Derivation of a formula for the probability of false alarm for the FFT filter bank-based J-out-of-L CFAR detector

A formula is derived for the probability of false alarm (P_fa) for the FFT filter bank-based J-out-of-L CFAR detector for AWGN channels when the input data is overlapped. Practical approximations for P_fa are then deduced. These approximations are valid when the overlap ratio, γ > 0, does not exceed 1/4 . For the Blackmail and Blackman-Harris windows, when 1/4 ≤ γ ≤ 1/2 , these approximations still hold. The validity of these approximations has been confirmed by simulation experiments. In addition, results showing the performance improvement that can be obtained from data overlapping for a given observation time are also given.