Proof of CFAR by the use of the invariant test

Many adaptive detectors regulate the detection threshold adaptively through an estimate of the clutter power level, which is formed by reference cell samples. This paper proves by the use of the invariant test that a large class of adaptive detectors possesses the constant false-alarm rate (CFAR) property when they satisfy certain weak conditions. The proof reveals the mechanism of this class of CFAR detectors and provides a general method of proving the CFAR property.