On Wilks' Theorem for Generalized Likelihood Ratio Test Performance of Cooperative Radar-Communications

The analysis of the generalized likelihood ratio test (GLRT) radar receiver when the radar is coexisting with a cooperative in-band communication (comm.) system is challenged by the discrete nature of the comm. symbols. While the asymptotic performance of the GLRT can be well-approximated by using the Fisher information matrix (FIM) for the Cramér-Rao bound (CRB) via Wilks' theorem, this only applies when the underlying data distribution for each hypothesis is continuous in the parameters. Thus, to accommodate the discrete nature of the comm. symbols an adaptation to Wilks' theorem is proposed in this work that uses the constrained CRB (CCRB) in place of the usual unconstrained CRB.