Adaptive Radar Detection in the Presence of Multiple Alternative Hypotheses Using Kullback-Leibler Information Criterion-Part I: Detector Designs

In this paper, we develop a new elegant systematic framework relying on the Kullback-Leibler Information Criterion to approach the design of one-stage adaptive detection architectures for multiple hypothesis testing problems in radar. Specifically, at the design stage, we assume that one out of 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 towards the adaptivity with respect to the entire parameter set, 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. Such a term arises 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 also show that the new architectures can be viewed as the result of a suitable regularization of the log-likelihood.