Active sequential multi-hypothesis testing under a strong-or-weak echo model

In a multi-hypothesis cognitive radar system based on Chernoff's sequential detection paradigm, the radar returns are used to learn from the environment which probing (or control) signal should be selected next, among a set of M prescribed waveforms. For this active sensing scenario, we introduce a model - referred to as strong or weak - in which each probing signal elicits a “strong” response from a specific target among an ensemble of M, but only a “weak” echo from any other target. Then, the optimal signal selection strategy for the Chernoff detector is derived and the asymptotic performance of such hypothesis test is provided, in the limit of vanishing risks, emphasizing how much can be gained by a clever selection of the control signals. Analytical results and experiments by computer simulations investigate the detection performance in non-asymptotic cases.