Chernoff Test for Strong-or-Weak Radar Models

The active management of the sensing stage in inference systems provides substantial gains in performance. This has been first shown by H. Chernoff in 1959 in the context of sequential hypothesis testing. This paper shows applications of these methods to cognitive radar systems. We propose a simple strong-or-weak model for the radar echoes, where the radar sequentially probes the surrounding environment using a sequence of waveforms, each tailored to a specific target. We provide an active multihypothesis sequential test in which the radar chooses the probing waveform based upon the past selections and the past radar returns. We determine how to select the sequence of waveforms, and provide simple analytical expressions for the resulting radar performance in the regime of small risks. Finally, computer simulations are used to corroborate the analytical approximations for values of risks of practical interest