Asymptotic distribution of generalized likelihood ratio test under model misspecification with application to cooperative radar-communications

The goal of this paper is to develop an expression for the asymptotic distribution of the generalized likelihood ratio test (GLRT) statistic under model misspecification, that is when the assumed data model is different from the true model. Under such a scenario, the asymptotic distribution under the null hypothesis was by derived by Foutz and Srivastava. A general expression for this distribution under the null as well as the alternative hypothesis under model misspecification has been derived in this paper, on the same lines as the derivation provided by Kay for the case when there is no model misspecification. Using this expression, the asymptotic receiver operating characteristic (ROC) performance of a cooperative radar-communications receiver has been analyzed, when the communications (comms.) channel gains are assumed to be constant, but in reality may vary with time.