Asymptotic Distribution of Channel Matrix-Based GLRT for Cognitive Radar/Sonar

Waveform optimization is central to the perception-action cycle of the cognitive radar system, where the system continuously learns and adapts to the environment by adjusting its waveforms. This work uses Wilks' theorem to obtain the asymptotic distribution of the generalized likelihood ratio test (GLRT) for the channel matrix-based cognitive radar/sonar framework. The resulting expression for the detection probability depends on the primary and secondary waveforms. It serves as a crucial step toward future research for improving the detection and cognitive capabilities of the radar system in adapting waveforms to changing environments.