximations [3] are more accurate than the Gaussian approximation, particularly for very small probabilities of false alarm, and should be preferred in practice. It is also demonstrated that the non-trivial task of computing the eigenvalues normally required to obtain the Pearson approximations can be bypassed, thereby achieving a useful simplification. The results of this paper are applicable to the practical implementation of the FFT filter bank-based summation CFAR detector.