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