General asymptotic analysis of the generalized likelihood ratio test for a Gaussian point source under statistical or spatial mismodeling

This paper investigates the robustness of the generalized likelihood ratio test (GLRT) for a far-field Gaussian point source. Given measurements from an array of sensors, the performance of the GLRT under two types of common modeling errors is investigated. The first type is spatial mismodeling, which relates to errors due to multipath effects or errors in the assumed number of sources, i.e, deviation from the single point source assumption. The second type is statistical mismodeling, which relates to errors due to non-Gaussianity in either the noise or the signal, i.e., deviation from the Gaussian assumption. It is shown that for some types of modeling errors, the detector's performance improves, and general conditions for such an improvement are found. Moreover, for both types of errors, the change in performance is analyzed and quantified. This analysis shows that for a distributed source with small spatial spreading, the degradation in performance is significant, whereas for a constant modulus point source, the performance improves. Simulations of various cases are shown to verify the analytical results.