False alarm analysis of the envelope detection GO-CFAR processor

The greatest of constant false alarm rate processor (GO CFAR) is a useful architecture for adaptively setting a radar detection threshold in the presence of clutter edges. The GO CFAR input is often the envelope detected in-phase (I) and quadrature (Q) channels of the baseband signal (x_e=√(I²+Q²)). This envelope detection can also be approximated using x=a max{|I|,|Q|}+b min{|I|,|Q|} which requires less complex hardware (a and b are simple multiplying coefficients). The envelope GO CFAR processor and several envelope approximation GO CFAR processors are compared in terms of the probability of false alarm (PFA) performance. Closed-form expressions which describe the PFA performance are given and their accuracy evaluated. It is shown that for all cases, the PFA is proportional to the number of reference cells n for small threshold multiplier T and inversely proportional to n for large T. A region of intersection occurs where the PFA is the same for two different values of n. For example, at T'=1.68 in the |I|+|Q| GO CFAR (a=1, b=1) the PFA for n=1 is equal to the optimal n=∞ fixed-threshold PFA (PFA=0.112)