Fast simulation of smallest-of and geometric-mean CFAR detectors

Continuing the development of fast estimation methods for the design and analysis of detection algorithms, certain techniques are described for smallest of (SO) and geometric-mean (GM) constant false-alarm rate (CFAR) detectors. Methods of fast stochastic simulation are effective when applied to the class of CFAR detection algorithms, as developed and described in a set of recent papers. They do not exhibit as much benefit over conventional Monte Carlo simulation for SO and GM variants of CFAR detectors as for other structures. Hence, a simple method of fast simulation for SO detectors is suggested based on conditional probability decompositions that provide enhanced gains and higher accuracies in detector threshold and performance estimation. The SO and greatest-of (GO) variants of the GM-CFAR detector are suggested and analysed for false-alarm probability (FAP) performance. A numerical method based on density approximations is also suggested for GM detectors. These structures can be used in ensemble processing for achieving robust radar detection