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In this paper, we develop a new elegant framework relying on theKullback-Leibler Information Criterion to address the design of one-stageadaptive detection architectures for multiple hypothesis testing problems.Specifically, at the design stage, we assume that several alternativehypotheses may be in force and that only one null hypothesis exists. Then,starting from the case where all the parameters are known and proceeding untilthe case where the adaptivity with respect to the entire parameter set isrequired, we come up with decision schemes for multiple alternative hypothesesconsisting of the sum between the compressed log-likelihood ratio based uponthe available data and a penalty term accounting for the number of unknownparameters. The latter rises from suitable approximations of theKullback-Leibler Divergence between the true and a candidate probabilitydensity function. Interestingly, under specific constraints, the proposeddecision schemes can share the constant false alarm rate property by virtue ofthe Invariance Principle. Finally, we show the effectiveness of the proposedframework through the application to examples of practical value in the contextof radar detection also in comparison with two-stage competitors. This analysishighlights that the architectures devised within the proposed frameworkrepresent an effective means to deal with detection problems where theuncertainty on some parameters leads to multiple alternative hypotheses.

A Unifying Framework for Adaptive Radar Detection in the Presence of Multiple Alternative Hypotheses