A unified approach to the construction of constant false alarm probability radar detectors

A unified approach to the construction of optimum constant false alarm probability (CFAP) radar detectors is provided. A CFAP radar detector is a detector for which the false alarm probability is known in advance to be a certain fixed value. Here an optimum CFAP detector is defined to mean a CFAP detector which has the largest possible detection probability for a given constant false alarm probability. The radar detection problem is reviewed and the need for CFAP detectors indicated. It is observed that CFAP detectors are equivalent to a class of well known statistical hypothesis tests. The optimum statistical theory for this class is then reviewed and it is found that the existing theory does not apply to all radar problems. Certain extensions of optimum statistical theory are obtained. These extensions enable the theory to be applied to most radar problems.